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

Q 31 :

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

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(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 32 :

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]

0%

(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 33 :

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]

0%

(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 34 :

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]

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(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 35 :

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

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(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 36 :

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

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(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 37 :

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]

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

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(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 38 :

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

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(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 39 :

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

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(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 40 :

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]

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

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(4)

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

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

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

Topic Question Set

Q 32 :

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]

0%

Q 33 :

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]

0%

Q 34 :

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 37 :

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 39 :

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 40 :

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]

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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