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

Q 21 :

A thermodynamic system is taken through cyclic process. The total work done in the process is:

100J
300J
200J
zero

1

2

3

4

(2)

$work done = Area of graph$

$W = \frac{1}{2} (400 - 100) (4 - 2)$

$W = 300 J$

Q 22 :

The volume of an ideal gas $(γ = 1.5)$ is changed adiabatically from 5 litres to 4 litres. The ratio of initial pressure to final pressure is:

$\frac{4}{5}$
$\frac{8}{5 \sqrt{5}}$
$\frac{2}{\sqrt{5}}$
$\frac{16}{25}$

1

2

3

4

(2)

Adiabatic process

Q 23 :

An ideal gas undergoes a four step cycle as shown in the P-V diagram below. During this cycle, positive work is done by the gas in

step 1
step 2
step 3
step 4

1

2

3

4

(1)

Heat and work depends on the path taken to reach a specific value. Hence, heat and work are path functions.

Q 24 :

Heat is supplied to a diatomic gas at constant pressure. Then the ratio of $ΔQ : ΔU : ΔW$ is ______. [2026]

2 : 3 : 5
5 : 3 : 2
2 : 5 : 7
7 : 5 : 2

1

2

3

4

(4)

$Diatomic gas (p = constant)$

$Δ Q = Δ Q_{p} = n C_{p} Δ T = \frac{7}{2} n R Δ T$

$Δ U = n C_{v} Δ T = \frac{5}{2} n R Δ T$

$Δ W = n R Δ T$

$Δ Q : Δ U : Δ W : : 7 : 5 : 2$

Q 25 :

Given below are two statements: one is labelled as Assertion A and the other is labelled as Reason R.

Statement I: Change in internal energy of a system containing $n$ mole of ideal gas can be written as

$Δ U = n C_{v} (T_{f} - T_{i}) = \frac{n R}{γ - 1} (T_{f} - T_{i}),$ where $γ = \frac{C_{p}}{C_{v}}, T_{i} = initial temperature, T_{f} =$ final temperature.

Statement II: Relation between degree of freedom $f$ and $γ (= \frac{C_{p}}{C_{v}})$ is $(γ = 1 + \frac{2}{f}) .$

Choose the correct answer from the options given below [2026]

Both A and R are true and R is the correct explanation of A
Both A and R are true but R is NOT the correct explanation of A
A is true but R is false
A is false but R is true

1

2

3

4

(2)

$Δ U = n C_{v} (T_{f} - T_{i}) = \frac{n R}{γ - 1} (T_{f} - T_{i})$

$γ = \frac{C_{p}}{C_{v}} = \frac{(\frac{f}{2} + 1) R}{\frac{f}{2} R} =$ $1 + \frac{2}{f}$

Q 26 :

Consider the following statements:

A. Zeroth law of thermodynamics gives concept of temperature

B. First law of thermodynamics gives concept of internal energy

C. In isothermal expansion of ideal gas, $ΔQ \neq ΔW$

D. Product of intensive and extensive variables is extensive

E. The ratio of any extensive variable to mass will be an extensive variable

Choose the correct combination of statements from the options given below: [2026]

C, D and E Only
A, B and C Only
A, B and D Only
B, C and D Only

1

2

3

4

(3)

A. True

B. True

C. False

D. True

E. False

Q 27 :

An ideal gas at pressure P and temperature T is expanding such that $P T^{3} = constant$ . The coefficient of volume expansion of the gas is ______. [2026]

$\frac{2}{T}$
$\frac{1}{T}$
$\frac{4}{T}$
$\frac{3}{T}$

1

2

3

4

(3)

$P T^{3} = k (constant)$

$(\frac{n R T}{V}) T^{3} = k \Rightarrow V = (\frac{n R}{k}) T^{4}$

$Volume expansion coefficient, γ = \frac{1}{V} (\frac{d V}{d T})$

$γ = \frac{k}{n R T^{4}} \cdot (\frac{n R}{k}) \cdot 4 T^{3} = \frac{4}{T}$

Q 28 :

A cylinder with adiabatic walls is closed at both ends and is divided into two compartments by a frictionless adiabatic piston. Ideal gas is filled in both (left and right) the compartments at same P, V, T. Heating is started from left side until pressure changes to $\frac{27 P}{8} .$ If initial volume of each compartment was 9 litres then the final volume in right-hand side compartment is ______ litres. (for this ideal gas $\frac{C_{p}}{C_{v}} = 1.5$ ) [2026]

3
4
14
9

1

2

3

4

(2)

$P_{Left} = P_{Right} = \frac{27 P}{8}$

$For right side process in Adiabatic$

$P_{i} V_{i}^{γ} = P_{f} V_{f}^{γ}$

$P {(9)}^{3 / 2} = \frac{27 P}{8} \times V_{f}^{3 / 2}$

$27 = \frac{27}{8} V_{f}^{3 / 2} \Rightarrow V_{f} = 4 litres$

Q 29 :

One mole of diatomic gas having rotational modes only is kept in a cylinder with a piston system. The cross-section area of the cylinder is 4 ${cm}^{2}$ . The gas is heated slowly to raise the temperature by $1.2 ° C$ during which the piston moves by 25 mm. The amount of heat supplied to the gas is ______ J. (Atmospheric pressure = 100 kPa, R = 8.3 J/mol·K) (Neglect mass of the piston) [2026]

24.8
25
15.04
29.98

1

2

3

4

(2)

$Q = Δ U + W$

$Q = \frac{f}{2} n R Δ T + P Δ V$

$Diatomic gas f = 5$

$Q = \frac{5}{2} \times 1 \times 8.3 \times 1.2 + 100 \times 10^{3} (4 \times 10^{- 4} \times 0.025)$

$Q = 24.9 + 1 = 25.9 J, nearest answer is 25$

$Here, please note that instead of the above method, if we use Q = n C_{p} Δ T, then also no option matches.$

Q 30 :

Initial pressure and volume of a monoatomic ideal gas are P and V. The change in internal energy of this gas in adiabatic expansion to volume $V_{final} = 27 V$ is ______ J. [2026]

$- 2 P V (3 \sqrt{3} - 1)$
$\frac{4}{3} P V$
$\frac{3}{4} P V$
$- \frac{4}{3} P V$

1

2

3

4

(4)

$P_{1} V_{1}^{γ} = P_{2} V_{2}^{γ}$

$Here, γ = \frac{5}{3}$

$P V^{5 / 3} = P_{2} \times {(27 V)}^{5 / 3}$

$\Rightarrow P_{2} = \frac{P}{{(27)}^{5 / 3}} = \frac{P}{3^{5}}$

$Δ U = n C_{v} Δ T = \frac{n R Δ T}{(γ - 1)}$

$Δ U = \frac{P_{2} V_{2} - P_{1} V_{1}}{(γ - 1)}$

$\Rightarrow Δ U = \frac{\frac{P}{3^{5}} \times 3^{3} \cdot V - P V}{(\frac{5}{3} - 1)} = - \frac{4}{3} P V$

Q 31 :

A vessel contains $0.15 m^{3}$ of a gas at pressure 8 bar and temperature $140 ° C$ with $C_{p} = 3 R$ and $C_{v} = 2 R$ . It is expanded adiabatically till pressure falls to 1 bar. The work done during this process is ________ kJ. (R is gas constant) [2026]

(120)

$γ = \frac{C_{p}}{C_{v}} = \frac{3}{2}$

$∵$ $P_{1} V_{1}^{γ} = P_{2} V_{2}^{γ} \Rightarrow V_{2} = {(\frac{P_{1}}{P_{2}})}^{1 / γ} V_{1}$

$\Rightarrow V_{2} = {(\frac{8}{1})}^{2 / 3} \times 0.15 = 0.6 m^{3}$

$Work done in adiabatic process, W = \frac{P_{1} V_{1} - P_{2} V_{2}}{γ - 1}$

$W = (\frac{8 \times 0.15 - 1 \times 0.6}{1.5 - 1}) \times 10^{5} = 1.2 \times 10^{5} J$

$\Rightarrow W = 120 kJ$

Q 32 :

5 moles of unknown gas is heated at constant volume from $10 ° C$ to $20 ° C$ . The molar specific heat of this gas at constant pressure $C_{p} = 8 cal/mol·°C$ and $R = 8.36 J/mol·°C$ . The change in the internal energy of the gas is __________ calorie. [2026]

(300)

$C_{p} - C_{v} = R \Rightarrow C_{v} = (C_{p} - R)$

$C_{v} = 6 cal/mol \cdot {}^{\circ}C$

$Δ U = n C_{v} Δ T = 5 \times 6 \times 10 = 300 cal$

Q 33 :

A certain gas is isothermally compressed to ${(\frac{1}{3})}^{rd}$ of its initial volume $(V_{0} = 3 litre)$ by applying required pressure. If the bulk modulus of the gas is $3 \times 10^{5} {N/m}^{2}$ , the magnitude of work done on the gas is _______ J. [2026]

(989)

$Initial volume (V_{1}) = 3 litre$

$Final volume (V_{2}) = \frac{V_{1}}{3} = 1 litre = 10^{- 3} m^{3}$

$For isothermal process, Bulk modulus = Pressure (B = P)$

$Bulk modulus of gas for isothermal process is not constant.$

$In the given solution we have considered it as initial bulk modulus.$

$For isothermal process work done, W = P_{1} V_{1} \ln (\frac{V_{2}}{V_{1}})$

$W = (3 \times 10^{5}) \times (3 \times 10^{- 3}) \ln (\frac{10^{- 3}}{3 \times 10^{- 3}})$

$W = - 988.75 J = 989 J$

Topic Question Set

Q 21 :

A thermodynamic system is taken through cyclic process. The total work done in the process is:

Q 22 :

The volume of an ideal gas $(γ = 1.5)$ is changed adiabatically from 5 litres to 4 litres. The ratio of initial pressure to final pressure is:

Q 23 :

An ideal gas undergoes a four step cycle as shown in the P-V diagram below. During this cycle, positive work is done by the gas in

Q 24 :

Heat is supplied to a diatomic gas at constant pressure. Then the ratio of $ΔQ : ΔU : ΔW$ is ______. [2026]

Q 27 :

An ideal gas at pressure P and temperature T is expanding such that $P T^{3} = constant$ . The coefficient of volume expansion of the gas is ______. [2026]

Q 30 :

Initial pressure and volume of a monoatomic ideal gas are P and V. The change in internal energy of this gas in adiabatic expansion to volume $V_{final} = 27 V$ is ______ J. [2026]

Q 31 :

A vessel contains $0.15 m^{3}$ of a gas at pressure 8 bar and temperature $140 ° C$ with $C_{p} = 3 R$ and $C_{v} = 2 R$ . It is expanded adiabatically till pressure falls to 1 bar. The work done during this process is ________ kJ. (R is gas constant) [2026]

Q 32 :

5 moles of unknown gas is heated at constant volume from $10 ° C$ to $20 ° C$ . The molar specific heat of this gas at constant pressure $C_{p} = 8 cal/mol·°C$ and $R = 8.36 J/mol·°C$ . The change in the internal energy of the gas is __________ calorie. [2026]

Q 33 :

A certain gas is isothermally compressed to ${(\frac{1}{3})}^{rd}$ of its initial volume $(V_{0} = 3 litre)$ by applying required pressure. If the bulk modulus of the gas is $3 \times 10^{5} {N/m}^{2}$ , the magnitude of work done on the gas is _______ J. [2026]

Want Us to Email you About Special Offers & Updates?

Topic Question Set

Q 21 : A thermodynamic system is taken through cyclic process. The total work done in the process is:

Q 22 : The volume of an ideal gas (γ=1.5) is changed adiabatically from 5 litres to 4 litres. The ratio of initial pressure to final pressure is:

Q 23 : An ideal gas undergoes a four step cycle as shown in the P-V diagram below. During this cycle, positive work is done by the gas in

Q 24 : Heat is supplied to a diatomic gas at constant pressure. Then the ratio of ΔQ : ΔU : ΔW is ______. [2026]

Q 27 : An ideal gas at pressure P and temperature T is expanding such that PT3=constant. The coefficient of volume expansion of the gas is ______. [2026]

Q 30 : Initial pressure and volume of a monoatomic ideal gas are P and V. The change in internal energy of this gas in adiabatic expansion to volume Vfinal=27V is ______ J. [2026]

Q 31 : A vessel contains 0.15 m3 of a gas at pressure 8 bar and temperature 140°C with Cp=3R and Cv=2R. It is expanded adiabatically till pressure falls to 1 bar. The work done during this process is ________ kJ. (R is gas constant) [2026]

Q 32 : 5 moles of unknown gas is heated at constant volume from 10°C to 20°C. The molar specific heat of this gas at constant pressure Cp=8 cal/mol·°C and R=8.36 J/mol·°C. The change in the internal energy of the gas is __________ calorie. [2026]

Q 33 : A certain gas is isothermally compressed to (13)rd of its initial volume (V0=3 litre) by applying required pressure. If the bulk modulus of the gas is 3×105 N/m2, the magnitude of work done on the gas is _______ J. [2026]

Want Us to Email you About Special Offers & Updates?

Q 21 :

A thermodynamic system is taken through cyclic process. The total work done in the process is:

Q 22 :

The volume of an ideal gas $(γ = 1.5)$ is changed adiabatically from 5 litres to 4 litres. The ratio of initial pressure to final pressure is:

Q 23 :

An ideal gas undergoes a four step cycle as shown in the P-V diagram below. During this cycle, positive work is done by the gas in

Q 24 :

Heat is supplied to a diatomic gas at constant pressure. Then the ratio of $ΔQ : ΔU : ΔW$ is ______. [2026]

Q 27 :

An ideal gas at pressure P and temperature T is expanding such that $P T^{3} = constant$ . The coefficient of volume expansion of the gas is ______. [2026]

Q 30 :

Initial pressure and volume of a monoatomic ideal gas are P and V. The change in internal energy of this gas in adiabatic expansion to volume $V_{final} = 27 V$ is ______ J. [2026]

Q 31 :

A vessel contains $0.15 m^{3}$ of a gas at pressure 8 bar and temperature $140 ° C$ with $C_{p} = 3 R$ and $C_{v} = 2 R$ . It is expanded adiabatically till pressure falls to 1 bar. The work done during this process is ________ kJ. (R is gas constant) [2026]

Q 32 :

5 moles of unknown gas is heated at constant volume from $10 ° C$ to $20 ° C$ . The molar specific heat of this gas at constant pressure $C_{p} = 8 cal/mol·°C$ and $R = 8.36 J/mol·°C$ . The change in the internal energy of the gas is __________ calorie. [2026]

Q 33 :

A certain gas is isothermally compressed to ${(\frac{1}{3})}^{rd}$ of its initial volume $(V_{0} = 3 litre)$ by applying required pressure. If the bulk modulus of the gas is $3 \times 10^{5} {N/m}^{2}$ , the magnitude of work done on the gas is _______ J. [2026]