Isothermal and adiabatic processes — practice questions

Question 1 · difficulty L2 · understanding

Heat is supplied to a diatomic gas at constant pressure. Then the ratio of $\Delta Q : \Delta U : \Delta W$ is ______.

• A. 2 : 3 : 5
• B. 5 : 3 : 2
• C. 2 : 5 : 7
• D. 7 : 5 : 2

Question 2 · difficulty L2 · understanding

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 $\alpha$ Joule ( $P_1=21.7 \mathrm{~Pa}$ and $\left.P_2=30 \mathrm{~Pa}, \mathrm{C}_v=21 \mathrm{~J} / \mathrm{K} . \mathrm{mol}, R=8.3 \mathrm{~J} / \mathrm{mol} . \mathrm{K}\right)$. The value of $\alpha$ is $\_\_\_\_$ .

• A. 21
• B. 28
• C. 24
• D. 15

Question 3 · difficulty L2 · understanding

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

• A. 16
• B. 32
• C. 28
• D. 40

Question 4 · difficulty L2 · understanding

Match List - I with List - II . List - I List - II (A) Isothermal (I) ΔW (work done) = 0 (B) Adiabatic (II) ΔQ (supplied heat) = 0 (C) Isobaric (III) ΔU (change in internal energy) ≠0 (D) Isochoric (IV) ΔU = 0 Choose the correct answer from the options given below :

• A. (A)-(III), (B)-(II), (C)-(I), (D)-(IV)
• B. (A)-(II), (B)-(IV), (C)-(I), (D)-(III)
• C. (A)-(IV), (B)-(II), (C)-(III), (D)-(I)
• D. (A)-(IV), (B)-(I), (C)-(III), (D)-(II)

Question 5 · difficulty L2 · understanding

Match List - I with List - II. List - I List - II (A) Isobaric (I) $\Delta Q=\Delta W$ (B) Isochoric (II) $\Delta Q=\Delta U$ (C) Adiabatic (III) $\Delta Q=$ zero (D) Isothermal (IV) $\Delta Q=\Delta U+P\Delta V$ $\Delta Q=$ Heat supplied $\Delta W=$ Work done by the system $\Delta \mathrm{U}=$ Change in internal energy $\mathrm{P}=$ Pressure of the system $\Delta \mathrm{V}=$ Change in volume of the system Choose the correct answer from the options given below :

• A. (A)-(IV), (B)-(I), (C)-(III), (D)-(II)
• B. (A)-(IV), (B)-(II), (C)-(III), (D)-(I)
• C. (A)-(IV), (B)-(III), (C)-(II), (D)-(I)
• D. (A)-(II), (B)-(IV), (C)-(III), (D)-(I)

Question 6 · difficulty L2 · understanding

In an adiabatic process, which of the following statements is true?

• A. The internal energy of the gas decreases as the temperature increases
• B. The molar heat capacity is zero
• C. Work done by the gas equals the increase in internal energy
• D. The molar heat capacity is infinite

Question 7 · difficulty L2 · understanding

The work done in an adiabatic change in an ideal gas depends upon only :

• A. change in its pressure
• B. change in its temperature
• C. change in its specific heat
• D. change in its volume

Question 8 · difficulty L2 · understanding

Water of mass $m$ gram is slowly heated to increase the temperature from $T_1$ to $T_\gamma$. The change in entropy of the water, given specific heat of water is $1 \mathrm{Jkg}^{-1} \mathrm{~K}^{-1}$, is :

• A. $\mathrm{m}\left(\mathrm{T}_2-\mathrm{T}_1\right)$
• B. zero
• C. $\mathrm{m} \ln \left(\frac{\mathrm{T}_1}{\mathrm{~T}_2}\right)$
• D. $\mathrm{m} \ln \left(\frac{\mathrm{T}_2}{\mathrm{~T}_1}\right)$

Question 9 · difficulty L2 · understanding

Using the given $P-V$ diagram, the work done by an ideal gas along the path $A B C D$ is :

• A. $3 \mathrm{P}_0 \mathrm{~V}_0$
• B. $-3 \mathrm{P}_0 \mathrm{~V}_0$
• C. $-4 \mathrm{P}_0 \mathrm{~V}_0$
• D. $4 \mathrm{P}_0 \mathrm{~V}_0$

Question 10 · difficulty L2 · understanding

Match the List - I with List - II List - I List - II (A) Pressure varies inversely with volume of an ideal gas. (I) Adiabatic process (B) Heat absorbed goes partly to increase internal energy and partly to do work. (II) Isochoric process (C) Heat is neither absorbed nor released by a system. (III) Isothermal process (D) No work is done on or by a gas. (IV) Isobaric process Choose the correct answer from the options given below:

• A. Â A-I, B-III, C-II, D-IV
• B. A-I, B-IV, C-II, D-III
• C. A-III, B-I, C-IV, D-II
• D. A-III, B-IV, C-I, D-II