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Students can Download Chapter 6 Depreciation, Provisions and Reserves Notes, Plus One Accountancy Notes helps you to revise the complete Kerala State Syllabus and score more marks in your examinations.

Kerala Plus One Accountancy Notes Chapter 6 Depreciation, Provisions and Reserves

Summary:
Meaning of depreciation:
Depreciation is decline in the value of a tangible fixed asset. In accounting depreciation is the process of allocating depreciable cost over useful life of a fixed asset.

Depreciation and similar terms:
Depreciation term is used in the context of tangible fixed assets. Depletion (in the context of extractive industries), and amortisation (in the context of intangible assets) are other related terms.

Factors Affecting Depreciation:

• Wear and Tear due to use and/or passage of time
• Expiration of Legal Rights
• Obsolescence

Importance of depreciation:

• Depreciation must be charged to ascertain true and fair profit or loss.
• Depreciation is a non-cash operating expense.

Methods of charging depreciation:
Depreciation amount can be calculated using:

• Straight line method, or
• Written down value method

Methods of recording depreciation:
In the books of account there are two types of arrangements for recording depreciation on fixed assets.

• Charging depreciation to asset account or
• Creating provision for depreciation/ accumulated depreciation account.

Charging depreciation to asset account:
According to this arrangement depreciation is deducted from the depreciable cost of the asset (credited to the asset account) and charged (or debited) to profit and loss account. Journal entries under this recording method are as follows:

2. Following two entries are recorded at the end of every year.
(a) For deducting depreciation amount from the cost of the asset.

(b) For charging depreciation to profit and loss account

3. Balance Sheet Treatment
When this method is used, the fixed asset appears at its net book value (ie. cost less depreciation charged till date) on the asset side of the balance sheet and not at its original cost (also known as historical cost).

Creating Provision for depreciation account/ Accumulated depreciation Account:
This method is designed to accumulate the depreciation provided on an asset in a separate account generally called “Provision for Depreciation” or “Accumulated Depreciation” account.

The following journal entries are recorded under this method:

2. The following two journal entries are recorded at the end of each year
(a) For crediting depreciation amount to provision for depreciation account.

(b) For charging depreciation to profit and loss account

3. Balance Sheet treatment
In the balance sheet the fixed asset continues to appear at its original cost on the asset side. The depreciation charged till that date appears in the provision for depreciation account, which is shown either on the “liabilities side” of the balance sheet or by way of deduction from the original cost of the asset concerned on the asset side of the balance sheet.

Disposal of Asset:
Disposal of asset can take place either

• At the end of its useful life or
• During the useful life (due to absolescence or any other abnormal factors). In this case the following journal entries are recorded.

1. For the sale of asset as scrap

2. For transfer of balance in asset account

In case, however “the provision for depreciation account” has been in use for recording the depreciation, then before passing the above entries transfer the balance of the provision for depreciation account to the asset account by recording the following journal entry.

Factors affecting the amount of depreciation:

• Depreciation amount is determined by Original cost
• Salvage value, and
• Useful life of the asset

Provisions and Reserves:
A provision is a charge against profit. It is created for a known current liability the amount of which is uncertain. Reserve on the other hand, is an appropriation of profit. It is created to strengthen the financial position of the business.

Types of Reserves:
Reserves may be:

• General reserve and specific reserve;
• Revenue reserve and capital reserve.

Secret Reserve:
When the total depreciation charged is higher than the total depreciable cost, the Secret reserve is created. The secret reserve is not explicitly shown in the balance sheet.

Students can Download Chapter 5 Trial Balance and Rectification of Errors Notes, Plus One Accountancy Notes helps you to revise the complete Kerala State Syllabus and score more marks in your examinations.

Kerala Plus One Accountancy Notes Chapter 5 Trial Balance and Rectification of Errors

Summary:
Meaning of trial balance:
A statement showing the abstract of the balance (debit/credit) of various accounts in the ledger.

Objectives of trial balance:
The main objectives of preparing the trial balance are:

• To ascertain the arithmetical accuracy of the ledger accounts;
• To help in locating errors; and
• To help in the preparation of the final accounts.

Preparation of trial balance by the balance method:
In this method, the trial balance has three columns. The first column is for the head of the account, the second column for writing the debit balance and the third for the credit balance of each account in the ledger.

Format of a Trial balance
Trial Balance of ………………… as on March 31.2005

It is normally prepared at the end of an accounting year. However, an organisation may prepare a trial balance at the end of any chosen period, which may be monthly, quarterly, half yearly or annually depending upon its requirements.
In order to prepare a trial balance following steps are taken:

• Ascertain the balances of each account in the ledger.
• List each account and place its balance in the debit or credit column as the case may be. (If an account has a zero balance, it may be included in the trial balance with zero in the column for its normal balance).
• Compute the total of debit balances column.
• Compute the total of the credit balances column.
• Verify that the sum of the debit balances equal the sum of credit balances. If they do not tally, it indicates that there are some errors. So one must check the correctness of the balances of all accounts.

It may be noted that all assets expenses and receivables account shall have debit balances whereas all liabilities, revenues and payables accounts shall have credit balances.

Illustrative Trial Balance

Various types of errors:
1. Errors of commission:
Errors caused due to wrong recording of a transaction, wrong totalling, wrong casting, wrong balancing, etc.

2. Errors of omission:
Errors caused due to omission of recording a transaction entirely or partly in the books of account.

3. Errors of principle:
Errors arising due to wrong classification of receipts and payments between revenue and capital receipts and revenue and capital expenditure.

4. Compensating errors:
Two or more errors committed in such a way that they nullify the effect of each other on the debits and credits.

Rectification of errors:
Errors affecting only one account can be rectified by giving an explanatory note or by passing a journal entry. Errors which affect two or more accounts are rectified by passing a journal entry.

Meaning and utility of suspense account:
An account in which the difference in the trial balance is put till such time that errors are located and rectified. It facilitates the preparation of financial statements even when the trial balance does not tally.

Disposal of suspense account:
When all the errors are located and rectified the suspense account stands disposed off.

Students can Download Chapter 4 Bank Reconciliation Statement Notes, Plus One Accountancy Notes helps you to revise the complete Kerala State Syllabus and score more marks in your examinations.

Kerala Plus One Accountancy Notes Chapter 4 Bank Reconciliation Statement

Summary
Bank Reconciliation Satement
A statement prepared to reconcile the bank balance as per cash book with the balance as per passbook or bank statement, by showing the items of difference between the two accounts.

Causes of difference
Timing of recording the transaction Errors made by business or by the bank.

Need for Reconciliation
It is generally experienced that when a comparison is made between the bank balance as shown in the firm’s cash book, the two balances do not tally. Hence, we have to first ascertain the causes of difference thereof and then reflect them in a statement called Bank Reconciliation Statement to reconcile (tally) the two balances.

In order to prepare a bank reconciliation statement we need to have a bank balance as per the cash book and a bank statement as on a particular day along with details of both the books.

If the two balances differ, the entries in both the books are compared and the items on account of which the difference has arisen are ascertained with the respective amounts involved so that the bank reconciliation statement may be prepared.

Proforma of bank reconciliation statement

It can also be prepared with two amount columns one showing additions (+ column) and another showing deduction (- column).

Proforma of bank reconciliation statement (table form)

Correct cash balance
It may happens that some of the receipts or payments are missing from either of the books and errors, if any, need to be rectified. This arises the need to look at the entries/errors recorded in both statements and other information available and compute the correct cash balance before reconciling the statements.

Students can Download Chapter 2 Theory Base of Accounting Notes, Plus One Accountancy Notes helps you to revise the complete Kerala State Syllabus and score more marks in your examinations.

Kerala Plus One Accountancy Notes Chapter 2 Theory Base of Accounting

Summary:
Generally accepted Accounting Principles (GAAP):
GAAP refers to the rules or guidelines adopted for recording and reporting to business transactions in order to bring uniformity in the preparation and presentation of financial statements. These principles are also referred to as concepts and conventions.

From the practicality viewpoint, the various terms such as principles, conventions, modifying principles, assumptions, etc., have been used interchangeably and are referred to as basic accounting concepts.

Systems of Accounting:
There are two systems of recording business transactions, i.e., double entry system and single entry system.

Basis of Accounting:
There are two broad approach of accounting are cash basis and accural basis. Under cash basis transactions are recorded only when cash are received or paid, where as under accural basis, revenue or costs are recognises when they Occur rather than when they are paid.

Accounting Standards:
Accounting standards are written statement of uniform accounting rules and guidelines in practice for preparing the uniform and consistent financial statements.

Students can Download Chapter 1 Introduction to Accounting Notes, Plus One Accountancy Notes helps you to revise the complete Kerala State Syllabus and score more marks in your examinations.

Kerala Plus One Accountancy Notes Chapter 1 Introduction to Accounting

Summary
Meaning of Accounting:
Accounting is a process of identifying, measuring, recording the business transactions and communicating thereof the required information to the interested users.

Accounting as a source of information:
Accounting as a source of information system is the process of identifying, measuring, recording and communicating the economic events of an organization to interested users of the information.

Users of accounting information:
Accounting plays a significant role in society by providing information to management at all levels and to those having a direct financial interest in the enterprise, such as present and potential investors and creditors.

Accounting information is also important to those having an indirect financial interests, such as regulatory agencies, tax authorities, customers, labour unions, trade associations, stock exchanges, and others.

Qualitative characteristics of Accounting:
To make accounting information decision-useful, it should possess the following qualitative characteristics.

• Reliability
• Understandability
• Relevance
• Comparability

The objective of accounting:
The primary objectives of accounting are to:

• Maintain records of business;
• Calculate profit or loss;
• Depict the financial position: and
• Make information available to various groups and users.

Role of accounting:
Accounting is not an end in itself. It is a means to an end. It plays the role of a:

• Language of a business
• Historical record
• Current economic reality
• Information system
• Service to users

Students can Download Chapter 8 Excretory Products and their Elimination Notes, Plus One Zoology Notes helps you to revise the complete Kerala State Syllabus and score more marks in your examinations.

Kerala Plus One Zoology Notes Chapter 8 Excretory Products and their Elimination

What is excretion?
Excretion is the elimination common nitrogenous wastes. Ammonia, urea and uric acid are the major forms of nitrogenous wastes excreted by the animals.

Ammonotelic.ureotelic and urecotelic animals and their excretion:
1. The process of excreting ammonia is Ammonotelism. eg: Many bony fishes, aquatic amphibians and aquatic insects are ammonotelic.

2. Mammals, many terrestrial amphibians and marine fishes mainly excrete urea and are called ureotelic animals.

3. Reptiles, birds, land snails and insects excrete nitrogenous wastes as uric acid in the form of pellet or paste with a minimum loss of water and are called uricotelic animals.

Where is urea produced?
Ammonia produced by metabolism is converted into urea in the liver and released into the blood which is filtered and excreted out by the kidneys.

Excretion in lower organisms:

Human Excretory System
In humans, the excretory system consists of

1. A pair of kidneys
2. One pair of ureters
3. A urinary bladder
4. A urethra.

Each kidney of an adult human measures 10 – 12 cm in length, 5 – 7 cm in width, 2 – 3 cm in thickness with an average weight of 120 – 170 g.

1. Centre of the inner concave surface of the kidney is a notch called hilum through which ureter, blood vessels and nerves enter.

2. Innerto the hilum is a broad funnel shaped space called the renal pelvis with projections called calyces.

3. Inside the kidney, there are two zones, an outer cortex and an inner medulla.

4. The medulla is divided medullary pyramids projecting into the calyces.

5. The cortex extends in between the medullary pyramids as renal columns called Columns of Bertini.

6. Each kidney has nearly one million complex tubular structures called nephrons, which are the functional units. A diagrammatic representation of a nephron showing blood vessels, duct and tubule Each nephron has two parts -1 The glomerulus & 2 Renal tubule.

7. Glomerulus is a tuft of capillaries formed by the afferent arteriole – a fine branch of renal artery.

8. Blood from the glomerulus is carried away by an efferent arteriole.

9. The renal tubule begins with a double walled cup-like structure calle Bowman’s capsule, which encloses the glomerulus.

10. Glomerulus alongwith Bowman’s capsule, is called the malpighian body or renal corpuscle

11. The tubule continues further to form a highly coiled network proximal convoluted tubule (PCT).

12. A hairpin shaped Henle’s loop is the next part of the tubule which has a descending and an ascending limb.

13. The ascending limb continues as another highly coiled tubular region called distal convoluted tubule (DCT).

14. The DCTs open into a straight tube called collecting duct, many of which open into the renal pelvis through medullary pyramids in the calyces.

15. The Malpighian corpuscle, PCT and DCT of the nephron are situated in the cortical region of the kidney whereas the loop of Henle dips into the medulla.

Types of Nephrons:
1. In majority of nephrons, the loop of Henle is too short and extends only very little into the medulla. Such nephrons are called cortical nephrons.

2. In some of the nephrons, the loop of Henle is very long and runs deep into the medulla.These nephrons are called juxta medullary nephrons. A minute vessel of capillary network runs parallel to the Henle’s loop forming a ‘LT shaped vasa recta. Vasa recta is absent or highly reduced in cortical nephrons.

Urine Formation
1. It involves three main processes namely, glomerular filtration, reabsorption and secretion

2. The first step in urine formation is the filtration of blood, which is carried out by the glomerulus and is called glomerular filtration.

3. 1100 – 1200 ml of blood is filtered by the kidneys per minute. The glomerular capillary blood pressure causes filtration of blood through 3 layers,

4. The epithelial cells of Bowman’s capsule called podocytes which possess minute spaces called filtration slits.

5. Blood is filtered through these membranes, that almost all the constituents of the plasma except the proteins pass onto the lumen of the Bowman’s capsule. It is the process of ultra filtration.

6. The kidneys have efficient mechanism for the regulation of glomerular filtration rate. It is carried out by juxta glomerular apparatus (JGA).JGA is found in the distal convoluted tubule .

7. A fall in GFR can activate the JG cells to release renin which can stimulate the glomerular blood flow and thereby the GFR back to normal.

8. Nearly 99 percent of the filtrate is reabsorbed by the renal tubules. This process is called reabsorption.

9. For example, substances like glucose, amino acids, Na⁺, etc., in the filtrate are reabsorbed actively whereas the nitrogenous wastes and water are absorbed by passive transport.

10. During urine formation, the tubular cells secrete substances like H⁺, K⁺ and ammonia into the filtrate.

11. Tubular secretion is helpful in the maintenance of ionic and acid-base balance of body fluids.

Function Of The Tubules
Proximal Convoluted Ttubule (PCT):
1. PCT consists of simple cuboidal brush border epithelium which increases the surface area for reabsorption.

2. All essential nutrients, and 70 – 80 per cent of electrolytes and water are reabsorbed by this segment.

3. PCT also helps to maintain the pH and ionic balance of the body fluids. It occurs through selective secretion of hydrogen ions, ammonia and potassium ions into the filtrate and by absorption of HCO₃^– from it.

Henle’s Loop
Function:
It helps to maintain high osmolarity of medullary interstitial fluid. The descending limb of loop of Henle is permeable to water but impermeable to electrolytes. This concentrates the filtrate as it moves down.

The ascending limb is impermeable to water but allows transport of electrolytes actively or passively. Therefore, as the concentrated filtrate pass upward, it gets diluted due to the passage of electrolytes to the medullary fluid.

Distal Convoluted Tubule (DCT):
The reabsorption of Na⁺, HCO₃^– and water takes place in this segment. In this segment selective secretion of hydrogen and potassium ions and NH₃ to maintain the pH and sodium-potassium balance in blood.

Collecting Duct:
It extends from the cortex of the kidney to the inner parts of the medulla. Large amounts of water is reabsorbed from this region to produce a concentrated urine. This part maintains pH and ionic balance of blood by the selective secretion of H⁺ and K⁺ ions.

Mechanism Of Concentration Of The Filtrate
The flow of filtrate in the two limbs of Henle’s loop is in opposite directions and thus forms a counter current. The flow of blood through the two limbs of vasa recta is also in a counter current pattern.

The proximity between the Henle’s loop and vasa recta, as well as the counter current in them help in maintaining an increasing osmolarity towards the inner medullary interstitium, i.e. from 300 mOsmolL^-1 in the cortex to about 1200 mOsmolL^-1 in the inner medulla. This gradient is mainly caused by NaCl and urea.

NaCl is transported by the ascending limb of Henle’s loop which is exchanged with the descending limb of vasa recta. NaCl is returned to the interstitium by the ascending portion of vasa recta. Similarly, small amounts of urea enterthe thin segment of the ascending limb of Henle’s loop which is transported back to the interstitium by the collecting tubule.

This transport is facilitated by the counter current mechanism This mechanism helps to maintain a concentration gradient in the medullary interstitium. Presence of such interstitial gradient helps in an easy passage of water from the collecting tubule thereby concentrating the filtrate (urine).

Regulation Of Kidney Function
The functioning of the kidneys is influenced by hypothalamus, JGA and to a certain extent, the heart in the body are activated by changes in blood volume.

How can diuresis is prevented in body?
The decrease of fluid from the body can activate these Osmoreceptors which stimulate the hypothalamus to release antidiuretic hormone (ADH) or vasopressin from the neurohypophysis. ADH facilitates water reabsorption Hence it prevents diuresis.

An increase in body fluid volume switch off the osmoreceptors and suppress the ADH release. ADH can also affect the kidney function by its constrictory effects on blood vessels. This causes an increase in blood pressure. An increase in blood pressure increase the glomerular blood flow and the GFR.

Micturition
It is the voluntary signal from the central nervous system (CNS). This signal is initiated by the stretching of the urinary bladder in response to the stretch receptors on the walls of the bladder.

The urine is slightly acidic (pH – 6.0) and has a characterestic odour. 25 – 30 gm of urea is excreted out per day. Analysis of urine helps to know malfunctioning of the kidney.

Role Of Other Organs In Excretion
Lungs remove large amounts of CO₂ (18 litres/day) and water every day. Liver secretes bile-containing substances like bilirubin, biliverdin, cholesterol, degraded steroid hormones, vitamins and drugs.

The sweat and sebaceous glands in the skin eliminates watery fluid containing NaCl, small amounts of urea, lactic acid, etc. Sebaceous glands eliminates sterols, hydrocarbons and waxes through sebum. This secretion provides a protective oily covering for the skin.

Disorders Of The Excretory System
Uemia:
It leads to the accumulation of urea in blood. It lead to kidney failure. In such patients, urea can be removed by a process called hemodialysis.

Procedure of Dialysis:
Blood drained from a artery is pumped into a dialysing unit after adding an anticoagulant like heparin.The unit contains a coiled cellophane tube surrounded by a fluid (dialysing fluid).

The porous cellophane membrance allows the passage of molecules based on concentration gradient.
As nitrogenous wastes are absent in the dialysing fluid, the cleared blood is pumped back to the body through a vein after adding anti-heparin to it.

Remedy for kidney damage:
Kidney transplantation is the ultimate method in the correction of acute renal failures (kidney failure). A functioning kidney is used in transplantation from a donor to minimise its chances of rejection by the immune system of the host.

Renal calculi:
Stone or insoluble mass of crystallised salts (oxalates, etc.) formed within the kidney.

Glomerulonephritis:
Inflammation of glomeruli of kidney

NCERT SUPPLEMENTARY SYLLABUS
Diabetes Insipidus:
Antidiuretic hormone (ADH) is released from the posterior pituitary, prevents dehydration. It helps in the reabsorption of water by the distal parts of the kidney tubules and prevents diuresis. Deficiency of ADH leads to diabetes insipedus, that means huge amounts of dilute urine is formed followed by intense thirst.

The name itself (diabetes = overflow; insipidus = tasteless) distinguishes it from diabetes .mellitus (mel = honey), in which insulin deficiency causes large amounts of blood sugar to be lost in the urine

Artificial kidney:
Hemodialysis machine is known as the artificial kidney. Hemodialysis is an artificial process of removing toxic substances from the blood in patients of kidney failure.

Students can Download Chapter 14 Oscillations Notes, Plus One Physics Notes helps you to revise the complete Kerala State Syllabus and score more marks in your examinations.

Kerala Plus One Physics Notes Chapter 14 Oscillations

Introduction
In this chapter, we study oscillatory motion. The description of an oscillatory motion requires some fundamental concept like period, frequency, displacement, amplitude and phase.

Periodic And Oscillatory Motions
Periodic Motion:
A motion that repeats itself at regular intervals of time is called periodic motion.
Example:

• The orbital motion of planets in the solar system.
• The piston in a steam engine going back and forth

Oscillations or Vibrations:
A body executes to and fro motion at regular intervals of time is called oscillatory (or) vibratory motion.

Note:
(1) When the frequency is small, we call it oscillation. When the frequency is high, we call it vibration.
Period and frequency:
Period (T):
Time taken to complete one oscillation is called period

Frequency (n):
The number of oscillations per second is called frequency.
frequency v = \(\frac{1}{T}\)Hz

Displacement:
Displacement of oscillation means the change of any physical property with time under consideration.

Explanation:
For example, consider the oscillation of block attached to a spring. In this case the displacement of block with time is referred to as displacement.

In the case if oscillation of simple pendulum, the angle from the vertical as a function of time may be regarded as a displacement variable. The voltage across a capacitor, changing with time in an a.c. circuit is also a displacement variable

Note:
The displacement variable may take both positive and negative values.

Mathematical expression for displacement:
The displacement of a periodic function can be written as

Simple Harmonic Motion (S.H.M.)
Simple harmonic motion is the simplest form of oscillatory motion.

The oscillatory motion is said to be simple harmonic motion if the displacement ‘x’ of the particle from the origin varies with time as

Where
x(t) = displacement x as a function of time t
A = amplitude
ω = angular frequency
(ω t+ Φ) = phase (time-dependent)
Φ = phase constant or initial phase

Graphical Variation of S.H.M.

The above graph shows the graphical representation of x(t) = A coswt with time.
(Initial phase Φ = 0)

Amplitude of S.H.M.
The maximum displacement of S.H.M. from mean position is called the amplitude of S.H.M.
Note:
1.

Two simple harmonic motions having, same w and Φ but different amplitudes A and B as shown in the above figure.

2.

Two simple harmonic motions having the same A and w but different phase angle Φ as shown in the above figure.

Simple Harmonic Motion And Uniform Circular Motion

Question 1.
Show that the projection of uniform circular motion on any diameter of the circle is S.H.M.

Answer:
Consider a particle moving along the circumference of a circle of radius ‘a’ and centre O, with uniform angular velocity w. AB and CD are two mutually perpendicular diameters along X and Y axis. At time t = 0. let the particle be at P₀ so that ∠P₀OB = Φ.

After time Y second, let the particle reach P so that ∠POP₀ = ωt. N is the foot of the perpendicular drawn from P on the diameter CD.

Similarly M is the foot of the perpendicular drawn from P to the diameter AB. When the particle moves along the circumference of the circle, the foot of the perpendicular executes to and fro motion along the diameter CD or AB with O as the mean position. From the right angle triangle O MP, we get
cos (ωt + Φ) = \(\frac{\mathrm{OM}}{\mathrm{OP}}\)
∴ OM = OP cos (ωt + Φ)
X = a cos (ωt + Φ) ………………. (1)
Similarly, we get
sin (ωt + Φ) = \(\frac{y}{a}\) (or)
Y = a sin (ωt + Φ) ……………… (2)
Equation (1) and (2) are similar to equations of S.H.M. The equation(1) and (2) shows that the projection of uniform circular motion on any diameter is S.H.M.
At t = 0, if the particle is at B, then Φ = 0. Then equations (1) and (2) reduce to
x = a cos ωt ………………….. (3)
y = a sin ωt …………………….(4)

Velocity And Acceleration In Simple Harmonic Motion B
Velocity Of S.H.M.
The y displacement of S.H.M. is given by
y = a sin ω t
∴ velocity in y direction

Case – 1
At the mean position y=0, therefore velocity is maximum. The maximum velocity is given by

Case – 2
At the extreme position, y = a
∴ V_minimum = \(\sqrt{a^{2}-a^{2}}\) = 0
So the velocity of a S.H.M. varies between o and wa

Acceleration of S.H.M
We know y = a sin ω t
Velocity v = \(\frac{d y}{d t}\) = a ω cos ω t
Acceleration a = \(\frac{d^{2} y}{d t^{2}}\) = -aω² sin ωt
a = -aω² sin ωt

This equation shows that acceleration of a SHM is directly proportional to the displacement and opposite to the displacement.

Variation of displacement Y with time t:

Variation of velocity (v) with time:

Variation of acceleration with time:

Force Law For Simple Harmonic Motion
According to Newton’s second law of motion F = ma
But a = -ω²y(t)
ie. force acting on the S.H.M. in Y direction
F = -mω²y(t)
(or) F = -ky(t)
Where k= mω²
From the above equation (1), we can take an alternative definition of simple harmonic motion.

Statement:
Simple harmonic motion is the motion executed by a particle subject to a force, which is proportional to the displacement of the particle and is directed towards the mean position.

Energy In Simple Harmonic Motion
A simple harmonically moving particle possesses both potential energy and kinetic energy. Potential energy is due to its displacement against restoring force. Kinetic energy is due to its motion.

Total energy of the S.H.M. is the sum of the kinetic energy and potential energy. Total energy remains a constant throughout its motion.

Expression for Kinetic energy:
Let m be the mass of the particle executing SHM. Let V be the velocity at any instant,

Expression for potential energy:
Potential energy is work required to take the particle against the restoring force.

Work done to displace the particle through a small distance dy, dw = force × displacement
= mω²y × dy [force = ω²y ]. Therefore total work done to take the particle from o to y.


This work done is stored in the particle as its potential energy.

At extreme position y = a

At equilibrium position y = 0
∴ PE = 0
Total energy of a S.H.M.
Total energy = PE + kE

∴ Total energy = maximum KE = maximum PE

Graphical variation of PE, KE and TE of S.H.M.

Some Systems Executing Simple Harmonic Motion
Oscillations due to a spring Hooks Law:
The force acting simple harmonic motion is proportional to the displacement and is always directed towards the centre of motion.
F α – x (or) F= kx
where k is called spring constant

Period of oscillation of a spring:

Consider a body of mass m attached to a massless spring of spring constant K. The other end of spring is connected to a rigid support as shown in figure. The body is placed on a frictionless horizontal surface.

If the body be displaced towards right through a small distance ‘x’, a restoring force will be developed.

The Simple Pendulum:

Consider a mass m suspended from one end of a string of length L fixed at the other end as shown in figure. Suppose P is the instantaneous position of the pendulum. At this instant its string makes an angle θ with the vertical.

The forces acting on the bob are (1) weight of bob F_g (mg) acting vertically downward. (2) Tension T in the string.

The gravitational force F_g can be divided into a radial component F_gCos θ and tangential component F_gSin θ. The radial component is cancelled by the – tension T. But the tangential component F_gSin θ produces a restoring torque.

Restoring torque τ = – F_g sin θ . L.
τ = -mg sin θ.L …………….. (1)
-ve sign shown that the torque and angular displacement θ are oppositely directed. For rotational motion of bob,.
τ = Iα …………. (2).
Where I is a moment of inertia about the point of suspension and α is angular acceleration. From eq (1) and eq (2).
Iα = -mg sin θ.L
If we assume that the displacement θ is small, sin θ ≈ θ.
∴ Iα = -mg θ.L
Iα + mg θ.L = 0

Damped Simple Harmonic Motion
Periodic oscillations of decreasing amplitude due to the presence of resistive forces of the medium are called damped oscillations.

Question 2.
Derive a differential equation for a damped simple harmonic oscillation.

Answer:
Consider a block of mass ‘m’ connected to one end of a massless spring of spring constant K. The other end of spring is connected to rigid support. The block is connected to a vane through a rod (The vane and rod are massless). The vane is submerged in a liquid.

Let the equilibrium position of block be ‘O’. If this block is moved along downward direction through a distance x, a damping force will be developed on vane due to liquid. This damping force is proportional to velocity of vane ie; damping force F_d α – v (or) F_d = -bv

where b is called damping constant. The value of b depends on the characteristics of the liquid and the vane.

The restoring force on the block due to spring. F_s = -kx. where x is the displacement of the mass from its equilibrium position.
∴ Total force on the block, F = -bv + -kx
ma = -bv + -kx
ma + bv + kx = 0
\(m \frac{d^{2} x}{d t^{2}}+b \frac{d x}{d t}+k x=0\)
This is the differential equation of S.H.M.

The motion of damped harmonic oscillator:
The solution of the above differential equation of damped harmonic oscillator is

Case – 1
b = 0 (There is no damping force). In this case, we get

The above result shows that, if there is no damping force (b = 0). The oscillator behaves like a undamped oscillator.

Case – 2
If b is small, the amplitude of the oscillator decreases continuously with time. The motion is approximately a periodic. The Variation of displacement x (t) with time T is shown below.

Case – 3
If damping constant b is large, the amplitude of the oscillator decreases to zero very quickly. The motion is not a periodic motion. The variation of displacement x (t) with time T is shown below.

The Energy variation of damped oscillator:
The energy of an undamped oscillator, E = \(\frac{1}{2}\)kA².
where A is the amplitude of an undamped oscillator. But for the damped oscillator, amplitude = Ae^-bt/2m.

The above equation shows that the energy of a damped oscillator decreases exponentially with time, which is shown below

Note:
Small damping means that the dimensionless ratio
\((b / \sqrt{k m})\) is much less than 1.

Forced oscillations and resonance
Free oscillation:
When a body oscillates in the absence of external forces (eg. friction etc.) the oscillations are said to be free oscillations.

Forced oscillation:
When an external periodic force is applied to a damped harmonic oscillator, the oscillator will vibrate with a constant amplitude and frequency of vibration will be that of the applied periodic force. This type of oscillation is called forced oscillation.

The differential equation of forced oscillator:
Let F(t) = F₀ cosω_dt is an external force applied to a damped oscillator.

The total force acting on the damped oscillator,
F = – bv – kx + F₀ cosω_dt
where -bv is the damping force and -kx is the linear restoring force.
F + bv + kx = F₀ cosω_dt
\(m \frac{d^{2} x}{d t^{2}}+b \frac{d x}{d t}+k x=F_{0} \cos \omega_{d} t\)
This is the differential equation of an oscillator of mass m on which a periodic force of (angular) frequency ω_d is applied. The oscillator initially oscillates with its natural frequency w. When we apply the external periodic force, the oscillation with the natural frequency die out, and the body oscillates with the (angular) frequency of the external periodic force.

The motion of forced oscillator:
The solution (displacement) of the above differential equation of forced oscillator can be written as
x(t) = Acos(ω_dt + Φ)

where m is the mass of the particle v₀ and x₀ are the velocity and the displacement of the particle at time t = 0, (which is the moment when we apply the periodic force)

Case -1
When b = 0 (damping force = 0) and ω = ω_d,
we get A = \(\frac{F_{0}}{0}\)
A = ∞
This is an ideal case. This case never arises in a real situation as the damping is never perfectly zero.

Case – 2
(Small damping, driving frequency far from natural frequency).
In this ω_db << m(ω² – ω_d²). Hence we can neglect ω_db. Hence amplitude of oscillation can be written as.

Case – 3
(Small damping, driving frequency close to natural frequency).
In this case m(ω² – ω_a²) << ω_db. Hence we can neglect m (ω² – ω_a²). Hence amplitude of oscillation can be written as

This equation shows that the maximum amplitude fora given driving frequency is governed by the driving frequency and damping constant.

Resonant Oscillation
When the frequency of the external periodic force is varied, it is found that the amplitude of the forced vibration increases and reaches a maximum value and then decreases.

The amplitude will be maximum when the frequency of the applied periodic force is equal to the natural frequency of the vibration. Such oscillations are called resonant oscillations and the phenomenon is called resonance.

Graphical variation amplitude with driving frequency:

Examples of resonance:
All mechanical structures have one or more natural frequencies, and if a structure is subjected to a strong external periodic driving force that matches one of these frequencies, the resulting oscillations of the structure may rupture it.

The Tacoma Narrows Bridge at Puget Sound, Washington, USA was opened on July 1, 1940. Four months later winds produced a pulsating resultant force in resonance with the natural frequency of the structure.

This caused a steady increase in the amplitude of oscillations until the bridge collapsed. It is for the same reason the marching soldiers break steps while crossing a bridge. Aircraft designers make sure that none of the natural frequencies at which a wing can oscillate match the frequency of the engines in flight! Earthquakes cause vast devastation.

In an earthquake, short and tall structures remain unaffected while the medium height structures fall down. This happens because the natural frequencies of the short structures happen to be higher and those of taller structures lower than the frequency of the seismic waves.

Students can Download Chapter 7 Body Fluids and Circulation Notes, Plus One Zoology Notes helps you to revise the complete Kerala State Syllabus and score more marks in your examinations.

Kerala Plus One Zoology Notes Chapter 7 Body Fluids and Circulation

Blood
Blood is a special connective tissue contains

• Fluid matrix
• Plasma
• Formed elements.

Plasma:
It constitute nearly 55 per cent of the blood. 90 – 92 percent of plasma is water and proteins (Fibrinogen, globulins and albumins) contribute 6 – 8 percent of it. Fibrinogens are needed for clotting or coagulation of blood.

Defence mechanism and osmotic balance:
Globulins primarly are involved in defense mechanisms of the body and the albumins help in osmotic balance. Plasma also contains small amounts of minerals like Na⁺, Ca⁺⁺, Mg⁺⁺, HCO₃^–, CI^–, etc. Factors for coagulation or clotting of blood are also present in the plasma in an inactive form.

What is serum?
Plasma without the clotting factors is called serum.

Formed Elements

1. Erythrocytes
2. Leucocytes
3. Platelets

They constitute nearly 45 per cent of the blood.
1. Erythrocytes or red blood cells (RBC):
They are the most abundant and on an average, 5 millions to 5.5 millions of RBCs mm-3 of blood. RBCs are formed in the red bone marrow in the adults. RBCs are devoid of nucleus in most of the mammals and are biconcave in shape. They have a red coloured, iron containing complex protein called haemoglobin.

A healthy individual has 12 – 16 gms of haemoglobin in every 100 ml of blood. These molecules play a significant role in transport of respiratory gases. RBCs have an average life span of 120 days after which they are destroyed in the spleen (graveyard of RBCs).

2. Leucocytes:
They are also known as white blood cells, colourless, nucleated and are relatively lesser in number which averages 6000 – 8000 mm-3 of blood. Leucocytes are generally short lived. The two main categories of WBCs granulocytes and agranulocytes.

• Neutrophils are the most abundant cells (60 – 65 percent) of the total WBCs and basophils are the least (0.5 – 1 percent) among them.
• Neutrophils and monocytes (6 – 8 per cent) are phagocytic cells which destroy foreign organisms entering the body.
• Basophils secrete histamine, serotonin, heparin, etc., and are involved in inflammatory reactions.
• Eosinophils (2 – 3 per cent) resist infections and are also associated with allergic reactions.

Lymphocytes (20-25 percent) are of two major types – ‘B’ and ‘T’ forms. Both B and T lymphocytes are responsible for immune responses of the body.

3. Platelets:
They are also called thrombocytes, are cell fragments produced from megakaryocytes (special cells in the bone marrow). Blood normally contains 1,500,00 – 3,500,00 platelets mm-3. Platelets are involved in the coagulation or clotting of blood. A reduction in their number can lead to clotting disorders which will lead to excessive loss of blood from the body.

Blood Groups
The ABO and Rh- are widely used all over the world.

ABO grouping
It is based on the presence or absence of two surface antigens on the RBCs namely A and B. The plasma of different individuals contain two natural antibodies (proteins produced in response to antigens). There are four groups of blood, A, B, AB and O.

Who are called as universal donor and receipient?
The group ‘O’ blood can be donated to persons with any other blood groupand hence ‘O’group individuals are called ‘universal donors’. Persons with ‘AB’ group can accept blood from persons with AB as well as the other grbups of blood, such persons are called ‘universal recipients’.

Rh grouping
Rh antigen is observed on the surface of RBCs of majority (nearly 80 percent) of humans. Such individuals are called Rh positive (Rh+ve) and without antigen are called Rh negative (Rh-ve). Rh group should also be matched before transfusions.

What is Rh incompatibility?
It is the mismatching of blood between the Rh-ve blood of a pregnant mother with Rh+ve blood of the foetus. Rh antigens of the foetus do not get exposed to the Rh-ve blood of the mother in the first pregnancy as the two bloods are well separated by the placenta.

But during the delivery of the first child, there is a possibility of mixing of the maternal blood to small amounts of the Rh+ve blood from the foetus. In such cases, the mother starts preparing antibodies against Rh in her blood. In subsequent pregnancies, the

Solving of Rh incompatibility:
This can be avoided by administering anti-Rh antibodies to the mother immediately after the delivery of the first child.

Coagulation of Blood
Blood coagulates or clots in response to an injury or trauma to prevent excessive loss of blood from the body. The network of threads called fibrins in which dead and damaged formed elements of blood are trapped.

Fibrins are formed by the conversion of inactive fibrinogens in the plasma by the enzyme thrombin. Thrombins are formed from another inactive substance present in the plasma called prothrombin.

An enzyme complex, thrombokinase, is required forthe above reaction. An injury stimulates the platelets in the blood to release certain factors which activate the mechanism of coagulation .Calcium ions play a very important role in clotting.

Lymph (tissue fluid)
As the blood passes through the capillaries in tissues, fluid released out is called the interstitial fluid or tissue fluid. It has the same mineral distribution as that in plasma. An elaborate network of vessels called the lymphatic system collects this fluid and drains it back to the major veins.

The fluid present in the lymphatic system is called the lymph. Lymph is a colourless fluid which are responsible forthe immune responses of the body. Lymph is also an important carrier for nutrients, hormones, etc. Fats are absorbed through lymph in the lacteals present in the intestinal villi.

Circulatory Pathways
The circulatory patterns are of two types – open or closed.

Open circulatory system:
It is present in arthropods and molluscs in which blood pumped by the heart passes through large vessels into open spaces or body cavities called sinuses.

Closed circulatory system:
It is present in Annelids and chordates in which the blood is pumped by the heart circulated through a closed network of blood vessels.
All vertebrates possess a muscular chambered heart.
1. Fishes have a 2-chambered heart with an atrium and a ventricle.

2. Amphibians and the reptiles (except crocodiles) have a 3-chambered heart with two atria and a single ventricle.

3. Crocodiles, birds and mammals possess a 4-chambered heart with two atria and two ventricles. In fishes the heart pumps out deoxygenated blood which is oxygenated by the gills and supplied to the body parts from where deoxygenated blood is returned to the heart (single circulation).

In amphibians and reptiles, the left atrium receives oxygenated blood from the gills/lungs/skin and the right atrium gets the deoxygenated blood from other body parts. However, they get mixed up in the single ventricle which pumps out mixed blood (incomplete double circulation).

In birds and mammals, oxygenated and deoxygenated blood received by the left and right atria respectively passes on to the ventricles of the same sides. The two separate circulatory pathways are present in these organisms, hence the animals have double circulation.

Human Circulatory System
Heart:
It is situated in the thoracic cavity, in between the two lungs. It is protected by a double walled membranous bag,pericardium, enclosing the pericardial fluid. It has four chambers, two small upper chambers called atria and two larger lower chambers called ventricles.

A thin, muscular wall called the inter atrial septum separates the right and the left atria, whereas a thick- walled, the inter-ventricular septum, separates the left and the right ventricles. The atrium and the ventricle of the same side are separated by a thick fibrous tissue called the atrioventricular septum.

Tricuspid and bicuspid valve:
The opening between the right atrium and the right ventricle is guarded by a valve formed of three muscularflaps or cusps, the tricuspid valve. Bicuspid or mitral valve guards the opening between the left atrium and the left ventricle.

Semilunar valve:
The openings of the right and the left ventricles into the pulmonary artery and the aorta respectively are provided with the semilunar valves.

Function of semilunar valve:
It allows the flow of blood only in one direction, i.e., from the atria to the ventricles and from the ventricles to the pulmonary artery or aorta. These valves prevent any backward flow.

SAN & AVN:
A specialised cardiac musculature called the nodal tissue is also distributed in the right upper corner of the right atrium called the sino-atrial node (SAN). Another mass of this tissue is seen in the lower left comer of the right atrium close to the atrio-ventricular septum called the atrio-ventricular node (AVN).

A bundle of nodal fibres, atrioventricular bundle (AV bundle) continues from the AVN which passes through the atrio-ventricular septa to emerge on the top of the interventrical sepyum and divides into a right and left bundle. These branches give rise to minute fibres throughout the ventricular musculature, they are called purkinje fibres.

These fibres alongwith right and left bundles are known as bundle of HIS. The nodal musculature has the ability to generate action potentials without any external stimuli.

What is the pacemaker of heart?
The SAN can generate the maximum number of action potentials, i.e., 70 – 75 min^-1, and is responsible for initiating and maintaining the rhythmic contractile activity of the heart. Hence it is called the pacemaker. Our heart normally beats 70 – 75 times in a minute (average 72 beats min^-1).

Cardiac Cycle
As the tricuspid and bicuspid valves are open, blood from the pulmonary veins and vena cava flows into the left and the right ventricle respectively. The semilunar valves are closed at this stage. The action potential is conducted to the ventricular side by the AVN and AV bundle from where the bundle of HIS transmits it through the entire ventricular musculature.

This causes the ventricular muscles to contract, (ventricular systole), the atria undergoes relaxation (diastole). As the ventricular pressure increases the semilunar valves open, allowing the blood in the ventricles to flow through these vessels into the circulatory pathways.

The ventricles relax (ventricular diastole) and the ventricular pressure falls causing the closure of semilunar valves which prevents the backflow of blood into the ventricles.

This sequential event in the heart which is cyclically repeated is called the cardiac cycle and it consists of systole and diastole of both the atria and ventricles. The heart beats 72 times per minute,i.e., that many cardiac cycles are performed per minute.

Cardiac output is the volume of blood pumped out by each ventricle per minute and averages 5000 mL or 5 litres in a healthy individual.

Sound produced in heart:
For example, the cardiac output of an athlete will be much higherthanthat of an ordinary man. During each cardiac cycle sounds are produced, the first heart sound (lub) is associated with the closure of the tricuspid and bicuspid valves whereas the second heart sound (dub) is associated with the closure of the semilunar valves. These sounds are of clinical diagnostic significance.

Electrocardiograph (ECG)
ECG is a graphical representation of the electrical activity of the heart during a cardiac cycle. Each peak in the ECG is identified with a letter from P to T that corresponds to a specific electrical activity of the heart.
1. The P-wave represents the electrical excitation Diagrammatic presentation of a standard ECG (or depolarisation) of the atria, which leads to the
contraction of both the atria.

2. The QRS complex represents the depolarisation of the ventricles, which initiates the ventricular contraction. The contraction starts shortly after Q and marks the beginning of the systole.

3. The T-wave represents the return of the ventricles from excited to normal state (repolarisation). The end of the T-wave marks the end of systole.

Since the ECGs obtained from different individuals have the same shape any deviation from this shape indicates abnormality or disease.

Doube Circulation
It involves two types of circulation,
1. Pulmonary circulation:
The deoxygenated blood pumped into the pulmonary artery is passed on to the lungs from where the oxygenated blood is carried by the pulmonary veins into the left atrium. This pathway constitutes the pulmonary circulation.

2. Systemic circulation:
The oxygenated blood entering the aorta is carried by a network of arteries, arterioles and capillaries to the tissues from where the deoxygenated blood is collected by a system of venules, veins and vena cava and emptied into the right atrium. This is the systemic circulation.

The systemic circulation provides nutrients, O₂ and other essential substances to the tissues and takes CO₂ and other harmful substances away for elimination. A vascular connection between the digestive tract and liver called hepatic portal system.

The hepatic portal vein carries blood from intestine to the liver before it is delivered to the systemic circulation. In Coronary system of blood vessels is present in our body exclusively for the circulation of blood to and from the cardiac musculature.

Regulation Of Cardiac Activity
Normal activities of the heart are auto regulated by specialised muscles (nodal tissue), hence the heart is called myogenic. Medulla oblangata control the cardiac function through autonomic nervous system (ANS).

Neural signals through the sympathetic nerves (part of ANS) increase the rate of heart beat. On the other hand, parasympathetic neural signals decrease the rate of heart beat. Adrenal medullary hormones can also increase the cardiac output.

Disorders Of Circulatory System
High Blood Pressure (Hypertension):
Hypertension is the term for blood pressure that is higherthan normal (120/80). In this measurement 120 mm Hg (millimetres of mercury pressure) is the systolic, or pumping, pressure and 80 mm Hg is the diastolic, or resting, pressure. High blood pressure leads to heart diseases and also affects vital organs like brain and kidney.

Coronary Artery Disease (CAD):
Coronary Artery Disease, often referred to as atherosclerosis, affects the vessels that supply blood to the heart muscle. It is caused by deposits of calcium, fat, cholesterol and fibrous tissues, which makes the lumen of arteries narrower.

Angina:
It is also called ‘angina pectoris’. A symptom of acute chest pain appears when no enough oxygen is reaching the heart muscle. It occurs due to conditions that affect the blood flow.

Heart Failure:
It is the state of heart when it is not pumping blood effectively enough to meet the needs of the body. Heart failure is not the same as cardiac arrest (when the heart stops beating) or a heart attack (when the heart muscle is suddenly damaged by an inadequate blood supply).

Students can Download Chapter 15 Waves Notes, Plus One Physics Notes helps you to revise the complete Kerala State Syllabus and score more marks in your examinations.

Kerala Plus One Physics Notes Chapter 15 Waves

Summary
The wave is the propagation of disturbance that carries energy from one point to another point, without translatory motion of particles in the medium. There are three types of wave.
1. Mechanical Wave: Requires medium for propagation.
Eg: Sound wave, Matter wave, Seismic wave, etc.

2. Electromagnetic Wave: No medium for propagation.
Eg: Light, X-rays, UV ray, etc.

3. Matter Wave: Wave associated with moving particles (microscopic particle).
Eg: Wave of moving electron, proton, etc.

Generation of longitudinal waves by tuning for k
When prongs of tuning fork moves outward, it compresses the surrounding air and a region of increased pressure is formed. This region is called condensation. When the prongs move inward a region of low pressure called rarefraction is formed. Thus condensations and rarefractions are alternately produced.

Expression for progressive wave (Displacement relation)
A plane progressive wave propagating along positive direction of ‘x’ is given by

The wave propagating along negative ‘x’ direction is given by y (x, t) = a sin (kx + ωt + Φ).
y(x, t) gives the transverse displacement of element at position x at time t.

Crust and Trough:
Crust is the point of maximum positive displacement of wave. Trough is the point of maximum negative displacement of wave.

Transverse and Longitudinal Wave
Based on the direction of propogation and vibration wave can be of two types.

Parameters of wave
Amplitude:
The magnitude of maximum displacement of element of the wave from initial position is called amplitude (a).
Phase and initial phase:
The value (kx + ωt + Φ) is called phase and f is the initial phase. The phase gives the state of motion of wave at position ‘x’ and at time V. Initial phase gives initial state of wave.
Wave length (λ):
The linear distance travelled by the wave in one complete oscillation(or vibration). Or it can be defined as distance between two conT secutive crusts or troughs. It is the distance travelled during time period T.
Wave number/Angular wave number/propagation constant:
Wave number ‘k’ is defined as

Its unit is radian/m
Time period (T):
Time for one complete oscillation/vibration is called time period.
Frequency (ν):
The number of oscillations/vibrations in one second is called frequency. Its unit is S^-1 or Hz (Hetz).
ν = \(\frac{1}{T}\)
Angular velocity or angular frequency (ω):
Angular displacement per unit time is called angular velocity or angular frequency.

The speed of travelling wave [Relation connecting V, ν and λ]

The wave propagating along x direction is represented by y = A sin (kx – ωt + Φ). As wave moves, each point on the wave from (like A) retains its displacement. This is possible only if (kx – ωt) is constant. As the wave moves both x and t are changing to keep (kx – ωt) as constant (x increase with t).

The velocity depends on wavelength and frequency. The wavelength and frequency of wave depends on the properties of medium, i.e. velocity of wave in a medium is determined by

• linear mass density
• Elastic properties.

Speed of wave in stretched string (Transverse wave)
The velocity of wave in stretched string depends on

• linear mass density (µ)
• The tension (T)

Speed of sound wave (Longitudinal wave)
The speed of sound in medium depends on

• density of medium (ρ)
• Modulus of elasticity

Case: 1( In solid )
If solid has Young’s modulus ‘Y’

Case: 2( In liquid )
If liquid has Bulk modulus ‘B’

Case: 3 In gas
The speed of sound waves in gas was determined by Newton. According to Newton, condensations and rare fractions are isothermal processes. Hence modulus of elasticity is equal to pressure.

This is called Newton’s formula.
Correction in Newton’s formula.

Question 1.
Find velocity of sound in air using Newton’s formula (P = 1.013 × 10⁵ ρ =1.239 kg m^-3)
Answer:

Note: The velocity of sound at STP is found to be 332 ms^-1
Laplace’s Formula:
Laplace corrected Newton’s formula taking condensation and rare fraction as adiabatic process. The
modulus of elasticity is now ‘γP‘ where γ = \(\frac{C_{p}}{C_{v}}\). C_p is specific heat capacity at constant pressure and C_v is specific heat capacity at constant volume.

The principle of superposition of waves
It states that when two or more waves pass through a media the net displacement of particle at any time is the algebraic sum of displacements due to each wave.

(or)

The overlapping waves algebraically add to produce a resultant wave.

Reflection of waves
Reflection from rigid boundary:
When a travelling wave is reflected by a rigid boundary, phase reversal (phase difference of π or 180°) will take place.

Reflection from open boundary:
When a travelling wave is reflected by an open boundary, no phase change will happen. The incident and reflected wave superimpose to give maximum displacement at boundary.

Standing waves

When two waves of same amplitude and frequency travelling in opposite direction superimpose the resulting wave pattern does not move to either sides. This pattern is called standing wave.
The wave travelling in positive direction of x axis y₁(x, t) = a sin(kx – ωt)
The wave travelling in negative direction of x axis y₂(x, t) = a sin(kx + ωt)
According to superposition Principle, the combined wave is
y(x, t) = y₁(x, t) + y₂(x, t)
y(x, t) = a sin(kx – ωt) + a sin(kx + ωt)
But sin A + sin B = 2 sin \(\frac{(A+B)}{2} \cos \frac{(A-B)}{2}\)
Hence we get,combined wave as

This wave has an amplitude of ‘2asinkx’, and it is not a moving wave.
Nodes & Antinodes:
The position of maximum amplitude in a standing wave is termed as anti node and position of minimum amplitude (zero) is termed as node.
Node: The amplitude of standing wave is ‘2 a sin kx’. It is zero when kx = 0, π, 2π…. etc.
ie kx = nπ.

Antinode:
The amplitude has maximum value 2a when (2a sin kx = 2a)
sinkx = 1;
ie; kx = π/2, 3π/2, 5π/2 …… etc

But k = \(\frac{2 \pi}{\lambda}\)
Hence we get

n = 0, 1, 2, 3 etc.

1. Standing Waves In Stretched String & Modes Of Vibration Of String:
A string of length L is fixed at two ends. The position of one end is chosen as x = 0, then the position of other end will be x = L. At x = 0, there will be node. To occur node at x = L, it must satisfy

The frequency of vibrations of stretched string of length L is

n = 1,2, 3…etc.
This set of frequencies at which the string can vibrate are called natural frequencies or modes of vibration or harmonics. The above equation shows that the modes of vibration (natural frequencies) of string are integral multiple of lowest frequency
n = \(\frac{V}{2 L}\) (for n = 1)
Fundamental mode(or) First harmonics:
For n = 1
ν₁ = \(\frac{V}{2 L}\)
This is the lowest frequency with which string vibrates. This is called fundamental mode or first harmonic of vibration.
Relation between I and L for first harmonics:

The string vibrate in a single segment as shown in figure.

Second harmonic:

For n = 2

Relation between I and L for second harmonics

Third harmonic:

For n = 3, there is 3^rd harmonic. Thus collection of all possible mode is called harmonic series and n is called harmonic number.

2. Vibrational modes of an air column:
(a) In closed tube:
In closed tube one end is closed and other end is open. Air column in a glass tube partially filled with water is an example of closed system. The air column in tube can be set into vibrations with the help of air excited by tuning fork.

The longitudinal waves thus generated is reflected at the closed end and a node is formed there [reflected and incident wave are out of phase and at the closed end, they superimpose to give minimum displacement]. At the open end, the displacement is maximum and antinode is formed. If L is the length of air column, anti node occurs at x = L.
We know the condition for antinode x = (n + 1/2) λ/2
Therefore L = (n + 1/2) λ/2
for n = 0, 1, 2, …….etc.
The wavelength, λ = \(\frac{2 \mathrm{L}}{(\mathrm{n}+1 / 2)}\) _____(1)
for n = 0, 1, 2, …. etc.
The frequency ν = (n + 1/2) \(\frac{V}{2 L}\) ____(2)
for n = 0, 1, 2, …….etc.
From this equation, it is clear that the air column can vibrate with different modes of frequencies (normal modes or harmonics)
Fundamental Mode(or) First harmonic:
We get fundamental mode when n=0 Substitute this in eq(2), we get
ν₁ = \(\frac{V}{4 L}\)
This is the fundamental frequency. The higher frequencies are odd harmonics of fundamental frequency ie;

(b) Open tube:
In open tube, both ends are open. At both ends, antinodes are formed.
The condition to get antinode x = n λ/2

The frequency (fundamental frequency):
We will get fundamental frequency in open tube,when n = 1. Substitute this in eq(4)
ν₁ = \(\frac{V}{2 L}\)
In open pipe all harmonies are generated whereas in closed pipe only odd harmonies are generated.
For n = 2, ν₂ = 2\(\frac{V}{2 L}\). This is second harmonic.
For n = 3, ν₃ = 3\(\frac{V}{2 L}\). This is 3rd harmonic.
ν₂ = 2 ν₁ & ν₃ = 3 .ν₁. Thus both odd and even harmonics are generated.

Beats:
When two sound waves of nearly same frequency and amplitude travelling in same direction super imposed and periodic variation of sound intensity (wavering of sound or waxing and waning of sound) is produced. This is called beats.
Explanation:
If two tuning forks of slightly different frequencies are sounded together, a regular rise and fall of sound can be heard. The sound travels in the form of condensation and rarefactions.

When two condensations due to two notes reach our ear at the same time, they superimpose to get maximum intensity (waxing of sound). If two rarefactions are reached simultaneously, they superimpose to get minimum intensity (waning of sound).

Analytical treatment of beats
Beats frequency
Suppose two sound waves of u₁ and u₂ propagating in the same direction through a medium. For simplicity let the listener be situated at x = 0 and the amplitudes of waves to be equal ie. a₁ = a₂ = a.
The displacements y₁ and y₂ due to each wave are given by
y₁ = a sin2pu₁t and y₁ = a sin2pu₂t
According to super position principle, the resultant displacement at the same time t is
y = y₁ + y₂
= a sin2pu₁t + a sin2pu₂t
y = a [sin2pu₁t + sin2pu₂t]

It is clear that, the amplitude of resultant wave (A) changes with time. It shows maxim and minima.
The resultant amplitude will be maximum, if,

Hence the amplitude of the resultant wave will be maximum at times

Time interval between successive maxima = \(\frac{1}{v_{1}-v_{2}}\)
resultant amplitude will be minimum if

Time internval between two consecutive minima = \(\frac{1}{v_{1}-v_{2}}\)
Frequency of minima = ν₁ – ν₂
Graphical representation of beats

Doppler Effect
The apparent change in the frequency of sound wave due to the relative motion of source or listener or both is called Doppler effect. It was proposed by John Christian Doppler and it was experimentally tested by Buys Ballot.

Considers source is producing sound of frequency n. Let V be the velocity of sound in the medium and I the wavelength of sound when the source and the listener are at rest. The frequency of sound heard by the listener is
ν = \(\frac{v}{\lambda}\)
Let the source and listener be moving with velocities v_s and v_l in the direction of propogation of sound from source to listener. (The direction S to L is taken as positive)
The relative velocity of sound wave with respect to the source = V – V_s.
Apparent wavelength of sound,
λ¹ = \(\frac{V-V_{s}}{v}\) ____(1)
Since the listener is moving with velocity v f, the rela¬tive velocity of sound with respect to the listener,
V¹ = V – V_l _____(2)

Question 2.
A string fixed one end is suddenly brought in to up and down motion.

1. What is the nature of the wane produced in the string and name the wave?
2. A brass wire 1 m long has a mass 6 × 10^-3 kg. If it is kept at a tension 60N, What is the speed of the wave on the wire?

Answer:
1. Transverse wave

2.

Students can Download Chapter 6 Breathing and Exchange of Gases Notes, Plus One Zoology Notes helps you to revise the complete Kerala State Syllabus and score more marks in your examinations.

Kerala Plus One Zoology Notes Chapter 6 Breathing and Exchange of Gases

What is respiration?
The process of exchange of O₂ from the atmosphere with CO₂ produced by the cells is called breathing, commonly known as respiration.

RESPIRATORY ORGANS:

Human Respiratory System:
The nostrils leads to a nasal chamber through the nasal passage. The nasal chamber opens into nasopharynx the common passage for food and air. Nasopharynx opens through glottis of the larynx region into the trachea.

Sound box in respiratory system:
Larynx is a cartilaginous box which helps in sound production called as the sound box. Glottis is covered by a thin elastic cartilaginous flap called epiglottis to prevent the entry of food into the larynx. Trachea is a straight tube which divides into a right and left primary bronchi.

Each bronchi undergoes repeated divisions to form the secondary and tertiary bronchi and bronchioles ending up in very thin terminal bronchioles.
Each terminal bronchiole gives rise to vascularised bag-like structures called alveoli. The branching network of bronchi, bronchioles and alveoli comprise the lungs.

The two lungs which are covered by a double layered pleura, with pleural fluid between them. It reduces friction on the lung surface. The conducting part transports the atmospheric air to the alveoli. Exchange part is the site of diffusion of O₂ and CO₂ between blood and atmospheric air.

Where is lung fitted in human body?
The lungs are situated in the thoracic chamber which is formed dorsally by the vertebral column, ventrally by the sternum, laterally by the ribs and on the lower side by the dome-shaped diaphragm. The anatomical setup of lungs in thorax is the arrangement essential for breathing, directly alterthe pulmonary volume.

Respiration involves the following steps:

• Breathing or pulmonary ventilation by which atmospheric air is drawn in and CO₂ rich alveolar air is released out.
• Diffusion of gases (O₂ and CO₂) across alveolar membrane.
• Transport of gases by the blood.
• Diffusion of O₂ and.CO₂ between blood and tissues.
• Utilisation of O₂ by the cells for catabolic reactions and resultant release of CO₂

MECHANISM OF BREATHING:
Breathing involves two stages:

1. Inspiration during which atmospheric air is drawn in and
2. Expiration by which the alveolar air is released out.

How does increase or decrease of pulmonary volume occur?
Inspiration is initiated by the contraction of diaphragm which increases the volume of thoracic chamber .The contraction of external inter-costal muscles lifts up the ribs and the sternum causing an increase in the volume of the thoracic chamber. It increase the pulmonary volume.

An increase in pulmonary volume decreases the intra-pulmonary pressure to less than the atmospheric pressure which forces the airfrom outside to move into the lungs,i.e., inspiration Relaxation of the diaphragm and the inter-costal muscles returns the diaphragm and sternum to their normal positions and reduce the thoracic volume.

It reduce the pulmonary volume. This leads to an increase in intra-pulmonary pressure to slightly above the atmospheric pressure causing the expulsion of airfrom the lungs, i.e., expiration.

Instrument used for measuring breathing movements:
A healthy human breathes 12 – 16 times/minute. The volume of air involved in breathing movements can be estimated by using a spirometer.

Respiratory Volumes and Capacities:

EXCHANGE OF GASES:
Alveoli are the sites of exchange of gases. O₂ and CO₂ are exchanged in these sites by simple diffusion.
Rate of diffusion:
Solubility of the gases and the thickness of the membranes are the important factors that affect the rate of diffusion.

Partial pressure of gases:
Pressure contributed by an individual gas in a mixture of gases is called partial pressure and is represented as pO₂ for oxygen and pCO₂ for carbon dioxide. As the solubility of CO₂ is 20 – 25 times higher than that of O₂, the amount of CO₂ that can diffuse through the diffusion membrane.

As the solubility of CO₂ is 20 – 25 times higher than that of O₂ the amount of CO₂ that can diffuse through the diffusion membrane.

The diffusion membrane is made up of three major layers such as

Its total thickness is much less than a millimetre.

TRANSPORT OF GASES:
Blood is the medium of transport for 02 and C02.

1. About 97 per cent of O₂ is transported by RBCs in the blood.
2. The remaining 3 per cent of O₂ is carried in a dissolved state through the plasma.
3. Nearly 20 – 25 per cent of CO₂ is transported by RBCs whereas 70 per cent of it is carried as bicarbonate.
4. About 7 per cent of CO₂ is carried in a dissolved state through plasma.

Transport of Oxygen:
O₂ bind with haemoglobin to form oxyhaemoglobin. Each haemoglobin molecule can carry a maximum of four molecules of O₂. Binding of oxygen with haemoglobin is related to partial pressure of O₂.

Oxygen dissociation curve is useful in studying the effect of factors like pCO₂, H⁺ concentration, etc., on binding of O₂ with haemoglobin.

Therefore O₂ gets bound to haemoglobin in the lung surface and gets dissociated at the tissues.

Transport of Carbon dioxide:
CO₂ is carried by haemoglobin as carbamino-haemoglobin (about 20 – 25 per cent). This binding is related to the partial pressure of CO₂. When pCO₂ is high and pO₂ is low as in the tissues, more binding of carbon dioxide occurs whereas, when the PCO₂ is low and pCO₂ is high as in the alveoli, dissociation of CO₂ from carbamino-haemoglobin takes place. RBCs contain a very high concentration of the enzyme, carbonic anhydrase which facilitates the reaction in both directions.

At the tissue site where partial pressure of CO₂ is high due to catabolism, CO₂ diffuses into blood (RBCs and plasma) and forms HCO₂ and H⁺. At the alveolar site where pCO₂ is low, the reaction proceeds in the opposite direction leading to the formation 0f CO₂ and H₂O. Every 100 ml of deoxygenated blood delivers approximately 4 ml of CO₂ to the alveoli.

Students can Download Chapter 13 Kinetic Theory Notes, Plus One Physics Notes helps you to revise the complete Kerala State Syllabus and score more marks in your examinations.

Kerala Plus One Physics Notes Chapter 13 Kinetic Theory

Summary
Introduction
The kinetic theory was developed in the nineteenth century by Maxwell, Boltzmann and other. It gives a molecular interpretation of pressure and temperature of a gas. It also explains gas laws and Avogadro’s hypothesis. It correctly explains specific heat capacities of many gases. It help us to find molecular sizes and masses.

Molecular Nature Of Matter
The scientific atomic theory is credited to John Dalton. Atomic theory is not the end of quest, but the beginning. Atoms consist of a nucleons and electrons. The nucleous itself is made up of protons and neutrons. The protons and neutrons are again made up of quarks. Even quarks may not be the end of the story.

There may be string-like elementary entities. In this chapter we shall limit ourselves to understanding the behavior of gases.

Behavior Of Gases
Gas Laws
1. Boyles law
The law states that at a given temperature, the volume of a given mass of gas varies inversely as its pressure.
It can be written as
\(P a \frac{1}{V}\) (at constant T)
PV = constant
PV = μ RT
μ → No. of moles, R → universal gas constant, T → temperature
Boyles law is not obeyed by gasses at all temperatures and pressure. Usually, Boyles, law is obeyed by gases at high temperature and low pressure (Graph is given below).

A real gas which obey this law is called ideal or perfect gas.

Variation of ‘R’ \(\left(=\frac{\mathrm{PV}}{\mathrm{T}}\right)\) with Pressure (for different temperatures)

Variation of R \(\left(=\frac{\mathrm{PV}}{\mathrm{T}}\right)\) with Pressure for temperature T₁ > T₂ > T₃ is shown in the above graph. The above graph shows that, all real gases approach ideal gas behavior at low pressure and high temperature.

At low pressure or high temperature, the molecules are for apart and molecular interactions are negligible. Without interactions the gas behaves like an ideal gas.

Note:
R = 8.324 J mol^-1 k^-1.
Variation of V with P for different temperature:

The above graph shows experimental PV curves for steam at three temperature The dotted line are the theoretical curves. (According to Boyles law). The theoretical value and experimental value comes in agreement at high temperatures and low pressures.

2. Charles law
Charles law states that the volume of a given mass of gas is proportional to its temperature when its pressure is kept constant.
V a T (P is constant)
i.e.,

The graph between V and T:

The above graph shows experimental T-V curves (solid lines) for Co₂ at three pressures compared with Charles law (dotted lines). T is in unit of 300 k and V in units of 0.13 litres.

Question 1.
Why theoretical value does not agree with experimental value?
Answer:
According to Charles law the graph between T and V is straight line. It means that when temperature decreases, the volume of gas decreases and finally becomes zero.

Practically volume will not be zero. Because the molecules require some finite space to exist. This implies that we cannot reduce its temperature to zero value. A zero kelvin temperature is only an idealized concept.

Dalton’s law of Partial Pressures:
It states that, the total pressure of a mixture of ideal gases is the sum of partial pressures.

Proof:
Consider a mixture of non-interacting ideal gases. μ₁, moles of gas 1, μ₂ moles of gas 2 etc. in a vessel of volume V at temperature T and pressure P. Using Boyles law, we can write
PV = (μ₁ + μ₂ +…………..)RT
P = \(\frac{\mu_{1} \mathrm{RT}}{\mathrm{V}}+\frac{\mu_{2} R T}{V}+\ldots \ldots \ldots\)
P = P₁ + P₂ +……………………

Kinetic Theory Of An Ideal Gas
The kinetic theory of gases has been developed by Clausius, Maxwell, Boltzmann and others. The theory is based on the following postulates.

• The gas is a collection of large number of molecules. The molecules are perfectly elastic hard spheres.
• The size of a molecule is negligible compared with the distance between the molecules.
• The molecules are always in random motion
• During their motion, the molecules collide with each other and with the walls of the containing vessel.
• The collisions are elastic and hence the total K.E energy and the total momentum of the colliding molecules before and after collisions are the same.
• The kinetic energy of a molecule is proportional to the absolute temperature of the gas.
• There is no force of attraction or repulsion between molecules.

The pressure of an ideal gas:

Consider molecules of gas in a container. The molecules are moving in random directions with velocity V. This is the velocity of a molecule in any direction. The velocity V can be resolved along x, y and z directions as V_x, V_y, and V_z respectively.

If we assume a molecule hits the area A of the container with velocity V_x and rebounds back with -V_x. (The velocities V_x and V_y do not change because this collision is perfectly an elastic one).

Therefore, the change in momentum imparted to the area A by the molecule
= mv_x^– – mV_x
= 2mV_x

To find the total number of collisions taking place in a time t, consider the motion of the molecules towards the wall. The molecules covers a distance V_xt along the x direction in a time t. All the molecules within the volume AV_xt will collide with the area in a time t.

If ‘n’ is the number of molecules per unit volume, the total number of molecules hitting the area A,
N = AV_xt n.

But on an average, only half of those molecules will be hitting the area, and the remaining molecules will be moving away from the area. Hence the momentum imported to the area in a time t
Q = 2mv_x × \(\frac{1}{2}\) AV_xtn.
= nmV_x²At
The rate of change of momentum,
\(\frac{Q}{t}\) = nmV_x²A
But rate of change of momentum is called force, ie. force F = nmV_x²A
∴ Pressure P = nmV_x² (P = \(\frac{F}{A}\))
Different molecules move with different velocities. Therefore, the average value V_x² is to be taken. If \(\overline{\mathbf{v}}_{\mathbf{x}}^{2}\) is the average value then the pressure.

\(p=n m \bar{v}_{x}^{2}\) ……………….. (1)

\(\overline{\mathbf{v}}_{\mathbf{x}}^{2}\) is known as the mean square velocity. Since the gas is isotropic (having the same properties in all directions), we can write

Kinetic Interpretation of gas laws:

Question 2.
Derive the ideal gas equation from P = \(\frac{1}{3} \mathrm{nm} \overline{\mathrm{v}}^{2}\)
Answer:
The average kinetic energy of the molecule is
KE = \(\frac{1}{2} m \bar{v}^{2}\) …………………….(3)
The eq (2) can be modified as

The average Kinetic energy of a molecule remains constant when the temperature is constant. That is when the temperature varies, \(\overline{\mathrm{KE}}\) also varies accordingly. The kinetic energy of a molecule is related to its absolute temperature by an equation
\(\overline{\mathrm{KE}}\) = \(\frac{3}{2}\)K_BT
Substitute equation (5) in equation (6); we get

N = μ N₀
P V = μ N₀K_BT
P V = μ R T…………………… (8)
(N_BK_B = R)
This is the ideal gas equation

Deduction of Boyles law:
If the temperature is constant for gas, the eq (8) can be written as
PV = Constant
This is called Boyles law

Deduction of Charles law:
If pressure of a gas is constant, the eq (8) can be written as
V a T

This is called Charles law.

Deduction of Avogadro’s Hypothesis:
If P₁, T₁, and V constant, N₀ will be constant, ie. equal Volumes of all gases, under the same conditions of pressure and temperature will contain the same number of molecules. This is known as Avogadro’s hypothesis.

Law Of Equipartion Of Energy
Degrees of freedom:
Degrees of freedom is number of independent ways by which a molecule can possess kinetic energy of translation, rotation and vibration.

Law of equipartition energy:
The total kinetic energy of a molecule is equally divided among the different degrees of freedom.

K.E. per degree of freedom:
The average energy per degree of freedom

Where K_B is Boltzman constant.

Degrees of freedom and energy of monoatomic gas:
A monoatomic atom has 3 degrees of freedom, ie; it can move in x, y and z-direction. The average energy of single monoatomic gas in the x-direction,

Note:
1. If a molecule is restricted to move in plane. It has 2 degrees of freedom.
2. If a molecule is restricted to move in a line, it has only 1 degrees of freedom.

Degrees of freedom and energy of single diatomic molecule (rigid rotator)

Consider a diatomic molecule as a rigid rotator (Rigid rotator means that the molecule does not vibrate). A rigid diatomic molecule has 3 translation degrees of freedom and 2 rotational degrees of freedom.
(Rotational degrees of freedom is shown in the above figure).
∴ Total average energy of diatomic rigid rotator,

Note:
A diatomic molecule has 3 rotational degrees of freedom. But we consider only 2 degrees of freedom. We neglect rotation along the line joining the atoms. Because it has very small moment of inertia.

Degrees of freedom and energy of single diatomic molecule of nonrigid rotator:
Molecules like ‘co’ even at moderate temperatures have a mode of vibration. The vibration energy of a diatomic molecule.

Where K is the force constant of the oscillator and y the vibrational coordinate. The vibration energy mode contain two terms (1) Kinetic energy (2) Potential energy. Hence a single mode of vibration of molecule is considered as 2 degrees of freedom (potential energy and kinetic energy)
∴ The total vibrational energy of a single-mode
= 2 × \(\frac{1}{2}\)K_BT
= K_BT
∴ The total energy of diatomic nonrigid rotator

Degrees of freedom and energy of polyatomic molecule, (non- rigid rotator):
If a polyatomic molecule has ‘f’ modes of vibration, total number of degrees freedom = 3 vibration + 3 rotator+f vibration.
∴ Total average energy of single polyatomic molecule,

Specific Heat Capacity
Monoatomic Gases (Molar specific heat capacity):
The energy of a single monoatomic gas = 3 × \(\frac{1}{2}\) K_BT
The energy of one mole monoatomic gas = 3 × \(\frac{1}{2}\) K_BT × N_A
[one-mole atom contain Avogadro number (N_A) of atoms]

A Diatomic Gas (Molar specific heat capacity):
A rigid diatomic molecule has 5 degrees of freedom : 3 translational and 2 rotational.
∴ energy of single diatomic (rigid) molecule = 5 × \(\frac{1}{2}\) K_BT
for one mole of diatomic molecule, energy U = 5 × \(\frac{1}{2}\) K_BT × N_A

Nonrigid diatomic molecule having a vibrational mode (Molar specific heat capacity):
If the diatomic molecule is not rigid but has a vibration mode. The energy of one mole,

Polyatomic Gas (Molar specific heat capacity):
In general a polyatomic molecule has 3 translational, 3 rotational degrees of freedom and a certain number (t) of vibrational modes.

The energy of one mole polyatomic gas,

Note: The experimental value of C_P and C_V of polyatomic gases are greater than the predicted values. The theoretical value and experimental value will be equal when we include vibrational modes of motion in the calculation.

Specific heat capacity of solids:
Consider a solid of N atoms. Each atom is vibrating about its mean position. Each vibration mode has two degrees of freedom (corresponding to potential energy and kinetic energy). Hence an oscillation in one dimension has average energy of

2 × \(\frac{1}{2}\) K_BT = K_BT
∴ Total energy in three dimension
= 3 × K_BT
= 3K_BT.

For one mole of solid, total energy,
U = 3K_BT × N_A
[N_A = Avagadro number]
= 3N_AK_BT
U = 3RT …………………. (1) [∴ R = K_BN_A].
We know specific heat capacity,

Note:
In solids, we do not consider the translational and rotational degrees of freedom. We consider only vibrational degrees of freedom.

Specific heat capacity of water:
We treat water like a solid. A water molecule has 3 atoms. Each atom in the molecule is vibrating about its mean position. A single vibration mode has 2 degrees of freedom (1) potential energy (2) kinetic energy.

ie; The energy of one atom in one dimensional vibration mode =
2 × \(\frac{1}{2}\) K_BT = K_BT

The energy of one atom having 3 dimensional vibration mode = 3 × K_BT
The energy of one H₂0 molecule having 3 dimension vibration mode
U = 3 × 3K_BT × N_A
U = 9RT [∵ R = K_B N_A]
∴ Specific heat capacity,
\(\mathrm{c}=\frac{\mathrm{dU}}{\mathrm{dT}}=\frac{\mathrm{d}}{\mathrm{dT}}(\mathrm{RT})\)
C = 9R.

Mean Free Path
Molecules in a gas have large speeds. Yet a gas leaking from a cylinder in a kitchen takes considerable time to diffuse to the other corners of the room. Why?

The molecules in a gas have a finite size. So they collide with other molecules during their motion. As a result, they cannot move straight like path. Their paths are continuously deflected.

Mean free path:
The mean free path is the average distance covered by a molecule between two successive collisions.

Expression for mean free path:

Suppose the molecules of a gas are spheres with diameterd. Let 〈v〉 be the average velocity of the molecule.
The volume covered by a molecule during its motion, in a time Δt = πd² 〈v〉 Δt.
If ‘n’ is the number of molecules per unit volume, the total number of molecules in the above volume
= πd² 〈v〉 Δt n.
The number collisions in a time Dt,
= πd² 〈v〉 Δt n.
Number of collisions in one second,
= n π d² 〈v〉
∴ The time between two successive collisions,
\(\tau=\frac{1}{n \pi d^{2}\langle v\rangle}\).
The average distance between two successive collisions,

In this derivation, we imagined the other molecules to be rest. But actually all other molecules are moving. Hence we must take relative velocity 〈v_r〉 instead of 〈v〉. A more exact treatment gives
\(\ell=\frac{1}{\sqrt{2} \mathrm{n} \pi \mathrm{d}^{2}} \dots(1)\)
The mean free path given by the above equation depends inversely on the number density and the size of the molecule.

Students can Download Chapter 5 Digestion and Absorption Notes, Plus One Zoology Notes helps you to revise the complete Kerala State Syllabus and score more marks in your examinations.

Kerala Plus One Zoology Notes Chapter 5 Digestion and Absorption

What is digestion?
This process of conversion of complex food substances to simple absorbable forms is called digestion.

DIGESTIVE SYSTEM:
It includes

• Alimentary canal
• Associated glands.

Alimentary canal:

The human digestive system
1. The alimentary canal begins with the mouth, and it leadsto the buccal cavity or oral cavity.

2. The oral cavity has a number of teeth and a musculartongue. Each tooth is embedded in a socket of jaw bone. This type of attachment is called thecodont.

3. Human being forms two sets of teeth during their life, a set of temporary milk or deciduous teeth replaced by a set of permanent or adult teeth. This type of dentition is called diphyodont.

Dental formula of adult human
An adult human has 32 permanent teeth which are of four different types (Heterodont dentition).

• incisors (I)
• canine (C)
• premolars (PM)
• molars (M).

Arrangement of teeth in each half of the upper and lower jaw in the order I, C, PM, M is represented by a dental formula which in human is
\(\frac{2123}{2123}\)

• The hardest part of teeth is made up of enamel, helps in the mastication oWood.
• The tongue is attached to the floor of the oral cavity by the frenulum.
• The upper surface of the tongue has small projections called papillae, some of which bear taste buds.
• The oral cavity leads pharynx which serves as a common passage for food and air.
• The oesophagus and the trachea (wind pipe) open into the pharynx.
• A cartilaginous flap called epiglottis prevents the entry of food into the glottis – opening of the wind pipe – during swallowing.
• The oesophagus is a thin, long tube which passing through the neck, thorax and diaphragm and leads to a ‘J’ shaped bag like structure called stomach.
• A muscular sphincter (gastro-oesophageal) regulates the opening of oesophagus into the stomach.

The stomach, located in the upper left portion of The abdominal cavity, has three major parts:

1. A cardiac portion into which the oesophagus opens
2. A fundic region and
3. A pyloric portion which opens into the first part of small intestine

Small intestine is distinguishable into three regions:

1. A ‘U’ shaped duodenum
2. A long coiled middle portion jejunum and
3. A highly coiled ileum

The opening of the stomach into the duodenum is guarded by the pyloric A sphincter. Ileum opens into the large intestine.

Large intestine:
It consists of

• caecum
• colon
• rectum.

Caecum:
It is a small blind sac consists of some symbiotic micro-organisms. A narrow finger-like tubular projection, the vermiform appendix which is a vestigial organ, arises from the caecum. The caecum opens into the colon.

colon:
It is divided into three parts-an ascending, a transverse and a descending part. The descending part opens into the Rectum.

Rectum: It opens out through the anus.
Wall layers of alimentary canal:
It consists of four layers namely

1. Serosa
2. muscularis
3. sub-mucosa &
4. mucosa.

1. Serosa is the outermost layer and is made up of a thin mesothelium with some connective tissues.
2. Muscularis is formed by smooth muscles
3. The submucosal layer is formed of loose connective tissues containing nerves, blood and lymph vessels.
4. The innermost layer lining of the alimentary canal is the mucosa.
   • In duodenum, glands are also present in sub-mucosa.
   • Mucosa forms irregular folds (rugae) in the stomach and small finger-like foldings called villi in the small intestine
   • The cells lining the villi produce numerous projections called microvilli giving a brush border appearance.
   • These modifications increase the surface area.
   • Villi are supplied with a network of capillaries and a large lymph vessel called the lacteal.
   • Mucosal epithelium has goblet cells which secrete mucus that help in lubrication.
   • Mucosa also forms glands in the stomach (gastric glands) and crypts in between the bases of villi in the intestine (crypts of Lieberkuhn).

Digestive Glands:
It includes

1. salivary glands
2. liver
3. pancreas.

1. Salivary glands:
Saliva is mainly produced by three pairs of salivary glands

• parotids (cheek)
• sub-maxillary/sub-mandibular (lower jaw)
• sublinguals (belowthe tongue).

The duct systems of liver, gall bladder and pancreas These glands situated just outside the buccal cavity secrete salivary juice into the buccal cavity.

2. Liver:

• It is the largest gland of the body weighing about 1.2 to 1.5 kg in an adult human.
• It is situated in the abdominal cavity, just below the diaphragm and has two lobes.
• The hepatic lobules are the structural andfunctional units of liver containing hepatic cells arranged in the form of cords.
• Each lobule is covered by a thin connective tissue sheath called the Glisson’s capsule.
• The bile secreted by the hepatic cells passes through the hepatic ducts and is stored in gall bladder.
• The duct of gall bladder (cystic duct) along with the hepatic duct from the liver forms the common bile. duct
• The bile duct and the pancreatic duct open together into the duodenum which is guarded by sphincter of Oddi.

3. Pancreas:
It is a heterocrine (both exocrine and endocrine) elongated organ situated between the limbs of the ‘U’ shaped duodenum.

Secretions of exocrine and endocrine:

• The exocrine portion secretes an alkaline pancreatic juice containing enzymes
• The endocrine portion secretes hormones, insulin and glucagons.

DIGESTION OF FOOD:

1. The process of digestion is accomplished by mechanical and chemical processes.
2. The teeth and the tongue with the help of saliva masticate and mix up the food thoroughly. *Mucus in saliva helps in lubricating and adhering the masticated food particles into a bolus.

Contents of saliva:
It contains electrolytes (Na⁺, K+⁺, Cl^–, HCO^–“) and enzymes, salivary amylase and lysozyme.
The chemical process of digestion is initiated in the oral cavity by the carbohydrate splitting enzyme, the salivary amylase( pH 6.8).

Digestion of starch:
About 30 percent of starch is hydrolysed here by salivary amylase (optimum pH 6.8) into a disaccharide -maltose.

Enzyme for preventing infections:
Lysozyme present in saliva acts as an antibacterial agent that prevents infections.

• The bolus is then passed into the pharynx and then into the oesophagus by swallowing or deglutition.
• The bolus further passes down through the oesophagus by successive waves of muscular contractions called peristalsis.
• The gastro-oesophageal sphincter controls the passage of food into the stomach.

Mucosa of stomach and gastric glands:
Gastric glands have three major types of cells namely

Digestion in stomach:
1. The food mixes thoroughly with the acidic gastric juice of the stomach by the churning movements of its muscular wall and is called the chyme.

2. The proenzyme pepsinogen, in the presence hydrochloric acid gets converted into the active enzyme pepsin, the proteolytic enzyme of the stomach.

3. Pepsin converts proteins into proteoses and peptones (peptides).

4. The mucus and bicarbonates play an important role in lubrication and protection of the mucosal epithelium from concentrated hydrochloric acid- pH (pH 1.8).

Special type of proteolytic enzyme in infants:
Rennin is a proteolytic enzyme found in gastric juice of infants which helps in the digestion of milk proteins. The bile, pancreatic juice and the intestinal juice are the secretions released into the, small intestine.

Pancreatic juice:
It contains inactive enzymes

Trypsinogen is activated by an enzyme, enterokinase, secreted by the intestinal mucosa into aqtive trypsin.

Contents of Bile and functions:
The bile released into the duodenum contains bile pigments (bilirubin and bili-verdin), bile salts, cholesterol and phospholipids but no enzymes Bile helps in emulsification of fats, i.e., breaking down of the fats into very smalfmicelles.

Bile also activates lipases. The intestinal mucosal epithelium has goblet cells which secrete mucus. The secretions of the brush border cells of the mucosa alongwith the mucus constitute the intestinal juice or succu sentericus.

Intestinal juice/succus entericus:
It contains enzymes like

1. disaccharidases (eg: maltase)
2. dipeptidases
3. lipases,
4. nucleosidases etc.

How does the intestine protect itself from digestion?
1. The mucus alongwith the bicarbonates from the pancreas protects the intestinal mucosa from acid as well as provide an alkaline medium (pH 7.8) for enzymatic activities.

2. Sub-mucosal glands (Brunner’s glands) also help in this.

The breakdown of biomacromolecules occurs in the duodenum region of the small intestine. The simple substances thus formed are absorbed in the jejunum and ileum regions of the small intestine. The undigested and unabsorbed substances are passed on to the large intestine.

Functions of large intestine:

1. Absorption of some water, minerals and certain drugs
2. Secretion of mucus which helps in adhering the waste (undigested) particles together and lubricating it for an easy passage.

The undigested, unabsorbed substances called faeces enters into the caecum of the large intestine through ileo-caecal valve, which prevents the back flow of the faecal matter. It is temporarily stored in the rectum till defaecation.

• The sight, smell and the presence of food in the oral cavity can stimulate the secretion of saliva.
• Gastric and intestinal secretions are also stimulated by neural signals.
• The muscular activities of different parts of the alimentary canal controlled by neural mechanisms, both local and through CNS.

ABSORPTION OF DIGESTED PRODUCTS:

1. The end products of digestion passthrough the intestinal mucosa into the blood or lymph.
2. It is carried out by passive, active or facilitated transport mechanisms.
3. Small amounts of monosacharides like glucose, amino acids and some of electrolytes like chloride ions are generally absorbed by simple diffusion.
4. Fructose and some amino acids are absorbed with the help of the carrier ions like Na⁺. This mechanism is called the facilitated transport.
5. Transport of water depends upon the osmotic gradient.
6. Various nutrients like amino acids, monosacharides like glucose,electrolytes like Na⁺ are absorbed into the blood by active transport and hence requires energy.

How does fat absorption occur?
Fatty acids and glycerol being insoluble, cannot be absorbed into the blood. They are first incorporated into small droplets called micelles which move into the intestinal mucosa. Then, the fat globules are coated with small protein called as chylomicrons which are transported into the lymph vessels (lacteals) in the villi.

These lymph vessels ultimately release the absorbed substances into the blood stream. The maximum absorption occurs in the small intestine. The absorbed substances finally reach the tissues which utilise them for their activities. This process is called assimilation.

The digestive wastes, solidified into faeces in the rectum initiate a neural reflex causing an urge for its removal. The egestion of faeces to the outside through the anal opening (defaecation) is a voluntary process and is carried out by a mass peristaltic movement.

DISORDERS OF DIGESTIVE SYSTEM:
Jaundice:
The liver is affected, skin and eyes turn yellow due to the deposit of bile pigments.

Vomiting:
It is the ejection of stomach contents through the mouth. This reflex action is controlled by the vomit centre in the medulla. „

Diarrhoea:
The abnormal frequency of bowel movement and increased liquidity of the faecal discharge is known as diarrhoea. It reduces the absorption of food.

Constipation:
In constipation, the faeces are retained within the rectum as the bowel movements occur irregularly. ‘

Indigestion:
In this condition, the food is not properly digested leading to a feeling of fullness. The causes are inadequate enzyme secretion, anxiety, food poisoning, overeating, and spicy food.

NCERT SUPPLEMENTARY SYLLABUS
Calorific value of carbohydrate, protein and fat:
Carbohydrates, proteins and fats are chief sources of energy in humans. These are oxidized and released energy stored in ATP, it is used for many activities of the cell.

calorific value kcal = 4.184kJ):
It is defined as the amount of heat produced in calories (cal) or in joules (J) from complete combustion of 1 gram food in a bomb calorimeter (a closed metal chamber filled with 02). One kilocalorie is the amount of heat energy needed to raise the temperature of one kilogram of water through 100C(1.80F).

The calorific values of carbohydrates, proteins and fats are 4.1 kcal /g, 5.65 kcal /g and 9.45 kcal/g, respectively. The actual amounts of energy liberated in the body by these nutrients referred to as the physiologic value of the food, and are 4.0 kcal /g, 4.0 kcal Ig and 9.0 kcal /g respectively.

DEFICIENCY DISEASES:
The low amount of nutrients (Vitamin A, iron and iodine) in the diet cause deficiency disorders The important among them is protein energy malnutrition (PEM). lt is major health and nutritional problems in India.

Young children (0-6 years) require more protein for each kilogram of body weight than adults. So they are more vulnerable to malnutrition. Malnutrition leads to permanent impairment of physical and mental growth and childhood mortality and morbidity. The details of the disorders are given below.

The child suffering from PEM can recover if adequate quantities of protein and carbohydrate rich food are given.

Students can Download Chapter 3 Structural Organisation in Animals Notes, Plus One Zoology Notes helps you to revise the complete Kerala State Syllabus and score more marks in your examinations.

Kerala Plus One Zoology Notes Chapter 3 Structural Organisation in Animals

What is a tissue?
In multicellular animals, a group of similar cells along with intercellular substances perform a specific function. Such an organization is called tissue.

ANIMAL TISSUES:
The tissues are different and are broadly classified into four types:

• Epithelial
• Connective
• Muscularand
• Neural.

Epithelial Tissue:
This tissues are found in the covering ora lining for some part of the body. The cells are compactly packed with little intercellular matrix.
There are two types of epithelial tissues namely:

1. SIMPLE EPITHELIUM
2. COMPOUND EPITHELIUM

1. Simple epithelium:

• Squamous
• Cuboidai
• Columnar

1. Squamous epithelium:
It forms single thin layer of flattened cells with irregular boundaries. They are found in the walls of blood vessels and air sacs of lungs and are involved in a functions like forming a diffusion boundary.

2. Cuboidai epithelium:
It is composed of a single layer of cube-like cells. This is commonly found in ducts of glands and tubular parts of nephrons in kidneys. Its main functions are secretion and absorption.

3. Columnar epithelium:
It is composed of a single layer of tall and slende cells. Their nuclei are located at the base. Free surface may have microvilli. They are found in the lining of stomach and intestine and help in secretion and absorption.

Ciliated epithelium:
If the columnar or cuboidai cells bear cilia on their free surface they are called ciliated epithelium Their function is to move particles or mucus in a specific direction overthe epithelium. They are present in bronchioles and fallopian tubes.

Glandular epithelium:
The modified columnar or cuboidal cells perform secretion and are called glandular epithelium.
They are mainly of two types:

• Unicellular (goblet cells of the alimentary canal)
• Multicellular(salivary gland).

On the basis of the mode of pouring of their secretions, glands are divided into two categories namely exocrine and endocrine glands.
Exocrine glands:
They secrete mucus, saliva, earwax, oil, milk, digestive enzymes and other cell products. These products are released through ducts or tubes.

Endocrine glands:
They do not have ducts. Their products called hormones are secreted directly into the blood.

2. Compound epithelium:
It is multi-layered of cells.
a. Their main function is to provide protection against chemical and mechanical stresses.

b. They cover the dry surface of the skin, the moist surface of buccal cavity, pharynx, inner lining of ducts of salivary glands and of pancreatic ducts.

Three types of cell junctions are found in the epithelium and other tissues. These are called as tight, adhering and gap junctions.

1. Tight junctions help to stop substances from leaking across a tissue.
2. Adhering junctions perform cementing to keep neighbouring cells together.
3. Gap junctions facilitate the cells to communicate with each other by connecting the cytoplasm of adjoining cells for rapid transfer of ions and molecules.

Connective Tissue:
Connective tissues helps to linking and supporting othertissues/organs of the body. They include

• cartilage
• bone
• adipose
• blood.

Collagen or elastin:
In all connective tissues except blood, the cells secrete fibres of structural proteins called collagen or elastin.
The fibres provide strength, elasticity and flexibility to the tissue.
These cells also secrete modified polysaccharides, which accumulate between cells and fibres and act as matrix (ground substance).
Connective tissues are classified into three types:

• Loose connective tissue
• Dense connective tissue and
• Specialised connective tissue

Loose connective tissue:
They are loosely arranged in a semi-fluid ground substance. For example,
Areolar tissue:
It is present beneath the skin. It contains fibroblasts (cells that produce and secrete fibres),macrophages and mast cells.

Adipose tissue:
It is the loose connective tissue located mainly beneath the skin. The cells of this tissue are specialised to store fats.

Dense connective tissues.
In this Fibres and fibroblasts are compactly packed and are called dense regular and dense irregular tissues. In the dense regular connective tissues, the collagen fibres are present injows between bundles of fibres.
eg:

• Tendons, which attach skeletal muscles to bones
• ligaments which attach one bone to another.

Dense irregular connective tissue has fibroblasts and many fibres (mostly collagen) that are present in the skin.

Specialized connective tissues: They are Cartilage, bones and blood.

Cartilage:
Cells of this tissue (chondrocytes) are enclosed in small cavities within the matrix. Most of the cartilages in vertebrate embryos are replaced by bones in adults. Cartilage is present in the tip of nose, outer ear joints, between adjacent bones of the vertebral column, limbs and hands in adults.

Bones:
They have a hard ground substance rich in calcium salts and collagen fibres which give bone its strength. Bones support and protect softer tissues and organs. The bone cells (osteocytes) are present in the spaces called lacunae.

Limb bones, such as the long bones of the legs, serve weight-bearing functions. They also interact with skeletal muscles attached to them to bring about movements. The bone marrow in some bones is the site of production of blood cells.

Blood:
It is a fluid connective tissue containing plasma, red blood cells (RBC), white blood cells (WBC) and platelets. It also helps in the transport of various substances.

Muscle Tissue:
It consists of long, cylindrical fibres arranged in parallel arrays. These fibres are composed of numerous fine fibrils, called myofibrils. Muscle fibres contract (shorten) in response to stimulation, then relax (lengthen) and in their uncontracted state. Muscles play an active role in all the movements of the body Muscles are of three types, skeletal, smooth, and cardiac.
1. Skeletal muscle:
It is the tissue is closely attached to skeletal bones. In a typical muscle such as the biceps, striated (striped) skeletal muscle fibres are bundled together in a parallel fashion.

2. Smooth muscle:
These fibres taper at both ends (fusiform) and do not show striations. The wall of internal organs such as the blood vessels, stomach and intestine contains this type of muscle tissue. Smooth muscles are ‘involuntary’ as their functioning cannot be directly controlled.

3. Cardiac muscle tissue:
It is a contractile tissue present only in the heart. Cell junctions fuse the plasma membranes of cardiac muscle cells and make them stick together In Communication when one cell receives a signal to contract, its neighbours are also stimulated to contract.

Neural Tissue:
Neurons, the unit of neural system are excitable cells The neuroglial cell which constitute the rest of the neural system protect and support neurons. Neuroglia make up more than one half the volume of neural tissue in our body.

Nerve impulse transmisssion:
When a neuron is suitably stimulated, an electrical disturbance is generated which swiftly travels along its plasma membrane and reaches at the neuron’s endings, or output zone, triggers events that may cause stimulation or inhibition of adjacent neurons and other cells.

ORGAN AND ORGAN SYSTEM:
Each organ in our body is made of one or more type of tissues. For example, our heart consists of all the four types of tissues, i.e., epithelial, connective, muscular and neural. In animals morphology refers to the external appearance of the organs or parts of the body.

EARTHWORM:
Earthworm is a reddish brown terrestrial invertebrate The common Indian earthworms are Pheretima and Lumbricus.

Morphology:
They have long cylindrical body.lt is divided into more than hundred short segments which are similar. The dorsal surface of the body is marked by a dark median mid dorsal line (dorsal blood vessel). The ventral surface is distinguished by the presence of genital openings (pores).

Anterior end consists of the mouth and the prostomium, a lobe which serves as a covering for the mouth . The prostomium is sensory in function. The first body segment is called the peristomium (buccal segment) which conjoins the mouth.

In a mature worm, segments 14-16 are covered by a prominent dark band of glandular tissue called clitellum. Thus the body is divisible into three prominent regions.

• preclitellar
• clitellar &
• postclitellar segments

Four pairs of spermathecal apertures are situated 5^th – 9^th segments. A single female genital pore is present in the mid-ventral line of 14^th segment. A pair of male genital pores are present on 18th segment.

Numerous minute pores called nephridiopores open on the surface of the body. In each body segment, except the first, last and clitellum, there are rows of S-shaped setae, Setae plays an important role is in locomotion.

Anatomy:
The body wall of the earthworm is covered externally by a thin non-cellular cuticle below which is the epidermis, two muscle layers and an innermost coelomic epithelium. The epidermis is made up of a single layer of columnar epithelial cells which contain secretory gland cells. A terminal mouth opens into the

1. buccal cavity (1 – 3 segments) which leads into muscular pharynx.
2. Oesophagus (5 – 7 segments), continues into a muscular gizzard (8 – 9 segments).

It helps in grinding the soil particles and decaying leaves etc. The stomach extends from 9 – 14 segments. The food of the earthworm is decaying leaves and organic matter mixed with soil. Calciferous glands, present in the stomach, neutralise the humic acid present in humus.

Intestine starts from the 15^th segment onwards and continues till the last segment. A pair of short and conical intestinal caecae project from the intestine on the 26^th segment. The characteristic feature of the intestine between 26 – 35 segments is the presence of internal median fold of dorsal wall called typhlosole.

This increases theeffective area of absorption in the intestine. The alimentary canal opens to the exterior by a small rounded aperture called anus. These simpler molecules are absorbed through intestinal membranes and are utilised. Pheretima shows closed type of blood vascular system, consisting of blood vessels, capillaries and heart.

Blood glands are present on the 4^th, 5^th and 6^th segments. They produce blood cells and haemoglobin which is dissolved in blood plasma. Blood cells are phagocytic in nature.

In Earthworms respiratory exchange occurs through moist body surface into their blood stream. The excretory organs occur as segmentally arranged coiled tubules called nephridia They are of three types:

• septal nephridia, present on both the sides of intersegmental septa of segment 15 to the last that open into intestine,
• integumentary nephridia, attached to lining of the body wall of segment 3 to the last that open on the body surface and
• pharyngeal nephridia, present as three paired tufts in the 4^th, 5^th and 6^th segments

Nephridia:
It regulate the volume and composition of the body fluids. A nephridium starts out as a funnel that collects excess fluid from coelomic chamber. The funnel connects with a tubular part of the nephridium which delivers the wastes.

Nervous system:
It is represented by ganglia arranged segment wise on the ventral paired nerve cord (3^rd and 4^th segments). The cerebral ganglia along with other nerves in the ring integrate sensory input as well as command muscular responses of the body.

Sensory system does not have eyes but does possess light and touch sensitive organs to distinguish the light intensities and to fee the vibrations in the ground. Worms have specialised chemoreceptors (taste receptors) which react to chemical stimuli. Earthworm is hermaphrodite (bisexual), i.e., testes and ovaries are present in the same individual.

There are two pairs of testes present in the 10^th and 11^th segments. Their vasa deferentia run up to the 18^th segment where they join the prostatic duct. Two pairs of accessory glands are present one pair each in the 17^th and 19^th segments. The common prostrate and spermatic duct opens to the exterior by a pair of male genital pores on the ventro-lateral side of the 18^th segment.

Four pairs of spermathecae are located in 6^th – 9^th segments (one pair in each segment).They receive and store spermatozoa during copulation. One pair of ovaries is attached at the 12^th and 13^th segments. Ovarian funnels are present beneath the ovaries which continue into oviduct, join together and open on the ventral side as a single median female genital pore on the 14^th segment.

A mutual exchange of sperm occurs between two worms during mating. Mature sperm and egg cells and nutritive fluid are deposited in cocoons produced by the gland cells of clitellum.

Fertilisation:
Fertilisation and development occur within the cocoons which are deposited in soil. The ova (eggs) are fertilised by the sperm cells within the cocoon. The cocoon holds the worm embryos. After about 3 weeks, each cocoon produces two to twenty baby worms. Earthworms development is direct, i.e., there is no larva formed.

Earthworms are known as ‘friends of farmers’ because they make burrows in the soil and make it porous which helps in respiration and penetration of the developing plant roots. The process of increasing fertility of soil by the earthworms is called vermicomposting. They are also used as bait in game fishing

COCKROACH:
Cockroaches are are included in class Insecta of Phylum Arthropoda. They are nocturnal omnivores that live in damp places throughout the world. They are found in human homes and thus are serious pests and vectors of several diseases.

Morphology:
The adults of the common species of cockroach, Periplaneta americana are about 34 – 53 mm long with wings that extend beyond the tip of the abdomen in males. The body of the cockroach is segmented and divisible into three distinct regions – head, thorax and abdomen. The body is covered by a hard chitinous exoskeleton.

Exoskeleton has hardened plates called sclerites that are joined to each other by a thin and flexible articular membrane (arthrodial membrane). Head is formed by the fusion of six segments and shows great mobility in all directions due to flexible neck It has compound eyes. A pair of antennae arise from sockets lying in front of eyes. They help in monitoring the environment.

Anterior end of the head bears appendages forming biting and chewing type of mouth parts. It consists of a labrum (upper lip), pair of mandibles, a pair of maxillae and a labium (lower lip). A median flexible lobe, acting as tongue (hypopharynx), lies within the cavity enclosed by the outhparts.
Thorax consists of three parts:

1. prothorax
2. mesothorax
3. metathorax.

Each thoracic segment bears a pair of walking legs. The first pair of wings arises from mesothorax and the second pair from metathorax. Forewings (mesothoracic) called tegmina are opaque dark and leathery and cover the hind wings when at rest. The hind wings are transparent, membranous and are used in flight.

The abdomen in both males and females consists of 10 segments. In females, the 7^th sternum is boat shaped and together with the 8^th and 9^th sterna forms a genital pouch whose anterior part contains female gonopore, spermathecal pores and collateral glands.

In males, genital pouch lies at the hind end of abdomen bounded dorsally by 9^th and 10^th terga and ventrally by the 9^th sternum. It contains dorsal anus, ventral male genital pore and gonapophysis. Males bear a pair of short, threadlike anal styles which are absent in females. In both sexes, the 10^th segment bears a pair of jointed filamentous structures called anal cerci.

Anatomy:
The alimentary canal is divided into three regions: foregut, midgut and hindgut The mouth opens into a short tubular pharynx, leading to a narrow tubular passage called oesophagus.

Oesophagus opens into a sac like structure called crop used for storing of food. The crop is followed by gizzard or proventriculus. Gizzard helps in grinding the food particles. A ring of 6 – 8 blind tubules called hepatic or gastric caecae is present at the junction of foregut and midgut, which secrete digestive juice.

At the junction of midgut and hindgut is present another ring of 100 – 150 yellow coloured thin filamentous Malphigian tubules. They help in removal of excretory products from haemolymph. The hindgut is differentiated into ileum, colon and rectum. The rectum opens out through anus.

Blood vascular system of cockroach is an open type Blood vessels are open into space (haemocoel). Visceral organs located in the haemocoel are bathed in blood (haemolymph).The haemolymph is composed of colourless plasma and haemocytes.

Heart of cockroach consists of elongated muscular tube lying along mid dorsal line of thorax and abdomen. Blood from sinuses enter heart through ostia and is pumped anteriorly to sinuses again. The respiratory system consists of a network of trachea, that open through 10 pairs of small holes called spiracles present on the lateral side of the body.

Thin branching tubes carry oxygen from the airto all the parts. Exchange of gases take place at the tracheoles by diffusion. During excretion Malpighian tubules absorb nitrogenous waste products and convert them into uric acid which is excreted out through the hindgut. Therefore, this insect is called uricotelic.

In addition, the fat body, nephrocytes and urecose glands also help in excretion. The nervous system of cockroach consists of segmentally arranged ganglia joined by paired longitudinal connectives. Three ganglia lie in the thorax, and six in the abdomen.


The nervous system of cockroach is spread throughout the body. If the head of a cockroach is cut off, it will still live for as long as one week. In the head region, the brain is represented by supra-oesophageal ganglion which supplies nerves to antennae and compound eyes. In cockroach, the sense organs are antennae, eyes, maxillary palps, larfial palps, anal cerci, etc.

Compound eves of cockroach:
The compound eyes are situated at the dorsal surface of the head. Each eye consists of about 2000 hexagonal ommatidia. With the help of several ommatidia, a cockroach can receive several images of an object. This kind of vision is known as mosaic vision with more sensitivity but less resolution, being common during night (hence called nocturnal vision).

Cockroaches are dioecious Male reproductive system consists of a pair of testes lying one on each lateral side in the 4^th – 6^th abdominal segments. From each testis arises a thin vas deferens, which opens into ejaculatory duct through seminal vesicle. The ejaculatory duct opens into male gonopore situated ventral to anus.

A characteristic mushroom shaped gland is present in the 6^th – 7^th abdominal segments which functions as an accessory reproductive gland. The external genitalia are represented by male gonapophysis or phallomere The sperms are stored in the seminal vesicles and are glued together in the form of bundles called spermatophores which are discharged during copulation.

The female reproductive sysytem consists of two large ovaries, lying laterally in the 2^nd – 6^th abdominal segments. Each ovary is formed of a group of eight ovarian tubules or ovarioles, containing a chain of developing ova. Oviducts of each ovary unite into a single median oviduct (also called vagina) which opens into the genital chamber.

Sperms are transferred through spermatophores. Their fertilised eggs are stored in capsules called oothecae. On an average, females produce 9 – 10 oothecae, each containing 14 – 16 eggs. The development of P. Americana is paurometabolous, meaning there is development through nymphal stage.

The nymph grows by moulting about 13 times to reach the adult form. The next to last nymphal stage haswing pads but only adult cockroaches have wings.

FROGS:
Frogs are belong to class Amphibia of phylum Chordata. The most common species of frog found in India is Rana tigrina. Their body temperature varies with the temperature of the environment. Such animals are called cold blooded or poikilotherms They have the ability to change the colour to hide them from their enemies (camouflage).

This protective coloration is called mimicry. During peak summer and winterthey take shelter in deep burrows to protect them from extreme heat and cold. This is called as summer sleep (aestivation) and wintersleep (hibernation).

Morphology:
The skin is maintained in a moist condition. The frog never drinks water but absorb it through the skin. Body of a frog is divisible into head and trunk. A neck and tail are absent. Above the mouth, a pair of nostrils is present. Eyes are bulged and covered by a nictitating membrane that protects them while in water.

On either side of eyes a membranous tympanum (ear) receives sound signals. The forelimbs and hind limbs help in swimming, walking, leaping and burrowing. The hind limbs end in five digits and they are larger and muscular than fore limbs that end in four digits.

Feet have webbed digits that help in swimming. Frogs exhibit sexual dimorphism. Male frogs can be distinguished by the presence of sound producing vocal sacs and also a copulatory pad on the first digit of the fore limbs which are absent in female frogs.

Anatomy:
The body cavity consists of organ systems such as digestive, circulatory, respiratory, nervous, excretory and reproductive systems. The digestive system consists of alimentary canal and digestive glands. The alimentary canal is short because frogs are carnivores and hence the length of intestine is reduced.

The mouth opens into the buccal cavity that leads to the oesophagus through pharynx. Oesophagus is a short tube that opens into the stomach which in turn continues as the intestine,rectum and finally opens outside by the cloaca. Liver secretes bile that is stored in the gall bladder. Pancreas, a digestive gland produces pancreatic juice containing digestive enzymes.

Digestion of food takes place by the action of HCI and gastric juices secreted from the walls of the stomach. Partiailv digested food called chyme is passed from stomach to the first part of the intestine, the duodenum. The duodenum receives bile from gall bladder and pancreaticjuicesfrom the pancreas through a common bile duct.

Bile emulsifies fat and pancreatic juices digest carbohydrates and proteins. Final digestion takes place in the intestine. Digested food is absorbed by the numerous finger-like folds in the inner wall of intestine called villi and microvilli. The undigested solid waste moves into the rectum and passes out through cloaca.

In water, skin acts as aquatic respiratory organ (cutaneous respiration). Dissolved oxygen in the water is exchanged through the skin by diffusion. On land, the buccal cavity, skin and lungs act as the respiratory organs. The respiration by lungs is called pulmonary respiration.

The lungs are a pair of elongated, pink coloured sac- like structures present in the upper part of the trunk region (thorax). Air enters through the nostrils into the buccal cavity and then to lungs. During aestivation and hibernation gaseous exchange takes place through skin. The blood vascular system involves heart, blood vessels and blood.

The lymphatic system consists of lymph, lymph channels and lymph nodes. Heart is a muscular structure situated in the upper part of the body cavity. It has three chambers, two atria and one ventricle and is covered by a membrane called pericardium. Atriangularstructure called sinus venosus joins the right atrium.

It receives blood through the major veins called vena cava. The ventricle opens into a saclike conus arteriosus on the ventral side of the heart. The blood from the heart is carried to all parts of the body by the arteries (arterial system).The veins collect blood from different parts of body to the heart and form the venous system.

Special venous connection between liver and intestine as well as the kidney and lower parts of the body are present in frogs. The former is called hepatic portal system and the latter is called renal portal system.

The blood is composed of plasma and cells. The blood cells are RBC (red blood cells) or erythrocytes, WBC (white blood cells) or leucocytes and platelets. RBC’s are nucleated and contain red coloured pigment namely haemoglobin. The lymph is different from blood. It lacks few proteins and RBCs.

The excretory system consists of a pair of kidneys, ureters, cloaca and urinary bladder. Each kidney is composed of several structural and functional units called uriniferous tubules or nephrons. Two ureters emerge from the kidneys in the male frogs. The ureters act as urinogenital duct which opens into the cloaca.

In females the ureters and oviduct open seperately in the cloaca. The thin-walled urinary bladder is present ventral to the rectum which also opens in the cloaca. The frog excretes urea and thus is a ureotelic animal.

The chemical coordination of various organs of the body is achieved by hormones which are secreted by the endocrine glands. The endocrine glands found in frog are pituitary, thyroid, parathyroid, thymus, pineal body, pancreatic islets, adrenals and gonads.

The nervous system is organized into a central nervous system (brain and spinal cord), a peripheral nervous system (cranial and spinal nerves) and an autonomic nervous system (sympathetic and parasympathetic). There are ten pairs of cranial nerves arising from the brain. Brain is enclosed in a bony structure called brain box(cranium).

The brain is divided into fore-brain, mid-brain and hind-brain. Forebrain includes olfactory lobes, paired cerebral hemispheres and unpaired diencephalon. The midbrain is characterised by a pair of optic lobes. Hind-brain consists of cerebellum and medulla oblongata.

The medulla oblongata passes out through the foramen magnum and continues into spinal cord, which is enclosed in the vertebral column. Frog has different types of sense organs, namely organs of touch (sensory papillae), taste (taste buds), smell (nasal epithelium), vision (eyes) and hearing (tympanum with internal ears).

Eyes in a frog are a pair of spherical structures situated in the orbit in skull. External ear is absent in frogs and only tympanum can be seen externally. The ear is an organ of hearing as well as balancing (equilibrium).

Male reproductive organs consist of a pair of yellowish ovoid testes which are found adhered to the upper part of kidneys by a double fold of peritoneum called mesorchium. Vasa efferentia are 10 – 12 in number that arise from testes. They enter the kidneys on their side and open into Bidder’s canal.

Finally it communicates with the urinogenital duct that comes out of the kidneys and opens into the cloaca. The cloaca is a small, median chamber that is used to pass faecal matter, urine and sperms to the exterior.

The female reproductive organs include a pair of ovaries. They are situated near kidneys and there is no functional connection with kidneys. A pair of oviduct arising from the ovaries opens into the cloaca separately. A mature female can lay 2500 to 3000 ova at a time.

Fertilisation is external and takes place in Water. Development involves a larval stage called tadpole. Tadpole undergoes metamorphosis to form the adult. Frogs are beneficial for mankind because they eat insects and protect the crop.

Frogs maintain ecological balance because these serve as an important link of food chain and foodweb in the ecosystem. In some countries the muscular legs of frog are used as food by man.

Students can Download Chapter 12 Thermodynamics Notes, Plus One Physics Notes helps you to revise the complete Kerala State Syllabus and score more marks in your examinations.

Kerala Plus One Physics Notes Chapter 12 Thermodynamics

Summary
Thermo dynamics is the branch of Physics that deals with concept of heat and temperature, their inter-conversions and other forms of energy. In thermo dynamics state of system is specified by macroscopic variables such as pressure, temperature, volume, mass, composition… etc.

Thermo Equilibrium
Thermo dynamic equilibrium:
A system is said to be in thermodynamic equilibrium if the macroscopic variables used to describe the system does not change with time.
Eg: Agas enclosed in a rigid container (characterized by P, V, T, m, and composition) The equilibrium of a thermodynamic system depends on surroundings and nature of wall that separates the system from surroundings. The wall can be

• Adiabatic wall – It does not allow flow of heat (energy).
• Diathermic wall – It allows the flow of heat (so that it can comes to thermal equilibrium).

Zeroth Law Of Thermodynamics
Zeroth law of thermodynamics gives concept of temperature. R.H Fowler formulated this law in 1931. According to Zeroth law of thermodynamics, the systems in thermal equilibrium with a third system separately are in thermal equilibrium with each other.

Let A & B are in thermal equilibrium with each other. If they are separately in thermal equilibrium with C, then the three systems are in thermal equilibrium
(T_A = T_B = T_C).

Heat, Internal Energy And Work
Internal Energy (U):
internal energy of a gas is the sum of potential energy and kinetic energy (translational kinetic energy, rotational kinetic energy and vibrational energy) Internal energy is a thermodynamic variable and hence it depends on state of the thermodynamic system.

Heat and Work:
The internal energy of a system can be changed either by heat or by work. Heat is energy transfer between a system and surroundings due to temperature difference. Work is mode of energy transfer brought about by means like moving piston (it is not due to temperature difference)

First Law Of Thermodynamics
According to first law of thermodynamics, heat supplied to a system is used to increase its internal energy and to do work.
If ∆Q is heat supplied to the system, ∆W is work done by the system and Au is change in internal energy, then ∆Q = ∆U + AW
Note:

• If the entire heat supplied to the system is used to do work, then ∆Q = ∆W
• The work done against constant pressure, ∆W = P∆V, ∆Q = ∆U + P∆V.

Specific Heat Capacity
Molar specific heat capacity of solid:
Consider a solid consisting of N atoms. Each atom have an average energy 3K_BT, where K_B is Botlzman constant. Total energy for one,mole
U = 3K_BT × N_A
N_A is avagadro number.
At constant pressure, ∆Q = ∆U + P∆V
For solid ∆V is negligible ∆Q = ∆U
Molar specific heat capacity

Thus molar specific heat capacity of solids is found to be 3R. But at low temperature molar specific heat capacity is not a constant.
Specific heat capacity of water:
The specific heat capacity of water is 4186 J Kg-‘K1. But the specific heat capacity of water changes with temperature as shown.

Mayor’s Relation; C_p – C_v = R
If molar specific heat capacity of constant pressure is C_p and that at constant volume is C_v then C_p – C_v = R, for an ideal gas.
Proof:
According to 1^st law of thermodynamics
∆Q = ∆U + P∆V
If ∆Q heat is absorbed at constant volume (∆V = 0)

From ideal gas equation for one mole PV = RT Differentiating w.r.t. temperature (at constant pressure)

Substituting in equation (2)

Equation (4) – Equation (1), we get C_p – C_v = R.

Thermodynamic State Variable And Equation Of State
Extensive and Intensive variables:
Thermodynamic variables can be extensive or intensive. Extensive variables depend on size of the system.
Eg: mass, internal energy, volume.
Intensive variables are independent of size of system.
Eg: Pressure, temperature, density.
Equation of state:
The relation between state variables of a system is called equation of state. For an ideal gas equation of state is PV = µRT

Thermodynamic process
1. Quasi-static process:
The thermodynamic process in which thermo dynamic variables (P, V, T… etc) changes so slowly that the system remains in thermal and mechanical equilibrium is called quasi static (nearly static) process. In quasi-static process change in temperature or pressure will be infinitesimally small. The different types of quasi static process are listed in the above table.

2. Work done in isothermal process:
For an isothermal process, the equation of state is
PV = constant = µRT
P = \(\frac{\mu \mathrm{RT}}{\mathrm{V}}\)
Let a system undergoes an isothermal process at temperature T, from the state (P₁, V₁) to (P₂, V₂). Let ‘DV’ be a small charge in volume due to pressure P.
Then work done (for ∆V)
∆W = P∆V

3. Work done by adiabatic process:
Let an ideal gas undergoes adiabatic charge from (P₁, V₁) to (P₂, V₂). The equation for adiabatic charge is PV^γ = constant = k

from equation (a) P₁V₁^γ = P₂V₂^γ = k

Substituting ideal gas equation.

Note:

1. The graph connecting P and V of isothermal process is called isotherm.
2. In adiabatic process
   • T₁ < T₂, then work is done on gas (w < 0)
   • T₁ > T₂, then work is done by gas (w > 0)
3. For Isothermal process
   • V₁ < V₂, w > 0 work is done by gas
   • V₁ > V₂, w < 0 work is done on gas.
4. In isochoric process no work is done on or by gas because volume is constant.

Cyclic process:
In cyclic process, the system returns to its initial state such that change in internal energy is zero. The P – V diagram for cyclic process will be closed loop and area of this loop gives work done or heat absorbed by system.

Heat Engines
Heat engines converts heat energy into mechanical energy. Heat engine is a device by which a system is made to undergo a cyclic process that results in conversion of heat to work.
Heat engines consists of:

1. Working substance (the system which undergoes cyclic process) eg: mixture of fuel vapor and air in diesel engine, steam in steam engine.
2. An external reservoir at a high temperature (T₁) – it is the source of heat.
3. An external reservoir at low temperature (T₂) or sink

Working:
The working substances absorbs an energy Q₁ from source reservoir at a temperature T₁. It undergoes cyclic process and releases heat Q₂ to cold reservoir. The change in heat (Q₁ – Q₂) is converted in to work (mechanical energy).
Efficiency of heat engine (η):
The efficiency of heat engine is the ratio of work done to input heat.

Note:

• Q₂ = 0, η = 1. When entire heat input is converted into work heat engine is 100% efficient. But practically 100% efficiency cannot be achieved. It is limited by second law of thermodynamics.
• Heat engine can be external combustion engine or internal combustion engine.

In external combustion engine, the fuel (system) is heated by external furnace.
Eg.: Steam engine.
In internal combustion engine, fuel is heated internally by exothermic chemical reactions.
Eg: Diesel engine, Patrol engine.

Refrigerators And Heat Pumps
Refrigerator is reverse of heat engine, the device used to cool a portion of space (inside a chamber) is refrigerator. The device used to pump heat into a portion of space (to warm-up room) is called heat pump.

In both devices, the working substance absorbs heat Q₂ from cold reservoir at temperature T₂. Some external work (by compression of gas by electric means) is done on it and heat Q₁ is supplied to hot reservoir at T₁.

The working cycle of refrigerator:
In refrigerator the working substance is a gas (freon)

Step1: The gaseous working substance is converted into vapor- liquid mixture at lower temperature (T₂)
Step 2: The cold fluid absorbs heat from region to be cooled (cold reservoir) and convert it into vapor.
Step 3: The vapor is heated by external work.
Step 4: The vapor release heat to surroundings and then comes to initial temperature T₂.

The coefficient of performance (α):
The coefficient of performance of refrigerator is defined as
α = \(\frac{Q_{2}}{W}\)
where Q₂ is heat extracted from cold reservoir and W is work done on system.
Note:

• The working substance in refrigerator is termed as refrigerant.
• For heat engine η can not exceed 1. But α can be greater than one.

Second law of Thermo dynamics
Kelvin – Plank statement:
No process is possible whose sole result is the absorption of heat from a reservoir and complete conversion of heat into work.
Clausius statement:
No process is possible whose sole result is the transfer of heat from a colder object to hotter object.

Reversible And Irreversible Processes
A themodynamic process is said to be reversible if the process can bring both system and surrounding back to the original state without any change.

A reversible thermodynamic process is ideal case. Most thermodynamic processes are irreversible because the process involves dissipative effects like friction, viscous force etc. and during such process, system passes through non-equilibrium states.
Note: Condition for a thermodynamic process to be reversible is

1. Quasi static
2. non-dissipative

Question 1.
What is the importance of reversibility in thermo dynamics?
Answer:
The main concern of thermodynamics is efficiency with which heat can be converted into work. According to second law of thermodynamics, the efficiency can not be 100%. The heat engine can have highest efficiency only if the cyclic process is reversible.

Carnot’S Engine
Carnot’s theorem:
Sadi carnot proposed Carnot’s theorem. According to Carnot’s theorem

1. No engine operating between two temperature can have efficiency more than that of Carnot’s engine,
2. The efficiency of Carnot’s engine is independent of nature of working substance.

Carnot’s engine:
A reversible heat engine operating between two temperatures is called Carnot’s engine.
Carnot’s cycle:
The Carnot cycle consists of two isothermal processes and two adiabatic processes.

The cylindar is placed on the source. The gas expands and temperature increases. This is the first stroke of the heat engine. The expansion is an isothermal expansion.

During this expansion the working substance originally at the state A (P₁, V₁, T₁) has new variable (P₂, V₂, T₁). The variation A to B is shown byAB in v-p graph.

During the second stroke, the cylinder is placed on the stand and the gas is allowed to expand further and reaches the state C. The new Co-ordinate are (P₃, V₃, T₂).

This expansion is adiabatic expansion. The third stroke is carried out when cylinder is placed on the zink. The cylinder undergoes for isothermal compression and coordinate becomes (P₄, V₄, T₂).

In the fourth and final stroke, the cylinder is placed on the non conducting stand. The gas is compressed back to state A. This is adiabatic compression.

1. The work done by gas in one Carnot cycle
Step 1: Isothermal expansion : The gas absorbs heat Q, from hot reserviorand undergoes Isothermal expansion.
[(P₁, V₁, T₁) → (P₂, V₂, T₂)]

Step 2: Adiabatic expansion
[(P₂, V₂, T₁) → (P₃, V₃, T₂)]

Step 3: Isothermal compression: The gas releases heat Q₂ to cold reservoir at T₂.
[(P₃, V₃, T₂) → (P₄, V₄, T₂)]

Step 4: Adiabatic compression
[(P₄, V₄, T₂) → (P₁, V₁, T₁)]

2. Efficiency of Carnot’s engine:

In adiabatic expansion from
(P₂, V₂, T₁) to (P₃, V₃, T₂)

In adiabatic compression
(P₄, V₄, T₂) to (P₁, V₁, T₁)

Thus equation (b) becomes η = 1 – \(\frac{T_{2}}{T_{1}}\) ……..(3)
Comparing this with equation (a)

Note:

• The equation
• Shows that efficiency of heat engine is independent of nature of working substance.

Students can Download Chapter 11 Thermal Properties of Matter Notes, Plus One Physics Notes helps you to revise the complete Kerala State Syllabus and score more marks in your examinations.

Kerala Plus One Physics Notes Chapter 11 Thermal Properties of Matter

Summary
Temperature And Heat
Temperature is a measure of hotness of a body. Heat is a form of energy transferred between two system (or system and surrounding) by virtue of temperature difference. The SI unit of heat is Joule (J) and that of tempera-ture is Kelvin (K).

Measurement Of Temperature
The instrument used to measure temperature is thermometer. The different temperature scales are Kelvin scale, Degree Celsius scale, and Fahrenheit scale. If t₁ and t_c are temperature in Fahrenheit scale and Celsius scale, then their linear relationship is given by

This relation can be graphically represented as shown

If T is temperature in kelvin scale, then
T = t_c + 273.15.
A comparison of the three temperature scales is shown

Ideal Gas Equation & Absolute Temperature Boyle’s law:
At constant temperature, pressure is inversely proportional to volume.
p α \(\frac{1}{V}\)
PV = constant _______(1)
Charle’s law: At constant pressure, volume is directly proportional to temperature
v α T
\(\frac{V}{T}\) = constant ______(2)
Combining (1) and (2), we get PV
\(\frac{PV}{T}\) = constant T
This is called ideal gas law. Generally, the law can be expressed for any quantity of dilute gas as

µ is the number of moles in given gas and R is universal gas constant.
The value of R is 8.31 J mol^-1 k^-1.
Absolute Temperature:
The minimum value of temperature for ideal gas is – 273.15°C (OK). This temperature is called absolute zero. On kelvin scale -273.15°C is taken as zero point.
Note:
The absolute temperature for a gas can be obtained by extrapolating the pressure versus temperature graph as shown below.

Thermal Expansion
The change in temperature of a body may change its length, area or volume. The fractional change in dimension [ratio of change in dimension to original dimension] is proportional to change in temperature.

The corresponding proportionally constant is called coefficient of thermal expansion or thermal expansivity. Thermal expansion can be defined as ratio of increase in dimension of body to increase in temperature.

There are different three types of thermal expansion, which are shown in the table given below
Note: (1)
Show that the coefficient of volume expansion for ideal gas is reciprocal of temperature
(α_v = 1/T)
Proof: Ideal Gas Equation is

At constant pressure P∆V = µR∆T ______(2).
Dividing we get

Anomalous behavior of water:
Generally volume of liquid increases with temperature .When water is heated, its volume starts to decrease from 0°C and reaches minimum at 4°C. Hence density of water is maximum at 4°C.

Question 1.
Derive the following relations

1. α_a = 2α_l
2. α_v = 3α_l

Answer:
Consider a cube of length ‘l’. Due to the increase in temperature ‘∆T’, length of cube increases by ∆l in all directions.
Coefficient of linear expansion, α_l = \(\frac{\Delta \ell}{\ell \Delta \mathrm{T}}\)
1. Increase in area of cube ∆A
= Final area – initial area
= (l + ∆l)² – l² = 2 × l × ∆l
[Neglecting ∆l²]
Area expansivity

Therefore, α_a = 2 . α_l.

2. Due to ‘∆T ’ the increase in volume of cube,
∆V = (l + + ∆l)³ – l³
= 3l²∆l²
[Neglecting ∆l² & ∆l³]

Therefore, α_v = 3 . α_l.

Specific Heat Capacity
Heat capacity:
Heat capacity (S) of substance is the quantity of heat required to increase the temperature of whole substance.
If ∆Q is the amount of heat required to increase the temperature by ∆T the heat capacity.

Specific heat capacity:
Specific heat capacity of a substance is defined as amount of heat required to increase temperature of unit mass of substance by one unit.
If ∆Q is amount of heat absorbed by substance of mass m and ∆T is change in temperature, then specific heat capacity is

The SI unit of specific heat capacity is J Kg^-1K^-1.
Molar specific heat capacity (C):
Molar specific heat capacity of a substance is the amount of heat required to increase the temperature of 1 mole of substance by one unit.
Its unit is J mol^-1 K^-1.
If a sample has ‘µ’ moles of substance, then its molar specific heat capacity is given by

Molar specific capacity are of two types:

• molar specific capacity at constant volume (CV)
• molar specific heat capacity at constant pressure (CP).

Note:

• Water has high specific heat capacity. So it is used as coolant in automobile radiators and as a heater in hot water bags.
• Due to high specific heat capacity of water, land is more warmer than water during daytime.

Calorimetry
Calorimetry means measurement of temperature. Calorimeter is a device used to measure heat. Calorimeter consists of a metallic vessel and a stirrer of same type. The vessel is kept inside a wooden jacket.

The wooden jacket contains insulating mate-rials like glass, wool etc. and hence it prevent heat loss. This jacket has a small opening at top and a thermometer is inserted into this hole.

Change Of State
A transition from one state (solid, liquid or gas) to another state is called change of state. There are four such transitions of state.

During change of state, the two different state coexist in thermal equilibrium and temperature remains constant until the completion of change of state.

Melting point:
The temperature at which solid and liquid coexist in thermal equilibrium with each other is called melting point. The melting point decreases with pressure

Boiling point.
The temperature at which liquid and vapour state of substance coexist in thermal equilibrium with each other is called boiling point. The boiling point increases with increase in pressure and it decreases with decrease in pressure.

Regelation

Take an ice block. Put a metal wire over the ice block and attach 5 kg. blocks at the two ends of wire as shown. Then we can see that the metal wire passes through the ice block to the other side without splitting it.

Explanation: The melting point of ice just below the wire decreases due to increase in pressure. As ice melts wire passes and refreeze (due to decrease in pressure). This process is called regelation.

Question 2.
Cooking is difficult at high altitude. Why?
Answer:
At high altitude, pressure is low. Boiling point decreases with decrease in pressure.

Question 3.
For cooking rice pressure cooker is preferred. Why?
Answer:
In pressure cooker, boiling point of water is increased by increasing pressure. Thus rice can be cooked at high temperature.

Question 4.
You might have observed the bubbles of steam coming from bottom of vessel when water is heated. These bubbles disappear as it reaches top of liquid just before boiling and they reach the surface at the time of boiling. Explain the reason?
Answer:
Just before boiling, the bottom of liquid will be warm and at the top, liquid will be cool. So the bubbles of steam formed at bottom rises to cooler water and condense, hence they disappear. At the time of boiling, temperature of entire mass of water will be 100°C. Now the bubbles reaches top and then escape.

1. Latent Heat:
The amount of heat per unit mass transferred during change of state of substance is called latent heat of substance for the process.
Eg: Latent heat of vaporization (L_v), Latent heat of fusion (L_f).
If ‘m’ is quantity of substance which undergoes change of state and Q is amount of heat required, then latent heat
L = \(\frac{Q}{m}\)
Latent heat is characteristic of substance and it depends on pressure. Its unit is JKg^-1.

Question 5.
Draw the temperature versus heat diagram for water. Mark the three phases of water (including its change of state).
Give reasons forthe following

1. The slope of phase line during change of state iszero.
2. The slope of phase line forthe three phases are different.

Answer:

1. During change of state temperature remains constant.
2. Specific heats of different phases are different.

Question 6.
Burns from steam are usually more serious than boil-ing water. Why?
Answer:
Latent heat of vaporization for water is 22.6 × 10⁵J Kg^-1 (ie; 22.6 × 10⁵J heat is required to convert 1 kg of water into steam at 100°C). So at 100°C, steam carries 22.6 × 10⁵J. (more heat than water).

Heat Transfer
Heat transfer occurs due to temperature difference. The three modes of heat transfer are

1. conduction
2. convection
3. radiation.

1. Conduction:
In conduction, heat transfers between two adjacent parts of a body due to temperature difference. Heat conduction can be considered as time rate of heat flow (heat current). At steady state the time rate of heat flow (H) is proportional to temperature difference ∆T area of cross section (A) and inversely proportional to length of conductor (L).

K is called thermal conductivity.
Its unit is JS^-1m^-1K^-1 or Wm^-1K^-1.

Question 7.
Some cooking pots have copper coating on its bottom. Why?
Answer:
Because of high thermal conductivity of copper, it distributes heat over the bottom of pot very quickly and promotes uniform cooking.

Note: In the house with concrete roof, a layer of insulatiori is made on the ceiling to prevent heat transfer and hence to keep the room cooler.

2. Convection:
In convection, different parts of fluid moves from one point to other. Convection can be natural of forced.
In natural convection when fluid is heated, it expands and becomes less dense. It then rises up and colder part replaces it. This process goes on as a cycle.

Question 8.
Explain the reason for sea breeze
Answer:
During the day, land heats up more quickly than water in lake (due to high specific heat capacity of water). The air on the surface of earth gets heated, expands, becomes less dense and rises up. The colder air (wind) replaces the space created by hot air. It creates a sea breeze. At night the land loses its heat very quickly than water. So water remains more warmer at night.

Note: In forced convection, material is forced to move by pump or by other physical means. Some examples are cooling system of automobile engines, heart that circulate blood throughout our body.

3. Radiation:
In radiation, energy is transferred in the form of electromagnetic radiation called heat radiation. Medium is not required for heat transfer. Earth receives energy from sun by means of radiation.

Thermal radiation:
The electromagnetic radiation entitled by a body by virtue of its temperature is called thermal radiation.

Question 9.
The untensils for cooking purpose are blackened at the bottom. Why?
Answer:
This is to absorb maximum heat from fire and hence to fast up cooking.

4. Black body radiation:
Black body:
A black body is one which absorbs radiations of all wavelengths incident on it. When a black body is heated it will emit radiations of all possible wavelengths. The wavelengths emitted by a perfect black body are called black body radiations.
Energy distribution in a black body radiation:

Lummer and Pringsheim performed an experiment to study the distribution of energy (among the radiation emitted by a black body) at different temperatures.
Result of experiment:
1. Fora given temperature the energy distribution is not uniform.

2. The energy associated with both longer and shorter wavelength of radiation emitted is small.

3. For each temperature there exists a particular wavelength corresponding to which the energy associated is maximum (λm).

4. This maximum energy carrying wavelength (λm) decreases with an increase in temperature of the black body.

5. The area under each curve represents the total energy emitted by the body at a particular temperature.

This area increases with increase of temperature. It is found that area is directly proportional to the fourth power of absolute temperature,
ie. E a T⁴
Wein’s displacement law:
Wein’s displacement law states that the product of the wavelength corresponding to maximum energy (λm) and the absolute temperature of black body is constant.
ie. λmT = constant
The value of the constant (Wein’s constant) is 2.9 × 10^-3mK.
This law explains why the colour of a piece of iron heated in a hot flame first becomes dull red, then reddish yellow and finally white hot.

Wein’s law is useful for estimating the surface temperatures of moon, sun and other stars. If red and blue stars emit radiations of continuous wavelengths, then blue star is hotter than red star.

Stefan’s law of radiation:
Stefan’s law states that the total radiant energy emitted persecond from unit area of the surface of a black body is directly proportional to the fourth power of its absolute temperature.
E a T⁴
E = sT⁴

Green house effect:
The earth surface is a source of thermal radiation because it absorbs energy received from sun. The wavelength of this radiation lies in the infrared region. But a larger portion of this radiation is absorbed by greenhouse gases, (CO₂, CH₄, etc).

This heats up the atmosphere. The net result is heating up of earths surface and atmosphere. This is known green house effect.

Newtons laws of cooling
According to Newton’s law of cooling the rate of loss of heat is directly proportional to difference of temperature between the body and its surroundings.

T₁ is temperature of surrounding medium and T₂ is temperature of body. K is constant that depends on nature of surface and area of exposed surface.
Note:

• The law is applicable for small temperature difference.
• For small temperature difference, cooling occurs due to a combination of conduction, convection, and radiation.
• The graph between difference in temperature and time is as shown in figure.