Arihant AIEEE Physics

D.B. Singh

Chapter 17

Laws of Thermodynamics - all with Video Answers

Educators

Chapter Questions

Problem 1

A boy weighing $50 \mathrm{~kg}$ eats bananas. The energy content of banana is $1000 \mathrm{cal}$, if this energy is used to lift the boy from ground, then the height through which he is lifted :
(a) $8.57 \mathrm{~m}$
(b) $10.57 \mathrm{~m}$
(c) $6.57 \mathrm{~m}$
(d) $5.57 \mathrm{~m}$

Ajay Singhal

Ajay Singhal

Numerade Educator

Problem 2

Which one of the following reversible cycles, represented by right angled triangles in a $T$ -S diagram, is the least efficient?

Ajay Singhal

Numerade Educator

Problem 3

An ideal gas is heated at constant pressure and absorbs amount of heat $Q$. If the adiabatic exponent is $\gamma$, then the fraction of heat absorbed in raising the internal energy and performing the work, is:
(a) $1-\frac{i}{\gamma}$
(b) $1+\frac{1}{\gamma}$
(c) $1-\frac{2}{\gamma}$
(d) $1+\frac{2}{\gamma}$

Ajay Singhal

Numerade Educator

Problem 4

The work done $\left(W_{A B}\right)$ by the gas, if 5 moles of an ideal gas is carried by a quasi state isothermal process at $500 \mathrm{~K}$ to twice its volume, is:
(a) $1500 \mathrm{~J}$
(b) $14407 \mathrm{~J}$
(c) $13380 \mathrm{~J}$
(d) $14890 \mathrm{~J}$

Ajay Singhal

Numerade Educator

Problem 5

The work done for the cycle shown in given figure, will be:
(a) $45 \mathrm{~J}$
(b) $54 \mathrm{~J}$
(c) $22.5 \mathrm{~J}$
(d) $32.5 \mathrm{~J}$

Ajay Singhal

Numerade Educator

Problem 6

A cyclic process for 1 mole of an ideal gas is shown in the $V-T$ diagram. The work done in $A B, B C$ and $C A$ respectively are:
(a) $0, R T_{1} \ln \left|\frac{V_{1}}{V_{2}}\right|, R\left(T_{1}-T_{2}\right)$
(b) $R\left(T_{1}-T_{2}\right), R, R T_{1} \ln \left|\frac{V_{1}}{V_{2}}\right|$
(c) $0, R T_{2} \ln \left|\frac{1 / 2}{\ddot{V}_{1}}\right|, \frac{R T_{1}}{V_{1}}\left(V_{1}-V_{2}\right)$
(d) $0, R T_{2} \ln \left|\frac{V_{1}}{V_{2}}\right|, R\left(T_{2}-T_{1}\right)$

Baskar P

Numerade Educator

Problem 7

An ideal monoatomic gas is taken around the cycle $A B C D A$ as shown in the $P-V$ diagram. The work done during cycle is given by:
(a) $\frac{1}{2} P V$
(b) $P V$
(c) $2 P V$
(d) $4 P V$

Ajay Singhal

Numerade Educator

Problem 8

Three moles of an ideal monoatomic gas performs a cycle as shown in the fig. The gas temperature in different states are $T_{1}=400 \mathrm{~K}, \quad T_{2}=800 \mathrm{~K}$,
$T_{3}=2400 \mathrm{~K}, T_{4}=1200 \mathrm{~K} .$ What
is the work done by the gas during the cycle ?
(a) $10 \mathrm{~kJ}$
(b) $20 \mathrm{~kJ}$
(c) $5 \mathrm{~kJ}$
(d) $8.3 \mathrm{~kJ}$

Ajay Singhal

Numerade Educator

Problem 9

In the given elliptical $P$ - $V$ diagram :
(a) the work done is positive
(b) the change in internal energy is non- zero
(c) the work done $=-\frac{\pi}{4}\left(P_{2}-P_{1}\right)\left(V_{2}-V_{1}\right)$
(d) the work done $=\pi\left(V_{2}-V_{1}\right)^{2}=\pi\left(P_{2}-P_{1}\right)^{2}$

Ajay Singhal

Numerade Educator

Problem 10

A mass of monoatomic gas is taken through a cycle as indicated in the diagram. The efficiency of the cycle is :
(a) $\frac{2}{12-\pi}$
(b) $\frac{2 \pi}{12+\pi}$
(c) $\frac{2 \pi}{24-\pi}$
(d) $\frac{1}{12-\pi}$

Ajay Singhal

Numerade Educator

Problem 11

A balloon that is initially flat, is inflated by filling it from a tank of compressed air. The final volume of the balloon is $5 \mathrm{~m}^{2}$. The barometer reads $95 \mathrm{kPa}$. The work done in this process is:
(a) $475 \times 10^{\overline{3}} \mathrm{~J}$
(b) $4.75 \times 10^{7} \mathrm{~J}$
(c) $4.75 \times 10^{3} \mathrm{~J}$
(d) $4.75 \times 10^{-} \mathrm{J}$

Ajay Singhal

Numerade Educator

Problem 12

What work will be done, when 3 moles of an ideal gas are compressed to half the initial volume at a constant temperature of $300 \mathrm{~K}$ ?
(a) $-5188 \mathrm{~J}$
(b) $5000 \mathrm{~J}$
(c) $5188 \mathrm{~J}$
(d) $-5000 \mathrm{~J}$

Ajay Singhal

Numerade Educator

Problem 13

Two moles of an ideal gas at a temperature of $T=273 \mathrm{~K}$ was isothermally expanded 4 times the initial volume and then heated isochorically, so that the final pressure becomes equal to the initial pressure. The ratio of molar specific heat capacities if total amount of heat imparted to the gas equals $Q=27.7 \mathrm{~kJ}$, is :
(a) $1.63$
(b) $1.66$
(c) $2.63$
(d) $1.49$

Ajay Singhal

Numerade Educator

Problem 14

A gas is contained in a cylinder and expands according to the relation $P V^{1.3}=$ constant. The initial pressure and initial volume of the gas is $30 \mathrm{~atm}$ and $30 \mathrm{~mm}^{3}$ respectively. If the final pressure is $15 \mathrm{~atm}$, then the work done on the face of piston by the pressure force of the gas, is :
(a) $5 \times 10^{i} \mathrm{~J}$
(b) $4.35 \times 10^{4} \mathrm{~J}$
(c) $3 \times 10^{4} \mathrm{~J}$
(d) $4 \times 10^{4} \mathrm{~J}$

Ajay Singhal

Numerade Educator

Problem 15

Two moles of an ideal monoatomic gas is confined in a cylinder by a spring loaded piston of cross-section area $4 \times 10^{-3} \mathrm{~m}$ - Initially the spring of spring constant $k=1920 \mathrm{~N} / \mathrm{m}$ is in its relaxed state. Now, the gas was heated by an electric heater, placed inside the cylinder, for some time and due to which gas expands and does $50 \mathrm{~J}$ of work in moving piston through a distance of $0.1 \mathrm{~m}$. The temperature of the gas increases by $50 \mathrm{~K}$. Assume piston and spring to be massless and there is no friction between the piston and the cylinder. Heat supplied by the heater:
(a) $1295 \mathrm{~J}$
(b) $1200 \mathrm{~J}$
(c) $1195 \mathrm{~J}$
(d) $1350 \mathrm{~J}$

Ajay Singhal

Numerade Educator

Problem 16

One mole of an ideal gas is enclosed in a conducting vertical cylinder under a light piston. If isothermally the volume of the gas is increased $n$ times, then the work done in increasing the volume is : [Assume atmospheric pressure is $P_{0}$ and temperature is $\left.T_{0}\right]$
(a) $R T_{0} \log _{e} n$
(b) $-R T_{0} \log _{t} n$
(c) $R T_{0} \log _{c} n-(n-1) R T_{0}$
(d) $(n-1) R T_{0}-R T_{0} \log _{e} n$

Ajay Singhal

Numerade Educator

Problem 17

If we consider molecules of an ideal gas in a box with a frictionless piston and now the box is heated and piston moves slowly outwards, then:
(a) the force on piston is due to molecular collision with piston
(b) the molecules collide with piston and return back with same speed
(c) the molecular collision with piston is inelastic
(d) both (a) and (b) are correct

Ajay Singhal

Numerade Educator

Problem 18

A vertical cylinder is divided into two parts by a frictionless piston in the ratio of $5: 4$. The piston is free to slide along the length of the vessel and length of the vessel is $90 \mathrm{~cm}$. Each of the two parts of the vessel contains $0.1$ mole of an ideal gas and the temperature of gas is $300 \mathrm{~K}$. The mass of the piston is:
(a) $14 \mathrm{~kg}$
(b) $12.7 \mathrm{~kg}$
(c) $16 \mathrm{~kg}$
(d) $15 \mathrm{~kg}$

Ajay Singhal

Numerade Educator

Problem 19

An adiabatic cylinder closed at both ends consists of a freely moving non-coducting thin piston which divides the cylinder into two equal parts and each part contains $28 \mathrm{~g}$ of $\mathrm{N}_{2}$. Initially $1 / 3 \mathrm{rd}$ molecules of nitrogen in the right part are dissociated into atoms. The length of the cylinder is $1 \mathrm{~m}$ and area of cross-section is $10^{-2} \mathrm{~m}^{2}$. The natural length of the spring connected to the piston and right wall of the cylinder is $l-50 \mathrm{~cm}$ and $k=\sqrt{2} \times 10^{3} \mathrm{~N} / \mathrm{m}$. If the initial pressure in each part is $P_{0}=\sqrt{2} \times 10^{5} \mathrm{~N} / \mathrm{m}^{2}$ that what work must be done by the gas in the right part?
(a) $-1414 \mathrm{~J}$
(b) $1414 \mathrm{~J}$
(c) $-1515 \mathrm{~J}$
(d) $1515 \mathrm{~J}$

Surendra Kumar

Numerade Educator

Problem 20

When a gas is allowed to expand suddenly into a vacuum chamber, then :
(a) heat supplied is zero
(b) temperature remains constant
(c) volume does not change
(d) both (a) and (b) are correct

Ajay Singhal

Numerade Educator

Problem 21

During an isothermal expansion of an ideal gas:
(a) its internal energy decreases
(b) its internal energy does not change
(c) the work done by the gas is equal to the quantity of heat absorbed by it
(d) both (b) and (c) are correct

Ajay Singhal

Numerade Educator

Problem 22

If a gas is compressed adiabatically:
(a) the internal energy of gas increases
(b) the internal energy of gas decreases
(c) the internal energy of gas does not change
(d) the work done is positive

Ajay Singhal

Numerade Educator

Problem 23

In a polytropic process, $P V^{n}=$ constant :
(a) If $n=1$, process is isothermal
(b) If $n=\infty$, process is isochoric
(c) If $n=0$, process is isobaric
(d) all the above

Ajay Singhal

Numerade Educator

Problem 24

In a given process for ideal gas, $d W=0$ and $d H>0$. Then for the gas :
(a) the volume remains constant
(b) the volume will increase
(c) temperature will increase
(d) both (a) and (c) are correct

Ajay Singhal

Numerade Educator

Problem 25

P-V diagram for adiabatic process is shown in the figure. Then:
(a) $v_{1}>v_{2}>v_{3}$
(b) $v_{1}<v_{2}<v_{3}$
(c) $v_{1}>v_{3}>v_{2}$
(d) none of the above

Ajay Singhal

Numerade Educator

Problem 26

In the given graph, adiabatic and isothermal curves are shown:
(a) the curve $A$ is isothermal
(b) the curve $B$ is isothermal
(c) the curve $A$ is adiabatic
(d) the curve $B$ is adiabatic
(e) both (b) and (c) are correct

Ajay Singhal

Numerade Educator

Problem 27

The process on an ideal gas, shown in figure is :
(a) isothermal
(b) isobaric
(c) isochoric
(d) none of the above

Ajay Singhal

Numerade Educator

Problem 28

Which of the following best represents the process of above problem?

Ajay Singhal

Numerade Educator

Problem 29

A thermodynamic cycle of an ideal gas is shown in the figure. Choose the correct option which represents the same cycle:

Ajay Singhal

Numerade Educator

Problem 30

$n$ moles of an ideal gas undergoes a process $1-2$ as shown in figure. Maximum temperature of gas during process is :
(a) $\frac{3 P_{0} V_{0}}{n R}$
(b) $\frac{4 P_{0} V_{0}}{n R}$
(c) $\frac{6 P_{0} V_{0}}{n R}$
(d) $\frac{9 P_{0} V_{0}}{n R}$

Ajay Singhal

Numerade Educator

Problem 31

$0.2$ moles of an ideal gas, is taken rouna the cvcle $a b c$ as shown in the figure. The path $b-c$ is adiabaric , ness, $a-b$ is isovolumic process and $c-a$ is isobaric process. The temperature at ' $a$ ' and ' $b$ ' are $T_{a}=300 \mathrm{~K}$ and $\quad T_{b}=500 \mathrm{~K}$
and pressure at ' $a^{\prime}$ is 1 atmosphere. The volume at $' c^{\prime}$ is :
(Given: $\gamma=\frac{C_{P}}{C_{V}}=\frac{5}{3}$, $R=8.205 \times 10^{-2}$ litre/atm/mol-K)
(a) $6.9 \mathrm{~L}$
(b) $6.68 \mathrm{~L}$
(c) $5.52 \mathrm{~L}$
(d) $5.82 \mathrm{~L}$

Ajay Singhal

Numerade Educator

Problem 32

The $P-V$ diagram shows that two adiabatic parts for the same gas intersect two isothermals at $I_{1}$ and $T_{2}$. How the ratio $\left(V_{a} / V_{d}\right)$ and $\left(V_{b} / V_{c}\right)$ are related to each other?
(a) $\left(\frac{V_{a}}{V_{d}}\right)=2\left(\frac{V_{b}}{V_{r}}\right)$
(b) $\left(\frac{V_{a}}{V_{d}}\right)=\left(\frac{V_{b}}{V_{c}}\right)$
(c) $\left(\frac{V_{a}}{V_{c}}\right)=\left(\frac{V_{b}}{V_{d}}\right)$
(d) $\left(\frac{V_{a}}{V_{c}}\right)=\left(\frac{V_{b}}{V_{r}}\right)^{2}$

Ajay Singhal

Numerade Educator

Problem 33

In $P-V$ graph of an ideal gas, which describe the adiabatic process:
(a) $A B$ and $B C$
(b) $A B$ and $C D$
(c) $A D$ and $B C$
(d) $B C$ and $C D$

Ajay Singhal

Numerade Educator

Problem 34

The initial state of an ideal gas is represented by the point $a$ on the $P-V$ diagram and its final state by the point $e$. The gas goes from the state $a$ to the state $e$ by:
(i) abe (ii) ace
(iii) ade The heat absorbed by the gas is :
(a) the same in all the three processes
(b) the same in processes (i) and (ii)
(c) greater in process (i) than in (iii)
(d) nene cf the above

Ajay Singhal

Numerade Educator

Problem 35

In the given $P-V$ diagram the path (2) from $A$ to $B$ is zig-zag path, but (1) is simple path. Then:
(a) $W_{1}=W_{2}$
(b) $\Delta U_{1}=\Delta U_{2}$
(c) $W_{1}>W_{2}$
(d) both (b) and (c) are correct

Ajay Singhal

Numerade Educator

Problem 36

A thermodynamic process is defined for an ideal gas. In this process $P V^{n}=$ constant. Mark the correct options:
(a) $n_{1}>n_{2}>n_{3}>n_{4}$
(b) $n_{2}>n_{1}>n_{4}>n_{3}$
(c) $n_{2}>n_{4}>n_{3}>n_{1}$
(d) None of the above

Ajay Singhal

Numerade Educator

Problem 37

At $27^{\circ} \mathrm{C}$, a motor car tyre has a pressure of 2 atmospheres. The temperature, if the tyre suddenly burst will be : (Given: $\gamma_{\text {air }}=1.4$ )
(a) $246.1 \mathrm{~K}$
(b) $250 \mathrm{~K}$
(c) $246.1^{\circ} \mathrm{C}$
(d) $248 \mathrm{~K}$

Ajay Singhal

Numerade Educator

Problem 38

If $V^{\prime}$ is the volume of a vessel, which is to be evacuated by means of a piston air pump, then how many strokes are required to reduce the pressure in the vessel $\eta$ times? One piston stroke captures the volume $\Delta V$. Assume the process to be isothermal and the gas ideal:
(a) $n=\frac{\log \eta}{\log \left(1-\frac{\Delta V}{V}\right)}$
(b) $n \cdot=\frac{\log \eta}{\log \left[1+\frac{\Delta V}{V}\right)}$
(c) $n=\frac{\log \eta}{\log \left(\frac{\Delta V}{V}\right)}$
(d) None of these

Ajay Singhal

Numerade Educator

Problem 39

A process on one mole of an ideal gas is defined as follow:
$$
\begin{aligned}
\left(P_{A}, V_{A}, T_{A}\right) & \longrightarrow\left(P=a, V=2 V_{A}, T=T_{A}\right) \\
& \longrightarrow\left(P_{1}=P, V_{1}=2 V_{A}, T_{1}=b\right) \\
& \longrightarrow\left(P_{2}=P_{A}, V_{2}=V_{A}, T_{2}=c\right)
\end{aligned}
$$
The values of $a, b$, and $c$ are :
(a) $\left(\frac{P_{A}}{2}, \frac{T_{A}}{2}, T_{A}\right)$
(b) $\left(P_{A}, T_{A}, T_{A}\right)$
(c) $\left(\frac{P_{A}}{4}, \frac{T_{A}}{4,} \frac{T_{A}}{3}\right)$
(d) none of these

Ajay Singhal

Numerade Educator

Problem 40

The value of $\frac{T_{B}}{I_{C}}$ is
(a) 1
(b) 2
(c) 3
(d) 4

Ajay Singhal

Numerade Educator

Problem 41

The table given below shows two different processes. Calculate the unknown values with help of first law of thermodynamics. All the data are in joule:
\begin{tabular}{crcccc}
Process & $\Delta Q$ & $\Delta W$ & $U_{1}$ & $U_{j}$ & $\Delta U=U_{f}-U_{f}$ \\
\hline $1 .$ & 35 & $\ldots$ & $-60$ & $\ldots$ & 50 \\
$2 .$ & $-15$ & $\ldots$ & 80 & 60 & $\ldots$
\end{tabular}
(a) for process $1 \rightarrow \Delta W=-15 \mathrm{~J} ; \quad U_{f}=-10 \mathrm{~J}$
for process $2 \rightarrow \Delta W=5 \mathrm{~J} ; \quad \Delta U=-20 \mathrm{~J}$
(b) for process $1 \rightarrow \Delta W=15 \mathrm{~J} ; \quad u_{f}=10 \mathrm{~J}$
for process $2 \rightarrow \Delta W=-5 \mathrm{~J} ; \quad \Delta U=-20 \mathrm{~J}$
(c) for process $1 \rightarrow \Delta W=-5 \mathrm{~J} ; \quad U_{f}=20 \mathrm{~J}$
for process $2 \rightarrow \Delta W=15 \mathrm{~J} ; \quad \Delta U=-10 \mathrm{~J}$
(d) data incompiete

Ajay Singhal

Numerade Educator

Problem 42

In an adiab-tic expansion, a gas does $25 \mathrm{~J}$ of work while in an adiabatic compression 100J of work is done on a gas. The change of internal energy in the two processes respectively are:
(a) $25 \mathrm{~J}$ and $-100 \mathrm{~J}$
(b) $-25 \mathrm{~J}$ and $100 \mathrm{~J}$
(c) $-25 \mathrm{~J}$ and $-100 \mathrm{~J}$
(d) $25 \mathrm{~J}$ and $100 \mathrm{~J}$

Ajay Singhal

Numerade Educator

Problem 43

A closed system undergoes a change of state by process $1 \rightarrow 2$ for which $Q_{12}=10 \mathrm{~J}$ and $W_{12}=-5 \mathrm{~J}$. The system is now returned to its initial state by a different path $2 \rightarrow 1$ for which $Q_{21}$ is $-3 \mathrm{~J}$. The total energy for the cycle is :
(a) $-8 \mathrm{~J}$
(b) zero
(c) $-2 \mathrm{~J}$
(d) $+5 \mathrm{~J}$

Ajay Singhal

Numerade Educator

Problem 44

Electrolysis is:
(a) reversible process
(b) irreversible process
(c) either reversible or irreversible
(d) neither reversible or irreversible

Ajay Singhal

Numerade Educator

Problem 45

The molar heat capacity of oxygen gas at STP is nearly 2.5R. As the temperature is increased, it gradually increases and approaches $3.5 R$. The most appropriate reason for this behaviour is that at high temperature:
(a) oxygen does not behave as an ideal gas
(b) oxygen molecules dissociate in atoms
(c) the molecules collide more frequently
(d) molecular vibrations gradually become effective

Ajay Singhal

Numerade Educator

Problem 46

During adiabatic change, specific heat is:
(a) zero
(b) greater than zero
(c) less than zero
(d) infinity

Ajay Singhal

Numerade Educator

Problem 47

Molar heat capacity is directly related to:
(a) temperature
(b) heat energy
(c) molecular structure
(d) mass

Ajay Singhal

Numerade Educator

Problem 48

If at NTP, velocity of sound in a gas is $1150 \mathrm{~m} / \mathrm{s}$, then the rms velocity of gas molecules at NTP is :
(Given: $R=8.3$ joule $\left./ \mathrm{mol} / \mathrm{K}, \mathrm{C}_{P}=4.8 \mathrm{cal} / \mathrm{mol} / \mathrm{K}\right)$
(a) $1600 \mathrm{~m} / \mathrm{s}$
(b) $1532.19 \mathrm{~m} / \mathrm{s}$
(c) $160 \mathrm{~m} / \mathrm{s}$
(d) $16 \mathrm{~m} / \mathrm{s}$

Ajay Singhal

Numerade Educator

Problem 49

What is the molar heat capacity for the process, when $10 \mathrm{~J}$ of heat added to a monoatomic ideal gas in a process in which the gas performs a work of $5 \mathrm{~J}$ on its surrounding?
(a) $2 R$
(b) $3 R$
(c) $4 R$
(d) $5 R$

Ajay Singhal

Numerade Educator

Problem 50

A gaseous mixture consists of $7 \mathrm{~g}$ of nitrogen and $20 \mathrm{~g}$ of argon. Assume gases to be ideal. The specific heat capacities $C_{V}$ and $C_{P}$ in $\mathrm{J} / \mathrm{g}-\mathrm{K}$ for gaseous mixture are :
(a) $C_{P}=0.66 \mathrm{~J} / \mathrm{g}-\mathrm{K}, \mathrm{C}_{V}=18.25 \mathrm{~J} / \mathrm{g}-\mathrm{K}$
(b) $C_{P}=1.66 \mathrm{~J} / \mathrm{g}-\mathrm{K}, \mathrm{C}_{V}=1.82 \mathrm{~J} / \mathrm{g}-\mathrm{K}$
(c) $C_{P}=0.421 \mathrm{~J} / \mathrm{g}-\mathrm{K}, \mathrm{C}_{V}=15.2 \mathrm{~J} / \mathrm{g}-\mathrm{K}$
(d) $C_{P}=0.65 \mathrm{~J} / \mathrm{g}-\mathrm{K}, \mathrm{C}_{V}=0.421 \mathrm{~J} / \mathrm{g}-\mathrm{K}$

Surendra Kumar

Numerade Educator

Problem 51

A gaseous mixture consists of $\mu_{1}=2$ moles of oxygen and $\mu_{2}=3$ moles of carbon di-oxide. Assume gases to be ideal. The value of $\gamma=\frac{C_{P}}{C_{V}}$ for the gaseous mixture is :
(a) $2.33$
(b) $1.33$
(c) $0.33$
(d) $3.33$

Ajay Singhal

Numerade Educator

Problem 52

The molar specific heat of mixture at constant volume, if one mole of a monoatomic gas is mixed with three moles of a diatomic gas is:
(a) $3.33 R$
(b) $2.25 R$
(c) $1.15 R$
(d) $6.72 R$

Ajay Singhal

Numerade Educator

Problem 53

If a gas is heated at constant pressure, then what percentage of total heat supplied is used up for external work? (Given: $\gamma$ for gas $=4 / 3$ )
(a) $25 \%$
(b) $50 \%$
(c) $75 \%$
(d) $80 \%$

Ajay Singhal

Numerade Educator

Problem 54

One mole of a gas isobarically heated by $40 \mathrm{~K}$ receives an amount of heat $1.162 \mathrm{~kJ}$. What is the ratio of specific heats of the gas?
(a) $1.7$
(b) $1.4$
(c) $1.3$
(d) $1.5$

Ajay Singhal

Numerade Educator

Problem 55

3 moles of a gaseous mixture having volume $V$ and temperature $T^{\prime}$ are compressed to $(1 / 5)$ th of its initial volume. The change in its adiabatic compressibility, if gas obeys the equation $P V^{19 / 13}=$ constant, is:
$(R=8.3 \mathrm{~J} / \mathrm{mol}-\mathrm{K})$
(a) $\Delta C=-0.0248 \frac{V}{T} \mathrm{~m}^{2} / \mathrm{N}$
(b) $\Delta C=-0.035 \frac{V}{T} \mathrm{~m}^{2} / \mathrm{N}$
(c) $\Delta C=\cdots 0.0426 \frac{V}{T} \mathrm{~m}^{2} / \mathrm{N}$
(d) $\Delta C=-0.0137 \frac{V}{T} \mathrm{~m}^{2} / \mathrm{N}$

Ajay Singhal

Numerade Educator

Problem 56

In a process $P T=$ constant, if molar heat capacity of a gas is $C=37.35 \mathrm{~J} / \mathrm{mol}-\mathrm{K}$, then the number of degrees of freedom of molecules in the gas is:
(a) $f=10$
(b) $f=5$
(c) $f=6$
(d) $f=7$

Ajay Singhal

Numerade Educator

Problem 57

If in an adiabatic process, the pressure is increased by $2 / 3 \%$, then volume decreases by $\left(\right.$ Assume $\left.\frac{C_{P}}{C_{V}}=\frac{3}{2}\right)$ :
(a) $\frac{4}{9} \%$
(b) $\frac{2}{3} \%$
(c) $4 \%$
(d) $\frac{9}{4} \%$

Ajay Singhal

Numerade Educator

Problem 58

A monoatomic ideal gas is expanded adiabatically to $n$ times of its initial volume. The ratio of final rate of collision of molecules with unit area of container walls to the initial rate will be :
(a) $n^{-4 / 3}$
(b) $n^{4 / 3}$
(c) $n^{2 / 3}$
(d) $n^{-5 / 3}$

Ajay Singhal

Numerade Educator

Problem 59

In the case of solid, number of degrees of freedom is :
(a) 3
(b) 5
(c) 6
(d) 7

Ajay Singhal

Numerade Educator

Problem 60

A given quantity of an ideal gas is at the pressure $P$ and the absolute temperature $T$. The isothermal bulk modulus of the gas is :
(a) $\frac{2}{3} P$
(b) $P$
(c) $\frac{3}{2} P$
(d) $2 P$

Ajay Singhal

Numerade Educator

Problem 61

If temperature of the atmosphere varies with height as $T=\left(T_{0}-a h\right)$, where $a$ and $T_{0}$ are positive constants, then find pressure as a function of height $(h) .$ Assume atmospheric pressure at sea level $(h=0)$ is $P_{0}$ and molecular mass $M$ of the air and acceleration due to gravity $g$ to be constant:
(a) $P=P_{0}\left(\frac{T_{0}-a h}{T_{0}}\right)^{M_{g} / R a}$
(b) $P=P_{0}\left(\frac{T_{0}-a h}{T_{0}}\right)_{\Delta A_{0} / R_{a}}^{2 M g / R a}$
(c) $P=P_{0}\left(\frac{T_{0}-a h}{T_{0}}\right)^{3 M g}$
(d) $P=P_{0}\left(\frac{T_{n}-a h}{T_{0}}\right)^{-4 M g / h}$

Surendra Kumar

Numerade Educator

Problem 62

At a temperature ' $t$ ' the moment of inertia of a body is $I$. When the temperature of the body is increased from $t+\Delta t$, its moment of inertia also increases from $I$ to $(I+\Delta l) .$ If coefficient of linear expansion of the body is $\alpha$ ', then the ratio $\frac{\Delta I}{I}$ is :
(a) $\frac{\Delta t}{t}$
(b) $\frac{2 \Delta t}{t}$
(c) $\alpha \Delta t$
(d) $2 \alpha \Delta t$

Ajay Singhal

Numerade Educator

Problem 63

A Carnot engine is made to work first between $200^{\circ} \mathrm{C}$ and $0^{\circ} \mathrm{C}$, and then between $0^{\circ} \mathrm{C}$ and $200^{\circ} \mathrm{C}$. The ratio of efficiencies $\left(\frac{\eta_{2}}{\eta_{1}}\right)$ of the engine in the two cases is
(a) $1: 15$
(b) $1: 1$
(c) $1: 2$
(d) $1.73: 1$

Ajay Singhal

Numerade Educator

Problem 64

The inside and outside temperatures of a refrigerator are $273 \mathrm{~K}$ and $303 \mathrm{~K}$ respectively. Assuming that refrigerator cycle is reversible, for every joule of work done, the heat delivered to the surrounding will be:
(a) $10 \mathrm{~J}$
(b) $20 \mathrm{~J}$
(c) $30 \mathrm{~J}$
(d) $50 \mathrm{~J}$

Ajay Singhal

Numerade Educator

Problem 65

The coefficient of performance, if in a mechanical refrigerator, the lower temperature coils of a evaporator are $-23^{\circ} \mathrm{C}$, and compressed gas in the condenser has a temperature of $77^{\circ} \mathrm{C}$, is :
(a) $70 \%$
(b) $20 \%$
(c) $0.23 \%$
(d) $2.5 \%$

Ajay Singhal

Numerade Educator