Kinetic Theory of Gases and ldeal Gas | Physics JEE previous year questions with Solutions

Q 11 :

A monoatomic gas having $γ = \frac{5}{3}$ is stored in a thermally insulated container and the gas is suddenly compressed to ${(\frac{1}{8})}^{th}$ of its initial volume. The ratio of final pressure and initial pressure is: ( $γ$ is the ratio of specific heats of the gas at constant pressure and at constant volume) [2025]

16
40
32
28

1

2

3

4

(3)

$P_{i} V_{i}^{γ} = P_{f} V_{f}^{γ}$

$\Rightarrow \frac{P_{f}}{P_{i}} = {(\frac{V_{i}}{V_{f}})}^{γ} = {(8)}^{5 / 3} = 32$

Q 12 :

An ideal gas initially at 0°C temperature, is compressed suddenly to one fourth of its volume. If the ratio of specific heat at constant pressure to that at constant volume is 3/2, the change in temperature due to the thermodynamics process is ________ K. [2025]

(273)

$T V^{γ - 1}$ = constant

$γ = \frac{3}{2}$

$273 \times V^{0.5} = T {(\frac{V}{4})}^{0.5}$

$T = 546 K \Rightarrow △ T = 273 K$

Q 13 :

An ideal gas has undergone through the cyclic process as shown in the figure. Work done by the gas in the entire cycle is ________ $\times 10^{- 1} J$ . (Take $π$ = 3.14) [2025]

(314)

Area of circle, $W = π (\frac{△ V}{2}) \cdot (\frac{△ P}{2})$

$W = \frac{π}{4} (500 - 300) \times 10^{3} (350 - 150) \times 10^{- 6}$

$W = 31.4 Joule$

$W = 314 \times 10^{- 1} Joule$

Q 14 :

In an isothermal change, the change in pressure and volume of a gas can be represented for three different temperatures; $T_{3} > T_{2} > T_{1}$ as [2023]

1

2

3

4

(1)

For isothermal process, P-V graph is a rectangular hyperbola.

As the dotted line is an isobaric line, which implies $T_{3} > T_{2} > T_{1}$ as the volume is increasing.

Q 15 :

Match List I with List II : [2023]

List I List II

A. Isothermal Process I. Work done by the gas decreases internal energy

B. Adiabatic Process II. No change in internal energy

C. Isochoric Process III. The heat absorbed goes partly to increase internal energy and partly to do work

D. Isobaric Process IV. No work is done on or by the gas

Choose the correct answer from the options given below :

A-I, B-II, C-IV, D-III
A-II, B-I, C-IV, D-III
A-I, B-II, C-III, D-IV
A-II, B-I, C-III, D-IV

1

2

3

4

(2)

$Δ U = n C_{V} Δ T$

For isothermal process, T is constant.

So, $Δ U = 0$

$A \to I I$

Adiabatic process

$Δ Q = 0$

$Δ Q = Δ U + Δ W$

$Δ U = - Δ W$

Work done by gas is positive,

so $Δ U$ is negative.

$B \to I$

For isochoric process, $Δ W = 0$

$C \to I V$

For isobaric process,

$Δ W = P Δ V \neq 0$

$Δ U = n C_{V} Δ T \neq 0$

Heat absorbed goes partly to increase internal energy and partly to do work.

Q 16 :

Given below are two statements. One is labelled as Assertion A and the other is labelled as Reason R. [2023]

Assertion A: If $d Q$ and $d W$ represent the heat supplied to the system and the work done on the system respectively, then according to the first law of thermodynamics $d Q = d U - d W .$

Reason R: First law of thermodynamics is based on law of conservation of energy.

In the light of the above statements, choose the correct answer from the option given below:

A is correct but R is not correct
A is not correct but R is correct
Both A and R are correct and R is the correct explanation of A
Both A and R are correct but R is not the correct explanation of A

1

2

3

4

(3)

First law of thermodynamics is based on the law of conservation of energy and it can be written as

$d Q = d U - d W$

where $d W$ is the work done on the system.

Q 17 :

The pressure (P) and temperature (T) relationship of an ideal gas obeys the equation $P T^{2} = constant .$ The volume expansion coefficient of the gas will be [2023]

$3 T^{2}$
$\frac{3}{T^{2}}$
$\frac{3}{T^{3}}$
$\frac{3}{T}$

1

2

3

4

(4)

$P T^{2} = constant$ , Using $P V = n R T$

$P = \frac{n R T}{V}$

$P T^{2} = \frac{n R T}{V} \times T^{2} = constant = K$

$\Rightarrow T^{3} = K V$

So, $\frac{d}{d T} (K V) = 3 T^{2}$

$\Rightarrow \frac{K d V}{d T} = 3 T^{2}$

$\Rightarrow d V = \frac{3 T^{2}}{K} d T = V γ d T$

$d V = V γ d T$

$\Rightarrow γ V = \frac{3 T^{2}}{K}$

$\Rightarrow γ = \frac{3 T^{2}}{K V}$ $= \frac{3 T^{2}}{T^{3}} = \frac{3}{T}$

Q 18 :

Heat is given to an ideal gas in an isothermal process.

A. Internal energy of the gas will decrease.
B. Internal energy of the gas will increase.
C. Internal energy of the gas will not change.
D. The gas will do positive work.
E. The gas will do negative work.

Choose the correct answer from the options given below: [2023]

A and E only
B and D only
C and E only
C and D only

1

2

3

4

(4)

$d Q = d U + d W$

$\Rightarrow d U = n C_{V} d T$

$d U = 0$ (For isothermal)

$∴$ $U = constant$

Also, $d Q > 0$ (supplied).

Hence $d W > 0$

Q 19 :

The pressure of a gas changes linearly with volume from A to B as shown in the figure. If no heat is supplied to or extracted from the gas, then the change in the internal energy of the gas will be [2023]

6 J
Zero
−4.5 J
4.5 J

1

2

3

4

(4)

$As Δ q = 0$

$Δ u = - W$

$W = \int P d V$

$Δ u = - W = 30 \times 10^{3} \times 150 \times 10^{- 6}$

$= 4500 \times 10^{- 3} = 4.5 J$

Q 20 :

A sample of gas at temperature T is adiabatically expanded to double its volume. The work done by the gas in the process is $(given, γ = \frac{3}{2})$ [2023]

$W = T R [\sqrt{2} - 2]$
$W = \frac{T}{R} [\sqrt{2} - 2]$
$W = \frac{R}{T} [2 - \sqrt{2}]$
$W = T R [2 - \sqrt{2}]$

1

2

3

4

(4)

$T_{1} V_{1}^{γ - 1} = T_{2} V_{2}^{γ - 1}$

$T V^{1 / 2} = T_{2} {(2 V)}^{1 / 2} \Rightarrow T_{2} = \frac{T}{\sqrt{2}}$

$W = \frac{R (T_{1} - T_{2})}{γ - 1} = \frac{R (T - \frac{T}{\sqrt{2}})}{1 / 2} = R T (2 - \sqrt{2})$

Q 21 :

A source supplies heat to a system at the rate of 1000 W. If the system performs work at a rate of 200 W, then the rate at which the internal energy of the system increases is [2023]

800 W
1200 W
600 W
500 W

1

2

3

4

(1)

$d Q = d U + d W$

$\frac{d U}{d t} = \frac{d Q}{d t} - \frac{d W}{d t}$

$\frac{d U}{d t} = 1000 - 200 = 800 W$

Q 22 :

Given below are two statements: [2023]

Statement I: If heat is added to a system, its temperature must increase.

Statement II: If positive work is done by a system in a thermodynamic process, its volume must increase.

In the light of the above statements, choose the correct answer from the options given below:

Both Statement I and Statement II are true
Statement I is false but Statement II is true
Both Statement I and Statement II are false
Statement I is true but Statement II is false

1

2

3

4

(2)

$Statement I: Δ Q > 0$

According to the first law of thermodynamics,

$Δ Q = Δ U + W$

If $Δ Q > 0$ , $Δ U < 0$ and $W > 0$ is also possible.

Hence $Δ T < 0$ , so temperature decreases.

$Statement I is false$

$Statement II: W > 0$

$∴$ $\int P d V > 0$

Therefore, volume of the system must increase during positive work done by the system.

$Statement II is true$

Q 23 :

Consider two containers $A$ and $B$ containing monoatomic gases at the same pressure $(P)$ , volume $(V)$ and temperature $(T)$ . The gas in $A$ is compressed isothermally to $\frac{1}{8}$ of its original volume, while the gas in $B$ is compressed adiabatically to $\frac{1}{8}$ of its original volume. The ratio of final pressure of gas in $B$ to that of gas in $A$ is: [2023]

$8$
$8^{1 / 2}$
$\frac{1}{8}$
$4$

1

2

3

4

(4)

$Isothermal process, T = constant$

$P V = n R T = constant$

$P_{1} V_{1} = P_{2} V_{2}$

$P V = P_{A} (\frac{V}{8})$

$P_{A} = 8 P$

$Adiabatic process, P V^{γ} = constant$

$γ for monoatomic gas is \frac{5}{3}$

$P_{1} V_{1}^{γ} = P_{2} V_{2}^{γ}$

$\frac{P_{B}}{P} = {(\frac{V_{1}}{V_{2}})}^{γ} = {(\frac{V}{V / 8})}^{5 / 3}$

$P_{B} = 32 P$

$\frac{P_{B}}{P_{A}} = \frac{32 P}{8 P} = 4$

Q 24 :

A gas is compressed adiabatically, which one of the following statement is NOT true? [2023]

There is no heat supplied to the system
The temperature of the gas increases
The change in the internal energy is equal to the work done on the gas
There is no change in the internal energy

1

2

3

4

(4)

$(1) Δ Q = 0$

$(2) Δ Q = Δ U + Δ W \Rightarrow Δ U = - Δ W$

$Adiabatic compression (V ↓)$

$Δ W = - ve \Rightarrow Δ U = + ve$

$Δ U ↑ \Rightarrow T ↑$

$Δ U \neq 0$

Q 25 :

1 kg of water at $100 ° C$ is converted into steam at $100 ° C$ by boiling at atmospheric pressure. The volume of water changes from $1.00 \times 10^{- 3} m^{3}$ as a liquid to ${1.671 m}^{3}$ as steam. The change in internal energy of the system during the process will be (Given latent heat of vaporisation $=2257 kJ/kg$ , atmospheric pressure $= {1×10}^{5} Pa$ ) [2023]

+ 2090 kJ
- 2090 kJ
- 2426 kJ
+ 2476 kJ

1

2

3

4

(1)

$Δ Q = Δ U + Δ W$

$∴$ $Δ U = Δ Q - Δ W = m L_{v} - P Δ V$

$= {(1 kg)(2257×10}^{3} J/kg)$

$- (1 \times 10^{5} Pa) ({1.671 m}^{3} - 1 \times 10^{- 3} m^{3})$

$= 2257 \times 10^{3} J - 167 \times 10^{3} J$ $= 2090 kJ$

Q 26 :

The thermodynamic process, in which internal energy of the system remains constant is [2023]

Isochoric
Isothermal
Adiabatic
Isobaric

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2

3

4

(2)

$T = constant \Rightarrow U = constant$

Q 27 :

The initial pressure and volume of an ideal gas are $P_{0}$ and $V_{0}$ . The final pressure of the gas when the gas is suddenly compressed to volume $\frac{V_{0}}{4}$ will be: (Given $γ =$ ratio of specific heats at constant pressure and at constant volume) [2023]

$P_{0} {(4)}^{1 / γ}$
$P_{0} {(4)}^{γ}$
$P_{0}$
$4 P_{0}$

1

2

3

4

(2)

$As gas is suddenly compressed, the process is adiabatic.$

$Equation of gas for adiabatic process is P V^{γ} = constant$

$\Rightarrow P_{1} V_{1}^{γ} = P_{2} V_{2}^{γ}$

$\Rightarrow P_{0} V_{0}^{γ} = P_{2} {(\frac{V_{0}}{4})}^{γ}$

$\Rightarrow P_{2} = P_{0} {(4)}^{γ}$

$Option (2) is correct.$

Q 28 :

A thermodynamic system is taken through a cyclic process. The total work done in the process is [2023]

100 J
300 J
Zero
200 J

1

2

3

4

(2)

$On P - V scale, area of loop = work done$

$\Rightarrow W = + \frac{1}{2} (2) \times 300$ $\Rightarrow W = 300 J$

Q 29 :

A thermodynamic system is taken through the cyclic process ABC as shown in the figure. The total work done by the system during the cycle ABC is ________ J. [2026]

(300)

$Work done = Area bounded by cycle$

$= \frac{1}{2} \times 3 \times 200 = 300 J$

Q 30 :

10 mole of an ideal gas is undergoing the process shown in the figure. The heat involved in the process from $P_{1}$ to $P_{2}$ is $α$ Joule ( $P_{1} = 21.7 Pa$ and $P_{2} = 30 Pa$ , $C_{v} = 21 J/K.mol$ , $R = 8.3 J/mol.K$ ). The value of $α$ is _______. [2026]

28
24
15
21

1

2

3

4

(4)

$Δ Q = n C_{v} Δ T (isochoric)$

$= \frac{C_{v}}{R} n R Δ T = \frac{C_{v}}{R} (P_{2} - P_{1}) V$

$= \frac{21}{8.3} \times (30 - 21.7) \times 1 = 21 J$

Q 31 :

When 300 J of heat is given to an ideal gas with $C_{p} = \frac{7}{2} R$ its temperature raises from $20 ° C$ to $50 ° C$ keeping its volume constant. The mass of the gas is (approximately) _______ g. ( $R = 8.314 J/mol.K$ ) [2026]

(481)

$For a constant volume process, the heat supplied (Q) is given by the formula:$

$Q = n C_{v} Δ T$

$Where:$

1. $n$ = number of moles of the gas.
2. $C_{v}$ = molar specific heat capacity at constant volume.
3. $Δ T$ = change in temperature $= 50 ° C - 20 ° C = 30 ° C = 30 K$

We are given the molar specific heat at constant pressure, $C_{p} = \frac{7}{2} R .$ Using Mayer's relation $(C_{p} - C_{v} = R)$ :

$C_{v} = C_{p} - R$

$\Rightarrow C_{v} = \frac{7}{2} R - R = \frac{5}{2} R$

Using the formula of heat,

$300 = n \times (\frac{5}{2} \times 8.314) \times 30$

$n = \frac{300 \times 2}{5 \times 8.314 \times 30} \approx 0.481 moles$

So, the amount of the gas is 0.481 moles. As the molar mass of the gas is not given in the question, we can't determine the mass of the gas directly.

Q 32 :

One mole of an ideal diatomic gas expands from volume V to 2V isothermally at a temperature 27 $° C$ and does W joule of work. If the gas undergoes same magnitude of expansion adiabatically from 27 $° C$ doing the same amount of work W, then its final temperature will be (close to) ______ $° C$ .

$(\log ₑ 2 = 0.693)$ [2026]

−189
−117
−30
−56

1

2

3

4

(4)

$For isothermal process$

$W_{isothermal} = n R T l n (\frac{V_{2}}{V_{1}})$

$= 1 \cdot R \cdot 300 \cdot l n (2)$

$= 300 R (0.693) \dots (1)$

$Now for adiabatic process,$

$It is given work done in isothermal = work done in adiabatic$

$W_{adiabatic} = \frac{n R (T_{1} - T_{2})}{γ - 1} \dots (2)$

$(1) = (2)$

$\frac{n R (300 - T_{final})}{1.4 - 1} = 300 R (0.693)$

$T_{final} = 216.84 K$

$= - 56.3 ° C$

Q 33 :

The internal energy of a monoatomic gas is 3nRT. One mole of helium is kept in a cylinder having internal cross sectional area of 17 $c m ²$ and fitted with a light movable frictionless piston. The gas is heated slowly by supplying 126 J heat. If the temperature rises by 4 $° C,$ then the piston will move ____ cm.
(atmospheric pressure = $10^{5}$ Pa) [2026]

15.5
1.45
14.5
1.55

1

2

3

4

(1)

$Δ U = 3 n R Δ T$

$Δ U = 3 \times 1 \times \frac{25}{3} \times 4 = 100 Joule$

$Δ Q = 126$

$W = 26 = P Δ V$

$26 = 10^{5} \times 17 \times 10^{- 4} Δ x$

$Δ x = \frac{26}{170} = 15.3$

Q 34 :

A diatomic gas $(γ = 1.4)$ does 100 J of work when it is expanded isobarically. Then the heat given to the gas ______ J. [2026]

(350)

$w = 100 J = n R Δ T for isobaric process.$

$Q = n C_{p} Δ T = (\frac{f}{2} + 1) n R Δ T$

$= \frac{7}{2} \cdot (100) = 350 Joule .$

Q 35 :

An insulated cylinder of volume $60 {cm}^{3}$ is filled with a gas at $27 ° C$ and 2 atmospheric pressure. Then the gas is compressed making the final volume as $20 {cm}^{3}$ while allowing the temperature to rise to $77 ° C$ . The final pressure is __________ atmospheric pressure. [2026]

(7)

$P V = n R T$

$\frac{P_{1} V_{1}}{R T_{1}} = \frac{P_{2} V_{2}}{R T_{2}}$

$\frac{2 \times 10^{5} \times 60}{300} = \frac{P_{2} \times 20}{350}$

$P_{2} = \frac{2 \times 10^{5} \times 7 \times 3}{6}$

$P_{2} = 7 \times 10^{5} = 7 atm$

Q 36 :

In the following p-V diagram, the equation of state along the curved path is given by ${(V - 2)}^{2} = 4 a p,$ where $a$ is a constant. The total work done in the closed path is [2026]

$- \frac{1}{a}$
$+ \frac{1}{3 a}$
$\frac{1}{2 a}$
$- \frac{1}{3 a}$

1

2

3

4

(4)

$w = Area of parabola$

$= \frac{2}{3} (Area of rectangle A C 31 A)$

$= \frac{2}{3} P_{0} (3 - 1) = \frac{4 P_{0}}{3}$

$When V = 1$

${(1 - 2)}^{2} = 4 a P_{0}$

$P_{0} = \frac{1}{4 a}$

$w = \frac{4}{3} P_{0} = \frac{4}{3} \cdot \frac{1}{4 a} = \frac{1}{3 a}$

$w_{gas} = - \frac{1}{3 a}$

Topic Question Set

Q 12 :

An ideal gas initially at 0°C temperature, is compressed suddenly to one fourth of its volume. If the ratio of specific heat at constant pressure to that at constant volume is 3/2, the change in temperature due to the thermodynamics process is ________ K. [2025]

Q 13 :

An ideal gas has undergone through the cyclic process as shown in the figure. Work done by the gas in the entire cycle is ________ $\times 10^{- 1} J$ . (Take $π$ = 3.14) [2025]

Q 14 :

In an isothermal change, the change in pressure and volume of a gas can be represented for three different temperatures; $T_{3} > T_{2} > T_{1}$ as [2023]

Q 17 :

The pressure (P) and temperature (T) relationship of an ideal gas obeys the equation $P T^{2} = constant .$ The volume expansion coefficient of the gas will be [2023]

Q 19 :

The pressure of a gas changes linearly with volume from A to B as shown in the figure. If no heat is supplied to or extracted from the gas, then the change in the internal energy of the gas will be [2023]

Q 20 :

A sample of gas at temperature T is adiabatically expanded to double its volume. The work done by the gas in the process is $(given, γ = \frac{3}{2})$ [2023]

Q 21 :

A source supplies heat to a system at the rate of 1000 W. If the system performs work at a rate of 200 W, then the rate at which the internal energy of the system increases is [2023]

Q 24 :

A gas is compressed adiabatically, which one of the following statement is NOT true? [2023]

Q 26 :

The thermodynamic process, in which internal energy of the system remains constant is [2023]

Q 27 :

The initial pressure and volume of an ideal gas are $P_{0}$ and $V_{0}$ . The final pressure of the gas when the gas is suddenly compressed to volume $\frac{V_{0}}{4}$ will be: (Given $γ =$ ratio of specific heats at constant pressure and at constant volume) [2023]

Q 28 :

A thermodynamic system is taken through a cyclic process. The total work done in the process is [2023]

Q 29 :

A thermodynamic system is taken through the cyclic process ABC as shown in the figure. The total work done by the system during the cycle ABC is ________ J. [2026]

Q 30 :

10 mole of an ideal gas is undergoing the process shown in the figure. The heat involved in the process from $P_{1}$ to $P_{2}$ is $α$ Joule ( $P_{1} = 21.7 Pa$ and $P_{2} = 30 Pa$ , $C_{v} = 21 J/K.mol$ , $R = 8.3 J/mol.K$ ). The value of $α$ is _______. [2026]

Q 31 :

When 300 J of heat is given to an ideal gas with $C_{p} = \frac{7}{2} R$ its temperature raises from $20 ° C$ to $50 ° C$ keeping its volume constant. The mass of the gas is (approximately) _______ g. ( $R = 8.314 J/mol.K$ ) [2026]

Q 34 :

A diatomic gas $(γ = 1.4)$ does 100 J of work when it is expanded isobarically. Then the heat given to the gas ______ J. [2026]

Q 35 :

An insulated cylinder of volume $60 {cm}^{3}$ is filled with a gas at $27 ° C$ and 2 atmospheric pressure. Then the gas is compressed making the final volume as $20 {cm}^{3}$ while allowing the temperature to rise to $77 ° C$ . The final pressure is __________ atmospheric pressure. [2026]

Q 36 :

In the following p-V diagram, the equation of state along the curved path is given by ${(V - 2)}^{2} = 4 a p,$ where $a$ is a constant. The total work done in the closed path is [2026]

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	List I		List II
A.	Isothermal Process	I.	Work done by the gas decreases internal energy
B.	Adiabatic Process	II.	No change in internal energy
C.	Isochoric Process	III.	The heat absorbed goes partly to increase internal energy and partly to do work
D.	Isobaric Process	IV.	No work is done on or by the gas

Topic Question Set

Q 12 : An ideal gas initially at 0°C temperature, is compressed suddenly to one fourth of its volume. If the ratio of specific heat at constant pressure to that at constant volume is 3/2, the change in temperature due to the thermodynamics process is ________ K. [2025]

Q 13 : An ideal gas has undergone through the cyclic process as shown in the figure. Work done by the gas in the entire cycle is ________ ×10–1 J. (Take π = 3.14) [2025]

Q 14 : In an isothermal change, the change in pressure and volume of a gas can be represented for three different temperatures; T3>T2>T1 as [2023]

Q 17 : The pressure (P) and temperature (T) relationship of an ideal gas obeys the equation PT2=constant. The volume expansion coefficient of the gas will be [2023]

Q 19 : The pressure of a gas changes linearly with volume from A to B as shown in the figure. If no heat is supplied to or extracted from the gas, then the change in the internal energy of the gas will be [2023]

Q 20 : A sample of gas at temperature T is adiabatically expanded to double its volume. The work done by the gas in the process is (given, γ=32) [2023]

Q 21 : A source supplies heat to a system at the rate of 1000 W. If the system performs work at a rate of 200 W, then the rate at which the internal energy of the system increases is [2023]

Q 24 : A gas is compressed adiabatically, which one of the following statement is NOT true? [2023]

Q 26 : The thermodynamic process, in which internal energy of the system remains constant is [2023]

Q 27 : The initial pressure and volume of an ideal gas are P0 and V0. The final pressure of the gas when the gas is suddenly compressed to volume V04 will be: (Given γ= ratio of specific heats at constant pressure and at constant volume) [2023]

Q 28 : A thermodynamic system is taken through a cyclic process. The total work done in the process is [2023]

Q 29 : A thermodynamic system is taken through the cyclic process ABC as shown in the figure. The total work done by the system during the cycle ABC is ________ J. [2026]

Q 30 : 10 mole of an ideal gas is undergoing the process shown in the figure. The heat involved in the process from P1 to P2 is α Joule (P1=21.7 Pa and P2=30 Pa, Cv=21 J/K.mol, R=8.3 J/mol.K). The value of α is _______. [2026]

Q 31 : When 300 J of heat is given to an ideal gas with Cp=72R its temperature raises from 20°C to 50°C keeping its volume constant. The mass of the gas is (approximately) _______ g. (R=8.314 J/mol.K) [2026]

Q 34 : A diatomic gas (γ=1.4) does 100 J of work when it is expanded isobarically. Then the heat given to the gas ______ J. [2026]

Q 35 : An insulated cylinder of volume 60 cm3 is filled with a gas at 27°C and 2 atmospheric pressure. Then the gas is compressed making the final volume as 20 cm3 while allowing the temperature to rise to 77°C. The final pressure is __________ atmospheric pressure. [2026]

Q 36 : In the following p-V diagram, the equation of state along the curved path is given by (V-2)2=4ap, where a is a constant. The total work done in the closed path is [2026]

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Q 12 :

An ideal gas initially at 0°C temperature, is compressed suddenly to one fourth of its volume. If the ratio of specific heat at constant pressure to that at constant volume is 3/2, the change in temperature due to the thermodynamics process is ________ K. [2025]

Q 13 :

An ideal gas has undergone through the cyclic process as shown in the figure. Work done by the gas in the entire cycle is ________ $\times 10^{- 1} J$ . (Take $π$ = 3.14) [2025]

Q 14 :

In an isothermal change, the change in pressure and volume of a gas can be represented for three different temperatures; $T_{3} > T_{2} > T_{1}$ as [2023]

Q 17 :

The pressure (P) and temperature (T) relationship of an ideal gas obeys the equation $P T^{2} = constant .$ The volume expansion coefficient of the gas will be [2023]

Q 19 :

The pressure of a gas changes linearly with volume from A to B as shown in the figure. If no heat is supplied to or extracted from the gas, then the change in the internal energy of the gas will be [2023]

Q 20 :

A sample of gas at temperature T is adiabatically expanded to double its volume. The work done by the gas in the process is $(given, γ = \frac{3}{2})$ [2023]

Q 21 :

A source supplies heat to a system at the rate of 1000 W. If the system performs work at a rate of 200 W, then the rate at which the internal energy of the system increases is [2023]

Q 24 :

A gas is compressed adiabatically, which one of the following statement is NOT true? [2023]

Q 26 :

The thermodynamic process, in which internal energy of the system remains constant is [2023]

Q 27 :

The initial pressure and volume of an ideal gas are $P_{0}$ and $V_{0}$ . The final pressure of the gas when the gas is suddenly compressed to volume $\frac{V_{0}}{4}$ will be: (Given $γ =$ ratio of specific heats at constant pressure and at constant volume) [2023]

Q 28 :

A thermodynamic system is taken through a cyclic process. The total work done in the process is [2023]

Q 29 :

A thermodynamic system is taken through the cyclic process ABC as shown in the figure. The total work done by the system during the cycle ABC is ________ J. [2026]

Q 30 :

10 mole of an ideal gas is undergoing the process shown in the figure. The heat involved in the process from $P_{1}$ to $P_{2}$ is $α$ Joule ( $P_{1} = 21.7 Pa$ and $P_{2} = 30 Pa$ , $C_{v} = 21 J/K.mol$ , $R = 8.3 J/mol.K$ ). The value of $α$ is _______. [2026]

Q 31 :

When 300 J of heat is given to an ideal gas with $C_{p} = \frac{7}{2} R$ its temperature raises from $20 ° C$ to $50 ° C$ keeping its volume constant. The mass of the gas is (approximately) _______ g. ( $R = 8.314 J/mol.K$ ) [2026]

Q 34 :

A diatomic gas $(γ = 1.4)$ does 100 J of work when it is expanded isobarically. Then the heat given to the gas ______ J. [2026]

Q 35 :

An insulated cylinder of volume $60 {cm}^{3}$ is filled with a gas at $27 ° C$ and 2 atmospheric pressure. Then the gas is compressed making the final volume as $20 {cm}^{3}$ while allowing the temperature to rise to $77 ° C$ . The final pressure is __________ atmospheric pressure. [2026]

Q 36 :

In the following p-V diagram, the equation of state along the curved path is given by ${(V - 2)}^{2} = 4 a p,$ where $a$ is a constant. The total work done in the closed path is [2026]