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NCERT Exemplar · Class 11 · Physics

Chapter 12: Thermodynamics

Practice each question, then open the answer or worked solution.

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Questions

27 questions
Q12.21Written answer

If the coefficient of performance of a refrigerator is 5 and operates at the room temperature, find the temperature inside the refrigerator.

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Worked solution

To find the temperature inside the refrigerator, we need to find the work done

W = 0

Q1 = Q2

β = ∞

Where β is the coefficient of performance

Given,

T1 = 27 + 273 = 300 K

Coefficient of performance of refrigerator ω = 5

Coefficient of performance is given as

Exemplar Solutions Physics Class 11 Chapter 12 Img 25

Using the above equation, the temperature can be determined

Exemplar Solutions Physics Class 11 Chapter 12 Img 26

T2 = -23oC.

Q12.22Written answer

The initial state of a certain gas is Pi, Vi, Ti. It undergoes expansion till its volume becomes Vf. Consider the following two cases:

a) the expansion takes place at constant temperature

b) the expansion takes place at constant pressure

Plot the P-V diagram for each case. In which of the two cases, is the work done by the gas more?

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Worked solution

Exemplar Solutions Class 11 Physics Chapter 12 - 9

Long Answers
Q12.23Written answer

Consider a P-V diagram in which the path followed by one mole of a perfect gas in a cylindrical container is shown in the figure.

Exemplar Solutions Class 11 Physics Chapter 12 - 10

a) find the work done when the gas is taken from state 1 to state 2

b) what is the ratio of temperature T1/T2 if V2 = 2V1

c) given the internal energy for one mole of gas at temperature T is (3/2)RT, find the heat supplied to the gas when it is taken from state 1 to 2 with V2 = 2V1.

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Worked solution

Given,

PV1/2 = K = constant

a) Work done for the process 1 to 2

Exemplar Solutions Physics Class 11 Chapter 12 Img 28

Solving the above equation, we get

Exemplar Solutions Physics Class 11 Chapter 12 Img 29

b) Ideal gas equation is

PV = nRT

T = PV/nR

Exemplar Solutions Physics Class 11 Chapter 12 Img 30

Exemplar Solutions Physics Class 11 Chapter 12 Img 31

Exemplar Solutions Physics Class 11 Chapter 12 Img 34

c) Internal energy, U = (3/2)RT

Exemplar Solutions Physics Class 11 Chapter 12 Img 31

Exemplar Solutions Physics Class 11 Chapter 12 Img 32

Exemplar Solutions Physics Class 11 Chapter 12 Img 33

Q12.24Written answer

A cycle followed by an engine is shown in the figure.

Exemplar Solutions Class 11 Physics Chapter 12 - 11

A to B: volume constant

B to C: adiabatic

C to D: volume constant

D to A: adiabatic

VC = VD = 2VA = 2VB

a) in which part of the cycle heat is supplied to the engine from outside?

b) in which part of the cycle heat is being given to the surrounding by the engine?

c) what is the work done by the engine in one cycle in terms of PA, PB, VA?

d) what is the efficiency of the engine?

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Worked solution

a) For process AB, the heat is supplied to the engine from outside.

dQ = dU + dW

dQ = dU = change in internal energy

b) For process CD, the volume remains constant and pressure decreases as the temperature for this process decreases.

c) Work  done by the engine in one cycle in terms of PA, PB, VA

Exemplar Solutions Physics Class 11 Chapter 12 Img 34

Exemplar Solutions Physics Class 11 Chapter 12 Img 35

d) Efficiency is given as:

Exemplar Solutions Physics Class 11 Chapter 12 Img 36

Q12.25Written answer

A cycle followed by an engine is shown in the figure. Find heat exchanged by the engine, with the surroundings for each section of the cycle considering Cv = (3/2)R.

Exemplar Solutions Class 11 Physics Chapter 12 - 12

AB: constant volume

BC: constant pressure

CD: adiabatic

DA: constant pressure

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Worked solution

a) AB: constant volume

Exemplar Solutions Physics Class 11 Chapter 12 Img 37

Exemplar Solutions Physics Class 11 Chapter 12 Img 38

b) BC: constant pressure

Exemplar Solutions Physics Class 11 Chapter 12 Img 39

c) CD: adiabatic QCD = 0

d) DA: constant pressure, there is compression of the gas from VD to VA at constant pressure PA.

Q12.26Written answer

Consider that an ideal gas is expanding in a process given by P = f(V), which passes through a point (V0, P0). Show that the gas is absorbing heat at (P0, V0) if the slope of the curve P = f(V) is larger than the slope of the adiabat passing through (P0, V0).

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Worked solution

Slope of the graph,

Exemplar Solutions Physics Class 11 Chapter 12 Img 40

Using the above relation, we can find that

Exemplar Solutions Physics Class 11 Chapter 12 Img 41

Exemplar Solutions Physics Class 11 Chapter 12 Img 42

Q12.27Written answer

Consider one mole of a perfect gas in a cylinder of unit cross-section with a piston attached. A spring is attached to the piston and to the bottom of the cylinder. Initially the spring is unstretched and the gas is in equilibrium. A certain amount of heat Q is supplied to the gas causing an increase of volume from V0 to V1.

Exemplar Solutions Class 11 Physics Chapter 12 - 13

a) what is the initial pressure of the system?

b) what is the final pressure of the system?

c) using the first law of thermodynamics, write down the relation between Q, Pa, V, V0, and k.

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Worked solution

a) The initial pressure of the system inside the cylinder is = Pa

b) The final pressure of the system is = Pf

Pf = Pa + K (V1 – V0)

Where V1 – V0 is the increase in volume

c) The relation between Q, Pa, V, V0, and k is:

dQ = dU + dW

dU = Cv (T – T0)

Where,

T is the final temperature of the gas

T0 is the initial temperature of the gas

n = 1

Exemplar Solutions Physics Class 11 Chapter 12 Img 43

Work done by the gas is given as:

Exemplar Solutions Physics Class 11 Chapter 12 Img 44

dQ = dU + dW

Using this equation, we get the following required relation:

Exemplar Solutions Physics Class 11 Chapter 12 Img 45