A Complete Resource Book in Physics for JEE Main

Sanjeev Kumar

Chapter 12

Thermodynamics - all with Video Answers

Educators

Chapter Questions

Problem 1

An ideal gas is taken through the cycle $A \rightarrow B \rightarrow C$ $\rightarrow A$ as shown in Fig. $12.8$. If the net heat supplied to the gas in the cycle is $5 \mathrm{~J}$, the work done by the gas in the process $C \rightarrow A$ is
(A) $-5 \mathrm{~J}$
(B) $-10 \mathrm{~J}$
(C) $-15 \mathrm{~J}$
(D) $-20 \mathrm{~J}$

Narayan Hari

Narayan Hari

Numerade Educator

Problem 2

For an adiabatic expansion process, the quantity $P V$
(A) decreases.
(B) increases.
(C) remains constant.
(D) depends on adiabatic exponent of the gas.

Narayan Hari

Numerade Educator

Problem 3

A gas is confined inside a container having a movable piston. The gas is allowed to expand isobarically. If the initial volume of gas is $V_{0}$ and the speed of sound in the gas is $C_{0}$, then the speed of sound when the volume of the gas increases to $4 V_{0}$ is
(A) $C_{0}$
(B) $2 C_{0}$
(C) $4 C_{0}$
(D) $C_{0} / 2$

Narayan Hari

Numerade Educator

Problem 4

An ideal gas is taken through cycle $A \rightarrow B \rightarrow C \rightarrow A$ as shown in Fig. $12.9$. If the net heat supplied to the gas is $10 \mathrm{~J}$, then the work done by the gas in process $B \rightarrow C$ is
Fig. $12.9$
(A) $-10 \mathrm{~J}$
(B) $-30 \mathrm{~J}$
(C) $-15 \mathrm{~J}$
(D) $-20 \mathrm{~J}$

Narayan Hari

Numerade Educator

Problem 5

The work of $146 \mathrm{~kJ}$ is performed in order to compress 1 kilo mole of gas adiabatically and in this process, the temperature of the gas increases by $7^{\circ} \mathrm{C}$. The gas is $\left(R=8.3 \mathrm{~J} \mathrm{~mol}^{-1} K^{-1}\right)$
(A) Monoatomic
(B) Diatomic(C) Triatomic
(D) A mixture of monoatomic and diatomic

Narayan Hari

Numerade Educator

Problem 6

If amount of heat given to a system is $50 \mathrm{~J}$ and work done on the system is $15 \mathrm{~J}$, then change in internal energy of the system is
(A) $35 \mathrm{~J}$
(B) $50 \mathrm{~J}$
(C) $65 \mathrm{~J}$
(D) $15 \mathrm{~J}$

Narayan Hari

Numerade Educator

Problem 7

Which one of the following statements is incorrect?
(A) If positive work is done by a system in a thermodynamic process, its volume must increase.
(B) If heat is added to a system, its temperature must increase.
(C) A body at $20^{\circ} \mathrm{C}$ radiates in a room, where room temperature is $30^{\circ} \mathrm{C}$.
(D) If pressure vs temperature graph of an ideal gas is a straight line, then work done by the gas is zero.

Narayan Hari

Numerade Educator

Problem 8

When a given quantity of an ideal monoatomic gas is at pressure $P$ and absolute temperature $T$, then the adiabatic bulk modulus of the gas will be
(A) $P$
(B) $\frac{5}{3} P$
(C) $T$
(D) $\frac{5 T}{2}$

Narayan Hari

Numerade Educator

Problem 9

Equal amount of same gas in two similar cylinders, $A$ and $B$, compressed to same final volume from same initial volume one adiabatically and another isothermally, respectively, then
(A) final pressure in $A$ is more than in $B$.
(B) final pressure in $B$ is greater than in $A$.
(C) final pressure in both equal.
(D) for the gas, value of $\gamma=\frac{C_{p}}{C_{V}}$ is required.

Ajay Singhal

Numerade Educator

Problem 10

$P-T$ curve of the following process will be

Narayan Hari

Numerade Educator

Problem 11

Work done in process $A B$ will be
(A) $900 \mathrm{~J}$
(B) $1500 \mathrm{~J}$
(C) $3300 \mathrm{~J}$
(D) $33 \mathrm{~J}$

Narayan Hari

Numerade Educator

Problem 12

Temperature of source is $330^{\circ} \mathrm{C}$. Temperature of sink is changed in order to increase the efficiency of engine from $\frac{1}{5}$ to $\frac{1}{4}, b y$
(A) $30^{\circ} \mathrm{K}$
(B) $303^{\circ} \mathrm{K}$
(C) $603^{\circ} \mathrm{K}$
(D) $60^{\circ} \mathrm{K}$

Narayan Hari

Numerade Educator

Problem 13

Two moles of an ideal gas at $300 \mathrm{~K}$ were cooled at constant volume so that the pressure is reduced to half the initial value. As a result of heating at constant pressure, the gas has expanded till it attains the original temperature. The total heat absorbed by gas, if $R$ is the gas constant
(A) $150 R$
(B) $300 R$
(C) $75 R$
(D) $100 R$

Ajay Singhal

Numerade Educator

Problem 14

P-V diagram of an ideal gas is as shown in Fig. $12.10$. Work done by the gas in the process $A B C D$ is
(A) $4 P_{0} V_{0}$
(B) $2 P_{0} V_{0}$
(C) $3 P_{0} V_{0}$
(D) $P_{0} V_{0}$

Narayan Hari

Numerade Educator

Problem 15

The total $\mathrm{KE}$ of all the molecules of helium having a volume $V$ exerting a pressure $P$ is $1500 \mathrm{~J}$. The total $\mathrm{KE}$ in joules of all the molecules of $N_{2}$ having the same volume $V$ and exerting a pressure $2 P$ is
(A) 3000
(B) 4000
(C) 5000
(D) 6000

Ajay Singhal

Numerade Educator

Problem 16

One mole of an ideal gas at an initial temperature of $T K$ does $6 R$ joules of work adiabatically. If the ratio of specific heats of this gas at constant pressure and at constant volume is $5 / 3$, the final temperature of gas will be
(A) $(T+2.4) \mathrm{K}$
(B) $(T-2.4) \mathrm{K}$
(C) $(T+4) \mathrm{K}$
(D) $(T-4) \mathrm{K}$

Narayan Hari

Numerade Educator

Problem 17

Two rigid boxes containing different ideal gases are placed on a table. Box $A$ contains one mole of nitrogen at temperature $T_{0}$, while Box $B$ contains one mole of helium at temperature (7/3) $T_{0}$. The boxes are then put into thermal contact with each other and heat flows between them until the gases reach a common final temperature. (Ignore the heat capacity of boxes.) Then, the final temperature of the gases, $T_{f}$, in terms of $T_{0}$ is
(A) $T_{f}=\frac{5}{2} T_{0}$
(B) $T_{f}=\frac{3}{7} T_{0}$
(C) $T_{f}=\frac{7}{3} T_{0}$
(D) $T_{f}=\frac{3}{2} T_{0}$

Ajay Singhal

Numerade Educator

Problem 18

Figure $12.11$ shows a process on a gas in which pressure and volume both changes. The molar heat capacity for this process is $C$. Then
(A) $C=0$
(B) $C=C_{V}$
(C) $C>C_{V}$
(D) $C<C_{V}$

Ajay Singhal

Numerade Educator

Problem 19

Heat energy absorbed by a system in going through a cyclic process shown in Fig. $12.12$ is
(A) $10^{7} \pi \mathrm{J}$
(B) $10^{4} \pi \mathrm{J}$
(C) $10^{2} \pi \mathrm{J}$
(D) $10^{-3} \pi \mathrm{J}$

Narayan Hari

Numerade Educator

Problem 20

The pressure-temperature $(P-T)$ phase diagram shown below corresponds to the
(A) curve of fusion of solids that expand on solidification.
(B) curve of sublimation of solids that directly go over to the vapour phase.
(C) curve of fusion of solids that contract on solidification.
(D) curve of fusion of solids that do not change in volume upon solidification.

Ajay Singhal

Numerade Educator

Problem 21

Three samples of the same gas $A, B$, and $C(\gamma=3 / 2)$ have initial equal volumes. Now the volume of each sample is doubled. The process is adiabatic for $A$, isobaric for $B$, and isothermal for $C$. If the final pressures are equal for all three samples, the ratio of their initial pressures is
(A) $2 \sqrt{2}: 2: 1$
(B) $2 \sqrt{2}: 1: 2$
(C) $\sqrt{2}: 1: 2$
(D) $2: 1: \sqrt{2}$

Ajay Singhal

Numerade Educator

Problem 22

A cylindrical tube of uniform cross-sectional area $A$ is fitted with two air tight frictionless pistons. The pistons are connected to each other by a metallic wire. Initially, the pressure of the gas is $P_{0}$ and temperature is $T_{0}$. Atmospheric pressure is also $P_{0}$. Now the temperature of the gas is increased to $2 T_{0}$, the tension in the wire will be
(A) $2 P_{0} A$
(B) $P_{0} A$
(C) $\frac{P_{0} A}{2}$
(D) $4 P_{0} A$

Ajay Singhal

Numerade Educator

Problem 23

P-V diagram of a diatomic gas is a straight line passing through origin. The molar heat capacity of the gas in the process will be
(A) $4 R$
(B) $2.5 R$
(C) $3 R$
(D) $4 R / 3$

Ajay Singhal

Numerade Educator

Problem 24

A system is taken from state $A$ to state $B$ along two different paths 1 and $2 .$ The heat absorbed and work done by the system along these two paths are $Q_{1}$ and $Q_{2}$ and $W_{1}$ and $W_{2}$, respectively.
(A) $Q_{1}=Q_{2}$
(B) $W_{1}=W_{2}$
(C) $Q_{1}+W_{1}=Q_{2}+W_{2}$
(D) None of these

Narayan Hari

Numerade Educator

Problem 25

$n$ moles of a gas expands from volume $V_{1}$ to $V_{2}$ at constant temperature $T$. The work done by the gas is
(A) $n R T\left(\frac{v_{2}}{v_{1}}\right)$
(B) $n R T\left(\frac{v_{2}}{v_{1}}-1\right)$
(C) $n R T \ln \left(\frac{v_{1}}{v_{2}}\right)$
(D) None of these

Narayan Hari

Numerade Educator

Problem 26

The molar specific heats of an ideal gas at constant pressure and volume are denoted by $C_{p}$ and $C_{v}$, respectively. Further, $\frac{C_{p}}{C_{v}}=\gamma$ and $R$ is the gas constant for 1 gm mole of a gas. Then $C_{v}$ is equal to
(A) $R$
(B) $\gamma R$
(C) $\frac{R}{\gamma-1}$
(D) $\frac{\gamma R}{\gamma-1}$

Narayan Hari

Numerade Educator

Problem 27

A gas expands under constant pressure $P$ from volume $V_{1}$ to $V_{2}$. The work done by the gas is
(A) $P\left(V_{2}-V_{1}\right)$
(B) $P\left(V_{1}-V_{2}\right)$
(C) $P\left(V_{1}^{\gamma}-V_{2}^{\gamma}\right)$
(D) $\frac{P V_{1} V_{2}}{V_{2}-V_{1}}$

Narayan Hari

Numerade Educator

Problem 28

The internal energy $U$ is a unique function of any state because of change in $U$
(A) does not depend upon path.
(B) depends upon path.
(C) corresponds to an adiabatic process.
(D) corresponds to an isothermal process.

Narayan Hari

Numerade Educator

Problem 29

The give curve represents the variation of temperature as a function of volume for one mole of an ideal gas. Which of the following curves represents the variation of pressure as a function of volume?
(A)
(B)
(C)
(D)

Narayan Hari

Numerade Educator

Problem 30

One mole of an ideal monatomic gas is taken from temperature $T_{0}$ to $2 T_{0}$ by the process $P T^{-4}=C$ Considering the following statements, choose the correct alternative.
I. Molar heat capacity of the gas is $-\frac{3 R}{2}$
II. Molar heat capacity of the gas is $\frac{3 R}{2}$
III. Work done is $-3 R T_{0}$ IV. Work done is $3 R T_{0}$
(A) Statements I and IV are correct.
(B) Statements I and III are correct.
(C) Statements II and IV are correct.
(D) Statements II and III are correct.

Narayan Hari

Numerade Educator

Problem 31

A vertical cylinder with a massless piston is filled with one mole of an ideal gas. The piston can move freely without friction. The piston is slowly raised so that the gas expands isothermally at temperature $300 \mathrm{~K}$. The amount of work done in increasing the volume two times is $R=\frac{25}{3} \mathrm{~J} / \mathrm{mol} / \mathrm{K}, \log _{\mathrm{e}} 2=0.7$
(A) $1750 \mathrm{~J}$
(B) $2500 \mathrm{~J}$
(C) $750 \mathrm{~J}$
(D) $4250 \mathrm{~J}$

Narayan Hari

Numerade Educator

Problem 32

Helium gas of $2 \mathrm{~g}$ is let through a thermal cycle shown in Fig. 12.13. The lowest temperature of the gas in the cycle is $-17^{\circ} \mathrm{C}$, the highest is $127^{\circ} \mathrm{C}$, and the temperature is equal at points $A$ and $B$. $[R=$ Universal gas constant $]$
(A) The temperature at $A$ and $B$ is $320 \mathrm{~K}$ and net work done by the gas during a cycle is $32 R$.
(B) The temperature at $A$ and $B$ is $320 \mathrm{~K}$ and net work done by the gas during a cycle is $8 R$.
(C) The temperature at $A$ and $B$ is $328 \mathrm{~K}$ and net work done by the gas during a cycle is $32 R$.
(D) The temperature at $A$ and $B$ is $328 \mathrm{~K}$ and net work done by the gas during a cycle is $8 R$.

Narayan Hari

Numerade Educator

Problem 33

One mole of an ideal gas is enclosed in a cylinder fitted with a frictionless piston and occupies a volume of $1.5$ litre at a pressure of $1.2 \mathrm{~atm} .$ It is subjected to a process given by equation $T=\alpha V^{2}, \gamma$ (adiabatic constant) for the gas $=1.5$. Choose the wrong statement. Given $R \alpha=80 \mathrm{~J} \mathrm{~mol}^{-1} \mathrm{lit}^{-2}(R=$ gas constant and $\alpha$ is constant)
(A) The $P-V$ diagram of the process is a straight line.
(B) The work done by the gas in increasing the volume of the gas to 9 litre is $3150 \mathrm{~J}$.
(C) The change in the internal energy of the gas is $12600 \mathrm{~J}$.
(D) The heat supplied to the gas in the process is 1575 J.

Narayan Hari

Numerade Educator

Problem 34

Temperature of $100 \mathrm{gm}$ water in changed from $0^{\circ} \mathrm{C}$ to $3^{\circ} \mathrm{C}$. In this process, heat supplied to water will be (specified heat of water $=1 \mathrm{cal} / \mathrm{gm}{ }^{\circ} \mathrm{C}$ )
(A) Equal to $300 \mathrm{cal}$
(B) Greater than $300 \mathrm{cal}$
(C) Less than $300 \mathrm{cal}$
(D) Data is insufficient

Narayan Hari

Numerade Educator

Problem 35

A gas is confined inside a container having a movable piston. The gas is allowed to expand isobarically. If the initial volume of gas is $V_{0}$ and the speed of sound in the gas is $C_{0}$, then the speed of sound when the volume of the gas increases to $4 V_{0}$ is
(A) $C_{0}$
(B) $2 C_{0}$
(C) $4 C_{0}$
(D) $C_{0} / 2$

Narayan Hari

Numerade Educator

Problem 36

Between two isotherms at temperatures $2 T$ and $T$, a process $A B C D$ is performed with an ideal monatomic gas. $A B$ and $C D$ are adiabatic expansion processes and $B C$ is isobaric expansion process. The average molar specific heat capacity of the overall process will be
(A) $-3 R / 2$
(B) $5 R / 2$
(C) $3 R / 2$
(D) $-5 R / 2$

Ajay Singhal

Numerade Educator

Problem 37

The pressure of a monatomic gas increases linearly from $4 \times 10^{5} \mathrm{~N} / \mathrm{m}^{2}$ to $8 \times 10^{5} \mathrm{~N} / \mathrm{m}^{2}$ when its volume
increases from $0.2 \mathrm{~m}^{3}$ to $0.5 \mathrm{~m}^{3}$. The work done by the gas and increase in its internal energy are given by
(A) $1.8 \times 10^{5} \mathrm{~J}, 1.8 \times 10^{5} \mathrm{~J}$
(B) $4.8 \times 10^{5} \mathrm{~J}, 4.8 \times 10^{5} \mathrm{~J}$
(C) $1.8 \times 10^{5} \mathrm{~J}, 4.8 \times 10^{5} \mathrm{~J}$
(D) $4.8 \times 10^{5} \mathrm{~J}, 1.8 \times 10^{5} \mathrm{~J}$

Narayan Hari

Numerade Educator

Problem 38

An ideal heat engine working between temperatures $T_{H}$ and $T_{L}$ has efficiency $\eta .$ If both the temperature are raised by $100 \mathrm{~K}$ each, the new efficiency of the heat engine will be
(A) equal to $\eta$.
(B) greater than $\eta$.
(C) less than $\eta$.
(D) greater or less than $\eta$ depending upon the nature of the working substance.

Narayan Hari

Numerade Educator

Problem 39

A gas is expanded from volume $V_{0}$ to $2 V_{0}$ under three different processes. Process 1 is isobaric process, process 2 is isothermal, and process 3 is adiabatic. Let $\Delta U_{1}, \Delta U_{2}$, and $\Delta U_{3}$ be the change in internal energy of the gas in these three processes. Then
(A) $\Delta U_{1}>\Delta U_{2}>\Delta U_{3}$
(B) $\Delta U_{1}<\Delta U_{2}>\Delta U_{3}$
(C) $\Delta U_{2}<\Delta U_{1}<\Delta U_{3}$
(D) $\Delta U_{2}>\Delta U_{3}>\Delta U_{1}$

Ajay Singhal

Numerade Educator

Problem 40

A cyclic process $A B C D$ is shown in the $P-V$ diagram. Which of the following curves represent the same process?
(A)
(B)
(C)
(D)

Ajay Singhal

Numerade Educator

Problem 41

An ideal gas undergoes four different processes from the same initial state (Fig. 12.14). Four processes are adiabatic, isothermal, isobaric, and isochoric. Out of $1,2,3$, and 4 which one is adiabatic?
$12.14$
(A) 4
(B) 3
(C) 2
(D) 1

Ajay Singhal

Numerade Educator

Problem 42

If an average person jogs, he produces $14.5 \times 10^{3} \mathrm{cal} / \mathrm{min}$. This is evaporated as sweat. The amount of sweat evaporated per min (assuming $1 \mathrm{~kg}$ requires $580 \times 10^{3}$ cal for evaporation) is
(A) $0.25 \mathrm{~kg}$
(B) $2.25 \mathrm{~kg}$
(C) $0.05 \mathrm{~kg}$
(D) $0.20 \mathrm{~kg}$

Ajay Singhal

Numerade Educator

Problem 43

Consider $P=V$ diagram for an ideal gas shown in Fig. $12.15$.
Fig. $12.15$ Out of the following diagrams, which one represents the $T=P$ diagram?
(i)
(ii)
(iii)
(iv)
(A) (iv)
(B) (ii)
(C) (iii)
(D) (i)

Ajay Singhal

Numerade Educator

Problem 44

An ideal gas undergoes cyclic process $A B C D A$ as shown in given $P-V$ diagram. The amount of work done by the gas is.
(A) $6 P_{0} V_{0}$
(B) $-2 P_{0} V_{0}$
(C) $+2 P_{0} V_{0}$
(D) $+4 P_{0} V_{0}$

Ajay Singhal

Numerade Educator

Problem 45

Consider two containers $A$ and $B$ containing identical gases at the same pressure, volume, and temperature. The gas in container $A$ is compressed to half of its original volume isothermally while the gas in container $B$ is compressed to half of its original value adiabatically. The ratio of final pressure of gas in $B$ to that of gas in $A$ is
(A) $2^{\gamma-1}$
(B) $\left(\frac{1}{2}\right)^{\gamma-1}$
(C) $\left(\frac{1}{1-\gamma}\right)^{2}$
(D) $\left(\frac{1}{\gamma-1}\right)^{2}$

Ajay Singhal

Numerade Educator

Problem 46

Three copper blocks of masses $M_{1}, M_{2}$, and $M_{3} \mathrm{~kg}$, respectively, are brought in to thermal contact till they reach equilibrium. Before contact, they were at $T_{1}, T_{2}, T_{3}\left(T_{1}>T_{2}>T_{3}\right)$. Assuming there is no heat loss to the surroundings, the equilibrium temperature $T$ is $(s$ is specific heat of copper)
(A) $T=\frac{T_{1}+T_{2}+T_{3}}{3}$
(B) $T=\frac{M_{1} T_{1}+M_{2} T_{2}+M_{3} T_{3}}{M_{1}+M_{2}+M_{3}}$
(C) $T=\frac{M_{1} T_{1}+M_{2} T_{2}+M_{3} T_{3}}{3\left(M_{1}+M_{2}+M_{3}\right)}$
(D) $T=\frac{M_{1} T_{1} s+M_{2} T_{2} s+M_{3} T_{3} s}{M_{1}+M_{2}+M_{3}}$

Ajay Singhal

Numerade Educator

Problem 47

Two gases have same initial pressure, volume, and temperature. They expand to same final volume, one adiabatically and the other isothermally.
(A) The final temperature is greater for isothermal process.
(B) The final temperature is lesser for isothermal process.
(C) The work done by the gas is greater for isothermal process.
(D) The work done by the gas is greater for adiabatic process.

Ajay Singhal

Numerade Educator

Problem 48

Two moles of a monatomic ideal gas undergo a thermodynamic process $\frac{V^{3}}{T^{2}}=$ constant, if the temperature is raised by $300 \mathrm{~K}$ then
(A) Work done by the gas is $400 \mathrm{R}$.
(B) Change in internal energy is $900 R$.
(C) Molar heat capacity of the gas for the process is $13 / 6 R$.
(D) Molar heat capacity of the gas for the process is $3 / 2 R$.

Narayan Hari

Numerade Educator

Problem 49

Density $(\rho)$ versus temperature ( $T$ ) graph of a thermodynamic cycle of an ideal gas is as shown. If $B C$ and $A D$ are the part of rectangular hyperbola, then which of the following graphs will represent the same thermodynamic cycle.
(A)
(B)
(C)
(D)

Narayan Hari

Numerade Educator

Problem 50

In Fig. 12.16, the amount of heat supplied to one mole of an ideal gas is plotted on the horizontal axis, and the amount of work performed by the gas is plotted on vertical axis. The experiment is done on two gases. The initial states for both the gases are same. Two of the straight lines are isobars. Then (Given $\theta_{3}=45^{\circ}$, $\left.\theta_{2}=30^{\circ}, \theta_{1}=25^{\circ}\right)$
(A) Curve 3 corresponds to isothermal process.
(B) Curves 1 and 2 corresponds to isobaric process.
(C) Curves 3 and 2 corresponds to isobaric process.
(D) Curves 1 and 3 corresponds to isobaric process.

Narayan Hari

Numerade Educator

Problem 51

In the arrangement shown in Fig. $12.17$, gas is thermally insulated. An ideal gas is filled in the cylinder having pressure $P$ greater than atmospheric pressure $P_{0}$. The spring of force constant $K$ is initially upstretched. The piston of mass $m$ and area s is frictionless. In equilibrium, the piston rises up a distance $x_{0}$, then
(A) Final pressure of the gas is $P_{0}+\frac{K x_{0}}{s}+\frac{m g}{s}$.
(B) Work done by the gas is $\frac{1}{2} K x_{0}^{2}+m g x_{0}$.
(C) Decrease in internal energy of the gas is $\frac{1}{2} K x_{0}^{2}+m g x_{0}+P_{0} s x_{0}$
(D) All of the above.

Narayan Hari

Numerade Educator

Problem 52

A thermally insulated chamber of volume $2 V_{0}$ is divided by a frictionless piston of area $S$ into two equal parts, $A$ and $B$. Part $A$ has an ideal gas at pressure $P_{0}$ and temperature $T_{0}$, and in part $B$ is vacuum. A massless spring of force constant $k$ is connected with piston and the wall of the container is as shown. Initially, spring is unstretched. Gas in chamber $A$ is allowed to expand. Let the equilibrium spring be compressed by $x_{0}$. Then
(A) Final pressure of the gas is $\frac{k x_{0}}{S}$.
(B) Work done by the gas is $\frac{1}{2} k x_{0}^{2}$.
(C) Change in internal energy of the gas is $\frac{1}{2} k x_{0}^{2}$.
(D) Temperature of the gas is decreased.

Ajay Singhal

Numerade Educator

Problem 53

The temperature of the gas at point $B$ is
(A) $27^{\circ} \mathrm{C}$
(B) $235^{\circ} \mathrm{C}$
(C) $327^{\circ} \mathrm{C}$
(D) None of these

Narayan Hari

Numerade Educator

Problem 54

The heat absorbed by the gas in the process $A \rightarrow B$ is
(A) $1500 R$
(B) $900 R$
(C) 0
(D) $600 \mathrm{R}$

Narayan Hari

Numerade Educator

Problem 55

The total work done by the gas during the complete cycle is
(A) $900 R$
(B) $1500 R$
(C) 0
(D) $600 \mathrm{R}$

Ajay Singhal

Numerade Educator

Problem 56

For $n$ moles of an ideal gas while going through different thermodynamic process Column-I Column-II -
(A) Isobaric expansion
1. Internal energy increases
(B) Adiabatic
2. Internal energy expansion decreases
(C) Isothermal
3. Work done on the gas compression is positive
(D) Adiabatic
4. Heat change for the compression gas is positive

Ajay Singhal

Numerade Educator

Problem 57

Pressure versus volume graph of a thermodynamic cyclic process of an ideal gas is as shown. When the gas does work, $\Delta W>0$ and when heat is absorbed by the gas, $\Delta Q>0$
\begin{tabular}{ll}
\multicolumn{1}{c} { Column-I } & \multicolumn{1}{c} { Column-II } \\
\hline (A) In process J-K & 1. $\Delta Q>0$ \\
(B) In process $\mathrm{K}-\mathrm{L}$ & 2. $\Delta Q<0$ \\
(C) In process $\mathrm{L}-\mathrm{M}$ & 3. $\Delta W>0$ \\
(D) In process $\mathrm{M}-\mathrm{J}$ & 4. $\Delta W<0$
\end{tabular}

Ajay Singhal

Numerade Educator

Problem 58

Figure $12.19$ given below shows different thermodynamic processes for a given amount of an ideal gas. $W$ is work done by the system and $\Delta Q$ is heat absorbed by the system.
(I)
(II)
(III)
(B) In Figure (II)
2. $W<0$

Khoobchandra Agrawal

Khoobchandra Agrawal

Numerade Educator

Problem 59

One mole of an ideal monoatomic gas is taken round the cyclic process ABCA as shown in the Fig. $12.20$. Then match the quantities of Column-I with their values in Column-II.
$12.20$
Column-I Column-II
path $C A$
(A) Heat exchange by the gas in
1. $-\frac{5}{2} P_{0} V_{0}$
(B) Heat exchange by the gas in
2. $3 P_{0} V_{0}$
path $A B$
path $B C$
(C) Heat exchange by the gas in
3. $\frac{P_{0} V_{0}}{2}$
(D) Net work done during $A B C A$
4. $P_{0} V_{0}$
is

Khoobchandra Agrawal

Khoobchandra Agrawal

Numerade Educator

Problem 60

Assertion: Suppose $\Delta Q$ is the heat given to an ice cube to melt it. Magnitude of work done by ice on surroundings is $\Delta W$. Then $\Delta U=\Delta Q-\Delta W$ Reason: First law of thermodynamics cannot be applied in this situation.
(A) A
(B) $\mathrm{B}$
(C) $\mathrm{C}$
(D) D

Ajay Singhal

Numerade Educator

Problem 61

Assertion: For an ideal gas, internal energy change is zero if the temperature is constant, irrespective of the process being cyclic or non-cyclic. Reason: $d U=n C_{v} d T$ for all processes and is independent of path.
(A) A
(B) $\mathrm{B}$
(C) $\overline{\mathrm{C}}$
(D) $\mathrm{D}$

Ajay Singhal

Numerade Educator

Problem 62

Assertion: In a complete thermodynamic cycle heat supplied to a system can be completely converted into mechanical work without rejecting any heat to the surrounding. Reason: Net change in internal energy in a cyclic process is zero.
(A) $\mathrm{A}$
(B) $\underline{B}$
(C) $\mathrm{C}$
(D) D

Ajay Singhal

Numerade Educator

Problem 63

Assertion: Adiabatic compressibility of an ideal gas is greater than its isothermal compressibility at same pressure. Reason: Slope of adiabatic $P=V$ graph has greater magnitude than the slope of isothermal $P=V$ graph at same pressure.
(A) $\mathrm{A}$
(B) $\mathrm{B}$
(C) $\mathrm{C}$
(D) $\overline{\mathrm{D}}$

Ajay Singhal

Numerade Educator

Problem 64

An insulated container is divided into two equal parts. One part contains an ideal gas at pressure $P$ and temperature $T$, while the other part is a perfect vacuum. If a hole is opened between the two parts, find the change in the temperature of the gas.

Narayan Hari

Numerade Educator

Problem 65

Water flows at the rate of $0.1500 \mathrm{~kg} / \mathrm{min}$ through a tube and is heated by a heater dissipating $25.2 \mathrm{~W}$. The inflow and outflow water temperatures are $15.2^{\circ} \mathrm{C}$ and $17.4^{\circ} \mathrm{C}$, respectively. When the rate of flow is increased to $0.2318 \mathrm{~kg} / \mathrm{min}$ and the rate of heating to $37.8 \mathrm{~W}$, the inflow and outflow temperatures are unaltered. Find:
(A) The specific heat capacity of water.
(B) The rate of loss of heat from the tube.

Khoobchandra Agrawal

Khoobchandra Agrawal

Numerade Educator

Problem 66

One mole of a gas is enclosed in a cylinder and occupies a volume of $1.51$ at a pressure $1.2$ atm. It is subjected to strong heating due to which temperature of the gas increases according to the relation $T=\alpha V^{2}$, where $\alpha$ is a positive constant and $V$ is volume of the gas.
(A) Find the work done by air in increasing the volume of gas to 91 .
(B) Draw the $P-V$ diagram of the process.
(C) Determine the heat supplied to the gas assuming $\gamma=1.5$

Khoobchandra Agrawal

Khoobchandra Agrawal

Numerade Educator

Problem 67

A cylinder contains $\mathrm{He}$ and $\mathrm{O}_{2}$ of equal volume, separated by a massless freely movable piston as shown in Fig. 12.21. If the gas is adiabatically compressed by moving the upper piston, so that volume of $\mathrm{He}$ becomes half, then find the volume occupied by $\mathrm{O}_{2}$. Cross-section area of cylinder is $A$.

Khoobchandra Agrawal

Khoobchandra Agrawal

Numerade Educator

Problem 68

Even Carnot engine cannot give $100 \%$ efficiency because we cannot
(A) prevent radiation.
(B) find ideal sources.
(C) reach absolute zero temperature.
(D) eliminate friction.

Narayan Hari

Numerade Educator

Problem 69

Which statement is incorrect?
(A) All reversible cycles have same efficiency.
(B) Reversible cycle as more efficiency than an 7 . irreversible one.
(C) Carnot cycle is a reversible one.
(D) Carnot cycle has the maximum efficiency in all cycles.

Narayan Hari

Numerade Educator

Problem 70

'Heat cannot be itself flow from a body at lower temperature to a body at higher temperature' is a statement or consequence of $[\mathbf{2 0 0 3}]$
(A) Second law of thermodynamics.
(B) Conservation of momentum.
(C) Conservation of mass.
(D) First law of thermodynamics.

Narayan Hari

Numerade Educator

Problem 71

During an adiabatic process, the pressure of a gas is found to be proportional to the cube of its absolute temperature. The ratio $C_{P} / C_{V}$ for the gas is [2003]
(A) $4 / 3$
(B) 2
(C) $5 / 3$
(D) $3 / 2$

Narayan Hari

Numerade Educator

Problem 72

Which of the following parameters does not characterize the thermodynamics state of matter? [2003]
(A) Temperature
(B) Pressure
(C) Work
(D) Volume

Narayan Hari

Numerade Educator

Problem 73

A Carnot engine takes $3 \times 10^{6}$ cal of heat from a reservoir at $627^{\circ} \mathrm{C}$ and gives it to a sink at $27^{\circ} \mathrm{C}$. The work done by the engine is [2003]
(A) $4.2 \times 10^{6} \mathrm{~J}$
(B) $8.4 \times 10^{6} \mathrm{~J}$
(C) $16.8 \times 10^{6} \mathrm{~J}$
(D) Zero

Narayan Hari

Numerade Educator

Problem 74

Which of the following statements is correct for any thermodynamic system?
(A) The internal energy changes in all processes.
(B) Internal energy and entropy are state functions.
(C) The change in entropy can never be zero.
(D) The work done in an adiabatic process is always zero.

Narayan Hari

Numerade Educator

Problem 75

A system goes from $A$ to $B$ via two processes $I$ and II as shown in Fig. 12.22. If $\Delta U_{1}$ and $\Delta U_{2}$ are the changes in internal energies in the processes I and II, respectively, then
(A) $\Delta U_{1}=\Delta U_{2}$
(B) relation between $\Delta U_{1}$ and $\Delta U_{2}$ cannot be determined.
(C) $\Delta U_{2}>\Delta U_{1}$.
(D) $\Delta U_{2}<\Delta U_{1}$.

Narayan Hari

Numerade Educator

Problem 76

The temperature-entropy diagram of a reversible engine cycle is given in the Fig. $12.23$. Its efficiency is $[2005]$
Fig. $12.23$
(A) $\frac{1}{2}$
(B) $\frac{1}{4}$
(C) $\frac{1}{3}$
(D) $\frac{2}{3}$

Narayan Hari

Numerade Educator

Problem 77

Which of the following is incorrect regarding the first law of thermodynamics? $[2005]$
(A) It is not applicable to any cyclic process.
(B) It is a restatement of the principle of conservation of energy.
(C) It introduces the concept of the internal energy.
(D) It introduces the concept of the entropy.

Narayan Hari

Numerade Educator

Problem 78

The work of $146 \mathrm{~kJ}$ is performed in order to compress 1 kilo mole of a gas adiabatically, and in this process, the temperature of the gas increases by $7^{\circ} \mathrm{C}$. The gas is $\left(\mathrm{R}=8.3 \mathrm{~J} \mathrm{~mol}^{-1} \mathrm{~K}^{-1}\right)$
(A) diatomic.
(B) triatomic.
(C) a mixture of monoatomic and diatomic.
(D) monatomic.

Narayan Hari

Numerade Educator

Problem 79

When a system is taken from state $i$ to state $f$ along the path iaf, it is found $Q=50 \mathrm{cal}$ and $W=20$ cal. Along the path $i b f, Q=36$ cal. $W$ along the path $i b f$ is [2007]
(A) $6 \mathrm{cal}$
(B) $16 \mathrm{cal}$
(C) $66 \mathrm{cal}$
(D) $14 \mathrm{cal}$

Ajay Singhal

Numerade Educator

Problem 80

A Carnot engine, having an efficiency of $\eta=\frac{1}{10}$ as heat engine is used as a refrigerator. If the work done on the system is $10 \mathrm{~J}$, the amount of energy absorbed from the reservoir at lower temperature is [2007]
(A) $99 \mathrm{~J}$
(B) $90 \mathrm{~J}$
(C) $1 \mathrm{~J}$
(D) $100 \mathrm{~J}$

Narayan Hari

Numerade Educator

Problem 81

An insulated container of gas has two chambers separated by an insulating partition. One of the chambers has volume $V_{1}$ and contains ideal gas at pressure $P_{1}$ and temperature $T_{1}$. The other chamber has volume $V_{2}$ and contains ideal gas at pressure $P_{2}$ and temperature $T_{2}$. If the partition is removed without doing any work on the gas, the final equilibrium temperature of the gas in the container will be:
(A) $\frac{T_{1} T_{2}\left(P_{1} V_{1}+P_{2} V_{2}\right)}{P_{1} V_{1} T_{1}+P_{2} V_{2} T_{2}}$
(B) $\frac{T_{1} T_{2}\left(P_{1} V_{1}+P_{2} V_{2}\right)}{P_{1} V_{1} T_{2}+P_{2} V_{2} T_{1}}$
(C) $\frac{P_{1} V_{1} T_{1}+P_{2} V_{2} T_{2}}{P_{1} V_{1}+P_{2} V_{2}}$
(D) $\frac{P_{1} V_{1} T_{2}+P_{2} V_{2} T_{1}}{P_{1} V_{1}+P_{2} V_{2}}$

Ajay Singhal

Numerade Educator

Problem 82

The net work done on the gas in the cycle $A B C D A$ is $[2009]$
(A) Zero
(B) $276 R$
(C) $1076 R$
(D) $1904 R$

Khoobchandra Agrawal

Khoobchandra Agrawal

Numerade Educator

Problem 83

A diatomic ideal gas is used in a Carnot engine as the working substance. If during the adiabatic expansion, part of the cycle and the volume of the gas increases from $\mathrm{V}$ to $32 \mathrm{~V}$, the efficiency of the engine is [2010]
(A) $0.25$
(B) $0.5$
(C) $0.75$
(D) $0.99$

Narayan Hari

Numerade Educator

Problem 84

Three perfect gases at absolute temperatures, $T_{1}, T_{2}$, and $T_{3}$, are mixed. The masses of molecules are $m_{1}, m_{2}$, and $m_{3}$ and the number of molecules are $n_{1}, n_{2}$, and $n_{3}$, respectively. Assuming no loss of energy, the final temperature of the mixture is [2011]
(A) $\frac{\left(T_{1}+T_{2}+T_{3}\right)}{3}$
(B) $\frac{n_{1} T_{1}+n_{2} T_{2}+n_{3} T_{3}}{n_{1}+n_{2}+n_{3}}$
(C) $\frac{n_{1} T_{1}^{2}+n_{2} T_{2}^{2}+n_{3} T_{3}^{3}}{n_{1} T_{1}+n_{2} T_{2}+n_{3} T_{3}}$
(D) $\frac{n_{1}^{2} T_{1}^{2}+n_{2}^{2} T_{2}^{2}+n_{3}^{3} T_{3}^{3}}{n_{1} T_{1}+n_{2} T_{2}+n_{3} T_{3}}$

Narayan Hari

Numerade Educator

Problem 85

Helium gas goes through a cycle $A B C D A$ (consisting of two isochoric and two isobaric lines) as shown in Fig. 12.23. Efficiency of this cycle is nearly (Assume the gas to be close to ideal gas) [2012]
Fig. $12.23$
(A) $15.4 \%$
(B) $9.1 \%$
(C) $10.5 \%$
(D) $12.5 \%$

Ajay Singhal

Numerade Educator

Problem 86

A Carnot engine, whose efficiency is $40 \%$, takes heat from a source maintained at a temperature of $500 \mathrm{~K}$. It is desired to have an engine of efficiency $60 \%$. Then, the intake temperature for the same exhaust (sink) temperature must be:
[2012]
(A) Efficiency of Carnot engine cannot be made larger than $50 \%$
(B) $1200 \mathrm{~K}$
(C) $750 \mathrm{~K}$
(D) $600 \mathrm{~K}$

Narayan Hari

Numerade Educator

Problem 87

The above $\mathrm{p}=\mathrm{v}$ diagram represents the thermodynamic cycle of an engine, operating with an ideal monoatomic gas. The amount of heat extracted from the source in a single cycle is
(A) $\left(\frac{13}{2}\right) p_{0} v_{0}$
(B) $\left(\frac{11}{2}\right) p_{0} v_{0}$
(C) $4 p_{0} v_{0}$
(D) $p_{0} v_{0}$

Ajay Singhal

Numerade Educator

Problem 88

One mole of diatomic ideal gas undergoes a cyclic process $A B C$ as shown in Fig. 12.24. The process $B C$ is adiabatic. The temperatures at $A, B$, and $C$ are $400 \mathrm{~K}$, $800 \mathrm{~K}$, and $600 \mathrm{~K}$, respectively. Choose the correct statement.
Fig. $12.24$
(A) The change in internal energy in whole cyclic process is $250 \mathrm{R}$.
(B) The change in internal energy in the process $C A$ is $700 \mathrm{R}$.
(C) The change in internal energy in the process $A B$ is $-350 \mathrm{R}$.
(D) The change in internal energy in the process $B C$ is $-500 \mathrm{R}$.

Narayan Hari

Numerade Educator

Problem 89

Consider an ideal gas confined in an isolated closed chamber. As the gas undergoes an adiabatic expansion, the average time of collision between molecules increases as $V^{q}$, where $V$ is the volume of the gas. The value of $q$ is $\left(\gamma=\frac{C_{p}}{C_{v}}\right)$ [2015]
(A) $\frac{3 \gamma-5}{6}$
(B) $\frac{\gamma+1}{2}$
(C) $\frac{\gamma-1}{2}$
(D) $\frac{3 \gamma+5}{6}$

Ajay Singhal

Numerade Educator

Problem 90

$n$ moles of an ideal gas undergoes a process $A \rightarrow B$ as shown in the figure. The maximum temperature of the gas during the process will be
(A) $\frac{3 P_{0} V_{0}}{2 n R}$
(B) $\frac{9 P_{0} V_{0}}{2 n R}$
(C) $\frac{9 P_{0} V_{0}}{n R}$
(D) $\frac{9 P_{0} V_{0}}{4 n R}$

Ajay Singhal

Numerade Educator

Problem 91

An ideal gas undergoes a quasi-static, reversible process in which its molar heat capacity $C$ remains constant. If during this process the relation of pressure $P$ and volume $V$ is given by $P V^{n}=$ constant, then $n$ is given by (Here $C_{P}$ and $C_{V}$ are molar specific heat of constant pressure and constant volume, respectively) [2016]
(A) $n=\frac{C-C_{P}}{C-C_{V}}$
(B) $n=\frac{C_{P}-C}{C-C_{V}}$
(C) $n=\frac{C-C_{V}}{C-C_{P}}$
(D) $n=\frac{C_{P}}{C_{V}}$

Narayan Hari

Numerade Educator