Objective Physics : NEET 2020 Examination textbook Gurukul Oswal

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Chapter 8

THERMODYNAMICS - all with Video Answers

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Section 1

Thermodynamics

Problem 1

When a body $\mathrm{A}$ is in thermal equilibrium with a body $\mathrm{B}$, and also separately with a body $\mathrm{C}$, then $\mathrm{B}$ and $\mathrm{C}$ will be in thermal equilibrium with each other.
(a) True
(b) False
(c) Data is insufficient
(d) None of these

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Problem 2

The zeroth law of thermodynamics states about:
(a) temperature.
(b) Heat content.
(c) pressure.
(d) Internal energy.

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Problem 3

Two systems in thermal equilibrium with a third system separately are in thermal equilibrium with each other.
(a) First law of thermodynamics
(b) Second law of thermodynamics
(c) Third law of thermodynamics
(d) Zeroth law of thermodynamics

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Problem 4

Internal energy of an ideal gas depends upon:
(a) Temperature and volume.
(b) Only volume.
(c) Only pressure.
(d) Only temperature.

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Problem 5

An ideal gas undergoing a change of state from $\mathrm{X}$ to Y through four different paths I, II, III, and IV are as shown in the $P-V$ diagram that leads to the same change of state, then the change in internal energy is:
(a) same in I and II, but not in III and IV.
(b) same in III and IV, but not in I and II.
(c) same in I, II, and III, but not in IV.
(d) same in all the four cases.

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Problem 6

Which of the following is true with regards to the energy of an isolated system?
(a) $Q \neq 0$
(b) $d W \neq 0$
(c) $E=$ constant
(d) All the mentioned above

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Problem 7

In the given $P-V$ diagram, the path (2) from $\mathrm{A}$ to $\mathrm{B}$ is zig-zag path, but path (1) is a simple path. Then,
(a) $\Delta U_{1}=\Delta U_{2}$
(b) $\Delta U_{1}>\Delta U_{2}$
(c) $\Delta U_{1}<\Delta U_{2}$
(d) $\Delta U_{1}=\Delta U_{2}=0$

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Problem 8

Which of the following is a path function?
(a) Temperature
(b) Internal energy
(c) Work done
(d) All of the above

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Problem 9

Air is expanded from $100 \mathrm{~L}$ to $150 \mathrm{~L}$ at two atmospheric pressures. The external work done is: (Given, $\left.1 \mathrm{~atm}=10^{5} \mathrm{Nm}^{-2}\right)$
(a) $1 \times 10^{4} \mathrm{~J}$
(b) $5 \times 10^{4} \mathrm{~J}$
(c) $1 \times 10^{6} \mathrm{~J}$
(d) $2 \times 10^{4} \mathrm{~J}$

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Problem 10

An electric heater supplies heat to a system at a rate of $120 \mathrm{~W}$. If system performs work at a rate of 90 $\mathrm{Js}^{-1}$, the rate of increase in internal energy is:
(a) $210 \mathrm{Js}^{-1}$
(b) $30 \mathrm{Js}^{-1}$
(c) $60 \mathrm{Js}^{-1}$
(d) $90 \mathrm{Js}^{-1}$

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Problem 11

$2 \mathrm{~kg}$ of water is heated from $40^{\circ} \mathrm{C}$ to $70^{\circ} \mathrm{C}$. If its volume remains constant, then the change in internal energy is: (Specific heat of water $=4148 \mathrm{Jkg}^{-1} \mathrm{~K}^{-1}$ )
(a) $1.24 \times 10^{5} \mathrm{~J}$
(b) $2.48 \times 10^{5} \mathrm{~J}$
(c) $1 \times 10^{5} \mathrm{~J}$
(d) $2 \times 10^{5} \mathrm{~J}$

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Problem 12

In the given $P-V$ diagram, the path (2) from $\mathrm{A}$ to $\mathrm{B}$ is zig-zag path, but path ( 1 ) is a simple path. Then,
(a) $W_{1}=W_{2}$
(b) $W_{1}<W_{2}$
(c) $W_{1}>W_{2}$
(d) $W_{1}+W_{2}=0$

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Problem 13

A system goes from $\mathrm{A}$ to $\mathrm{B}$ by two different paths in the $P-V$ diagram as shown in figure. Heat given to the system in path (1) is $1300 \mathrm{~J}$, the work done by the system along path ( 1 ) is more than path (2) by $350 \mathrm{~J}$. The heat exchanged by the system in path:
(a) $950 \mathrm{~J}$
(b) $1650 \mathrm{~J}$
(c) $800 \mathrm{~J}$
(d) $350 \mathrm{~J}$

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Problem 14

A system is taken from a given initial state to a given final state along various paths represented on a $P-V$ diagram. The quantity that is independent of the path is:
(a) Amount of heat transferred $(Q)$
(b) Amount of work done $(W)$
(c) Change in internal energy $(\Delta U)$
(d) None of these

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Problem 15

Which of the following is not a thermodynamic coordinate?
(a) Volume $(V)$
(b) Pressure $(P)$
(c) Temperature $(T)$
(d) Gas constant $(\mathrm{R})$

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Problem 16

Which is an intensive property?
(a) Density
(b) Work done
(c) Mass
(d) Volume

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Problem 17

Which is an extensive property?
(a) Temperature
(b) Work done
(c) Internal energy
(d) Both (b) and (c)

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Problem 18

Which of the following process is correct for given $P-V$ diagram?
(a) Isothermal process
(b) Adiabatic process
(c) Isochoric process
(d) Isobaric process

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Problem 19

Match the following with correct one. \begin{tabular}{lcl}
(a) $A-(i i), B-(i), C-(i v), D-(i i i)$ \\
(b) $A-(i i), B-(i i i), C-(i), D-(i v)$ \\
(c) $A-(i i i), B-(i v), C-(i i), D-(i)$ \\
(d) $A-(i v), B-(i i i), C-(i i), D-(i)$
\end{tabular}

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Problem 20

In a thermodynamic process with 2 moles of gas, $30 \mathrm{~J}$ of heat is released and $22 \mathrm{~J}$ of work is done on the gas. Given that initial internal energy of the sample was $20 \mathrm{~J}$, what will be the final internal energy?
(a) $72 \mathrm{~J}$
(b) $32 \mathrm{~J}$
(c) $28 \mathrm{~J}$
(d) $12 \mathrm{~J}$

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Problem 21

One mole of oxygen is expanded from a volume $1 \mathrm{~L}$ to $5 \mathrm{~L}$ at a constant temperature $T=280 \mathrm{~K}$. The change in internal energy is:
(a) $0.22 \mathrm{~kJ}$
(b) $22 \mathrm{~kJ}$
(c) $0 \mathrm{~kJ}$
(d) $11 \mathrm{~kJ}$

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Problem 22

A sample of perfect gas is compressed isothermally to half its volume. If it is compressed adiabatically to the same volume, the final pressure of the gas will be:
(a) more.
(b) less.
(c) same.
(d) more or less depending upon the initial temperature of the gas.

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Problem 23

Which of the following statements is true about the indicator diagram of adiabatic and isothermal processes?
(a) The slope of isothermal is more than that of adiabatic.
(b) The slope of adiabatic is more than that of isothermal.
(c) Both are parallel curves.
(d) Data is insufficient.

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Problem 24

The given $P-V$ diagram is an expansion of a gas. Which one of the following statement is true?
(a) $X$ is isothermal and $Y$ is isobaric process.
(b) $X$ is isothermal and $Y$ is isochoric process.
(c) $X$ is isothermal and $Y$ is adiabatic process.
(d) Both are adiabatic process.

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Problem 25

The possibility of increase in the temperature of a gas without adding heat to it happens in:
(a) adiabatic expansion.
(b) adiabatic compression.
(c) isothermal compression.
(d) isothermal expansion.

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Problem 26

The ideal gas equation for an adiabatic process is:
(a) $P V^{\gamma}=$ constant
(b) $P V^{\gamma+1}=$ constant
(c) $P V^{\gamma}=0$
(d) $P V^{\gamma-1}=$ constant

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Problem 27

If an ideal gas undergoes isothermal process from some initial state $A$ to the final state $B$, then the change in internal energy during this process is:
(a) $d U=d W \quad$ (b) $d U=d Q$
(c) $\quad d W=d Q \quad$ (d) $\quad d W=-d Q$

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Problem 28

The isothermal diagram of a gas at three different temperatures $T_{A}, T_{\mathrm{B}}$, and $T_{\mathrm{C}}$ is shown in the given figure. Then,
(a) $T_{\mathrm{A}}>T_{\mathrm{B}}>T_{\mathrm{C}}$
(b) $T_{\mathrm{A}}<T_{\mathrm{B}}>T_{\mathrm{C}}$
(c) $T_{\mathrm{A}}<T_{\mathrm{B}}<T_{\mathrm{C}}$.
(d) $T_{\mathrm{A}}>T_{\mathrm{B}}<T_{\mathrm{C}}$.

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Problem 29

The relation between the slope of isothermal curve and slope of adiabatic curve:
(a) slope of isothermal curve $=\gamma$ times slope of adiabatic curve.
(b) slope of adiabatic curve $=\gamma$ times slope of isothermal curve.
(c) slope of isothermal curve $=\gamma^{2}$ times slope of adiabatic curve.
(d) slope of adiabatic curve $=\gamma^{-1}$ times slope of isothermal curve.

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Problem 30

An ideal gas at $27^{\circ} \mathrm{C}$ is compressed adiabatically to $8 / 27$ of its original volume. The rise in temperature is: (Take, $\gamma=5 / 3$ )
(a) $475^{\circ} \mathrm{C}$
(b) $150^{\circ} \mathrm{C}$
(c) $275^{\circ} \mathrm{C}$
(d) $402^{\circ} \mathrm{C}$

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Problem 31

A monoatomic gas $(\gamma=5 / 3)$ at pressure $\mathrm{P}$ is suddenly compressed to $1 / 64$ th of its volume adiabatically. Then, pressure of gas is:
(a) $8 p$
(b) $14 p$
(c) $256 p$
(d) $1024 p$

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Problem 32

A gas is compressed adiabatically till its temperature is doubled. The ratio of its final volume to initial volume will be:
(a) Equal to $0.5$
(b) More than $0.5$
(c) Less than $0.5$
(d) Between 1 and 2

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Problem 33

One mole of an ideal gas at an initial temperature of $T \mathrm{~K}$ does $6 \mathrm{R} \mathrm{J}$ 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) $(T-4) \mathrm{K}$

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Problem 34

Consider a cycle followed by an engine as shown in figure.
$\mathrm{A}$ to $\mathrm{B}$ is isothermal, $\mathrm{B}$ to $\mathrm{C}$ is adiabatic, and $\mathrm{C}$ to $\mathrm{A}$ is adiabatic. Such a process does not exist because:
(a) heat is completely converted to mechanical energy in such a process, which is not possible.
(b) curves representing an adiabatic process and an isothermal process don't intersect.
(c) mechanical energy is completely converted to heat in this process, which is not possible.
(d) curves representing two adiabatic processes can intersect.

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Problem 35

Which of the following $P-V$ diagram represents the graph of isobaric process?
(a) (i)
(b) (ii), (iii)
(c) (iii)
(d) (iv)

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Problem 36

Helium gas expanded from volume to $V_{0}$ to $3 V_{0}$ under three different processes, as shown in the figure. 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) $\Delta U_{1}>\Delta U_{2}>\Delta U_{3}$
(d) $\Delta U_{1}>\Delta U_{2}<\Delta U_{3}$

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Problem 37

Two identical cylinders $\mathrm{A}$ and $\mathrm{B}$ with frictionless pistons contain the same ideal gas at the same temperature and the same volume $V$. The mass of gas $\mathrm{A}$ is $m_{\mathrm{A}}$ and that of $\mathrm{B}$ is $m_{\mathrm{B}}$. The gas in each cylinder is now allowed to expand isothermally to the same final volume $2 V$. The change in the pressure in $\mathrm{A}$ and $\mathrm{B}$ are found to be $\Delta P$ and $2 \Delta P$ respectively. Then,
(a) $4 m_{\mathrm{A}}=9 m_{\mathrm{B}}$
(b) $3 m_{\mathrm{A}}=5 m_{\mathrm{B}}$
(c) $2 m_{\mathrm{A}}=m_{\mathrm{B}}$
(d) $3 m_{\mathrm{A}}=2 m_{\mathrm{B}}$

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Problem 38

A heat insulating cylinder with a movable piston contains 5 moles of hydrogen at standard temperature and pressure of the gas is compressed to quarter of its original volume then the pressure of the gas is increased by $(\gamma=1.5)$ :
(a) $2^{1.5}$
(b) $4^{1.5}$
(c) $5^{1.5}$
(d) $6^{1.5}$

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Problem 39

Two different adiabatic parts for the same gas intersect two isothermals at $T_{1}$ and $T_{2}$ as shown in $P-V$ diagram. Then the ratio of $V_{2}$ and $V_{h}$ will be:
(a) $\gamma \frac{V_{d}}{V_{c}}$
(b) $2 \gamma \frac{V_{d}}{V_{c}}$
(c) $\frac{V_{d}}{V_{c}}$
(d) $\frac{V_{c}}{V_{d}}$

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Problem 40

One mole of an ideal gas goes from an initial state $\mathrm{A}$ to final state B via two processes: It first undergoes isothermal expansion from volume $V$ to $3 \mathrm{~V}$ and then its volume is reduced from $3 V$ to $V$ at constant pressure. The correct $P-V$ diagram representing the two processes is:
(a) (i)
(b) (ii)
(c) (iii)
(d) (iv)

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Problem 41

An ideal gas at pressure $P$ is adiabatically compressed so that its density becomes five times the initial value. The final pressure of the gas will be:
(a) $5(\gamma+1) P$
(b) $5(\gamma-1) P$
(c) $5^{\gamma} P$
(d) $2.5 \gamma P$

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Problem 42

The work done in adiabatic process is given by:
(a) $\frac{n \mathrm{R}\left(T_{1}-T_{2}\right)}{\gamma}$
(b) $\frac{n \mathrm{R}\left(T_{1}-T_{2}\right)}{\gamma-2}$
(c) $\frac{n \mathrm{R}\left(T_{1}-T_{2}\right)}{\gamma-1}$
(d) $n \mathrm{R}\left(T_{1}-T_{2}\right)$

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Problem 43

A gas is compressed at a constant pressure of $50 \mathrm{Nm}^{-2}$ from a volume of $10 \mathrm{~m}^{3}$ to a volume of $4 \mathrm{~m}^{3}$. Energy of $100 \mathrm{~J}$ is then added to the gas by heating. Its internal energy is:
(a) increased by $400 \mathrm{~J}$
(b) increased by $200 \mathrm{~J}$
(c) increased by $100 \mathrm{~J}$
(d) decreased by $200 \mathrm{~J}$

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Problem 44

A gas is expanded at a constant pressure of $50 \mathrm{Nm}^{-2}$ from a volume of $5 \mathrm{~m}^{3}$ to a volume of $10 \mathrm{~m}^{3}$. Energy of $100 \mathrm{~J}$ is then added to the gas by heating. Its internal energy is:
(a) increased by $150 \mathrm{~J}$
(b) decreased by $150 \mathrm{~J}$
(c) increased by $350 \mathrm{~J}$
(d) decreased by $350 \mathrm{~J}$

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Problem 45

A gas is compressed at a constant pressure of $30 \mathrm{Nm}^{-2}$ from a volume of $20 \mathrm{~m}^{3}$ to a volume of $10 \mathrm{~m}^{3}$. Energy of $300 \mathrm{~J}$ is then added to the gas by heating. Its internal energy is:
(a) decreased by $600 \mathrm{~J}$
(b) decreased by $-100 \mathrm{~J}$
(c) increased by $600 \mathrm{~J}$
(d) increased by $100 \mathrm{~J}$

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Problem 46

A sample of gas expands from volume $V_{1}$ to $V_{2} .$ The amount of work done by the gas is greatest when the expansion is
(a) adiabatic.
(b) isobaric.
(c) isothermal.
(d) equal in all the three cases.

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Problem 47

A sample of gas expands from volume $V_{1}$ to $V_{2}$. The amount of work done by the gas is minimum when the expansion is
(a) adiabatic.
(b) isobaric.
(c) isothermal.
(d) equal in all the three cases.

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Problem 48

The relation between internal energy $U$, pressure $P$ and volume $V$ of a gas in an adiabatic process is $U=a+b$ $P V$, where $a$ and $b$ are positive constants. What is the value of $\gamma$ ?
(a) $\frac{a}{b}$
(b) $\frac{a+1}{b}$
(c) $\frac{b+1}{b}$
(d) $\frac{b}{a}$

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Problem 49

Three samples of the same gas $X, Y$, and $Z(\gamma=1.5)$ have equal volume initially. Now, the volume of each sample is doubled. For $X$, the process is adiabatic, for $Y_{1}$ it is isobaric and for $Z$, the process is isothermal. If the final pressures are equal for all the three samples, the ratio of their initial pressures is:
(a) $2: 1: \sqrt{2}$
(b) $1: 2: \sqrt{2}$
(c) $2 \sqrt{2}: 1: 2$
(d) $2 \sqrt{2}: 2: 1$

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Problem 50

Two mole of an ideal gas expands adiabatically at constant pressure such that its temperature $T \propto \frac{1}{\sqrt{V}}$, The value of $\gamma$ for the gas is:
(a) $1.2$
(b) $1.3$
(c) $1.4$
(d) $1.5$

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Problem 51

A thermodynamic system is taken through the cycle PQRSP process. The net work done by the system is:
(a) $20 \mathrm{~J}$
(b) $40 \mathrm{~J}$
(c) $-200 \mathrm{~J}$
(d) $400 \mathrm{~J}$

Ashok Prajapati

Ashok Prajapati

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Problem 52

A thermodynamic system is taken through the cycle PQRSP process. The net work done on the system is:
(a) $-20 \mathrm{~J}$
(b) $-40 \mathrm{~J}$
(c) $20 \mathrm{~J}$
(d) $40 \mathrm{~J}$

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Problem 53

An ideal gas is taken around ABCA as shown in the above $P-V$ diagram. The work done during a cycle is:
(a) $2 \overline{P V}$
(b) $3 \mathrm{PV}$
(c) $4 P V$
(d) $2.5 \mathrm{PV}$

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Problem 54

An ideal gas is taken around $\mathrm{ABCA}$ as shown in the above $P-V$ diagram. The amount of heat given to the system during a cycle is:
(a) $2 \mathrm{PV}$
(b) $3 \mathrm{PV}$
(c) $4 P V$
(d) $5 \mathrm{PV}$

Ashok Prajapati

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Problem 55

An ideal gas is taken around $\mathrm{ABCA}$ as shown in the above $P-V$ diagram. The change in its internal energy:
(a) $-3 \mathrm{PV}$
(b) $3 \mathrm{PV}$
(c) $0 P V$
(d) $2 P V$

Ashok Prajapati

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Problem 56

In pressure-volume diagram given below, the isochoric, isothermal, and isobaric parts respectively, are:
(a) $\mathrm{BA}, \mathrm{AD}, \mathrm{DC}$
(b) DC, CB, BA
(c) $\mathrm{AB}, \mathrm{BC}, \mathrm{CD}$
(d) $\mathrm{CD}, \mathrm{DA}, \mathrm{AB}$

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Problem 57

Pressure $P$, volume $V$ and temperature $T$ of a certain material are related by $P=\alpha T^{2} / V$ where $\alpha$ is constant. Work done by the material when temperature changes from $T_{0}$ to $3 T_{0}$ and pressure remains constant is:
(a) $2 \alpha T_{0}^{2}$
(b) $4 \alpha T_{0}^{2}$
(c) $4 \alpha T_{0}^{2}$
(d) $8 \alpha T_{0}^{2}$

Ashok Prajapati

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Problem 58

The relation between internal energy $U$, pressure $P$ and volume $V$ of a gas in an adiabatic process is $U=x+y$ $P V$, where, $x$ and $y$ are positive constants. What is the value of $\gamma ?$
(a) $\frac{x}{y}$
(b) $\frac{x+1}{x}$
(c) $\frac{y+1}{y}$
(d) $\frac{y}{x}$

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Problem 59

Two moles of helium gas undergo a cyclic process as shown in figure. Assuming the gas to be ideal. The net work done by the gas is:
(a) $200 \mathrm{R} \ln 3$
(b) $300 \mathrm{R} \ln 2$
(c) $-300 \mathrm{R} \ln 3$
(d) $600 \mathrm{R} \ln 3$

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Problem 60

20 moles of helium gas undergo a cyclic process as shown in figure. Assuming the gas to be ideal. The net work done by the gas for path $A B$ and $C D$ is:
(a) $1662 \mathrm{~J}$
(b) $3326 \mathrm{~J}$
(c) 0
(d) $-3326 \mathrm{~J}$

Ashok Prajapati

Ashok Prajapati

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Problem 61

20 moles of helium gas undergo a cyclic process as shown in figure. Assuming the gas to be ideal. The net work done by the gas for path $B C$ and $D A$ is:
(a) $2000 \mathrm{R} \ln 3$
(b) $300 \mathrm{R} \ln 2$
(c) $14000 \mathrm{R} \ln 3$
(d) $8000 \mathrm{R} \ln 3$

Ashok Prajapati

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Problem 62

Two identical containers $X$ and $Y$ with friction less pistons contain the same ideal gas at the same temperature and the same volume $V .$ The mass of gas $X$ is $m_{x}$ and that of $Y$ is $m_{y}$. The gas in each cylinder is now allowed to expand isothermally to the same final volume $2 \mathrm{~V}$. The change in the pressure in $X$ and $Y$ are found to be $\Delta P$ and $3 \Delta P$ respectively. Then,
(a) $4 m_{x}=9 m_{y}$
(b) $4 m_{x}=m_{y}$
(c) $3 m_{x}=m_{y}$
(d) $3 m_{x}=2 m_{y}$

Ashok Prajapati

Ashok Prajapati

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Problem 63

A cyclic process is shown in the figure. Work done during the cyclic process PQRSP is:
(a) $100 \mathrm{~J}$
(b) $120 \mathrm{~J}$
(c) $150 \mathrm{~J}$
(d) $170 \mathrm{~J}$

Ashok Prajapati

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Problem 64

One mole of an ideal monatomic gas at temperature $T_{0}$ expands slowly according to the law $P / V=$ constant. If the final temperature is $3 T_{0}$, heat supplied to the gas is:
(a) $\frac{3}{2} \mathrm{R} T_{0}$
(b) $3 \mathrm{RT}_{0}$
$\begin{array}{ll}\text { (c) } 4 \mathrm{R} T_{0} & \text { (d) } 1.5 \mathrm{R} T_{0}\end{array}$

Ashok Prajapati

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Problem 65

The $P-V$ diagram of a gas undergoing a cyclic process (PQRSP) is shown in the graph, where $P$ is in units of $\mathrm{Nm}^{-2}$ and $V$ in $\mathrm{cm}^{3}$. Identify the incorrect statement.
(a) $0.4 \mathrm{~J}$ of work is done by the gas from $\mathrm{P}$ to $\mathrm{Q}$.
(b) $0.2 \mathrm{~J}$ of work is done on the gas from $\mathrm{R}$ to $\mathrm{S}$.
(c) No work is done by the gas from $\mathrm{Q}$ to $\mathrm{R}$.
(d) Work is done by the gas from $\mathrm{Q}$ to $\mathrm{R}$ and on the gas from $S$ to $P$.

Ashok Prajapati

Ashok Prajapati

Numerade Educator

Problem 66

$800 \mathrm{cc}$ volume of a gas having $\gamma=5 / 2$ is suddenly compressed to $200 \mathrm{cc}$. If the initial pressure is $P$, then the final pressure will be:
(a) $3.2 P$
(b) $32 P$
(c) $16 P$
(d) $1.6 P$

Ashok Prajapati

Ashok Prajapati

Numerade Educator

Problem 67

A monatomic gas initially at $315 \mathrm{~K}$ is suddenly compressed to one-eighth of its original volume. The temperature after compression is:
(a) $560 \mathrm{~K}$
(b) $1260 \mathrm{~K}$
(c) $1160 \mathrm{~K}$
(d) $880 \mathrm{~K}$

Ashok Prajapati

Ashok Prajapati

Numerade Educator

Problem 68

When an ideal gas with pressure $P$ and volume $V$ is compressed isothermally to one-fourth of its volume, the pressure is $P_{1}$. When the same gas is compressed polytropically according to the equation $P V^{1.5}=$ constant, to one-fourth of its initial volume, the pressure is $P_{2}$. The ratio $P_{2} \cdot P_{1}$ is:
(a) $1: 2$
(b) $3: 2$
(c) $2: 1$
(d) $2: 3$

Ashok Prajapati

Ashok Prajapati

Numerade Educator

Problem 69

An ideal gas at pressure $P$ and volume $V$ is expanded to volume $3 \mathrm{~V}$. Column I represents the thermodynamic processes used during expansion. Column II represents the work done during these processes in the random order.
(a) $\mathrm{A}-(\mathrm{i}), \mathrm{B}-(\mathrm{ii}), \mathrm{C}-(\mathrm{iii})$
(b) $\mathrm{A}-(\mathrm{ii}), \mathrm{B}-(\mathrm{iii}), \mathrm{C}-(\mathrm{i})$
(c) $\mathrm{A}-(\mathrm{ii}), \mathrm{B}-(\mathrm{i}), \mathrm{C}-(\mathrm{iii})$
(d) A-(iii), B-(i), C-(ii)

Ashok Prajapati

Ashok Prajapati

Numerade Educator

Problem 70

A gas expands with temperature according to the relation $V=K T^{2 / 3}$ where $K$ is a constant. The work done by the gas when the temperature changes by $60 \mathrm{~K}$ is:
(a) $4 \mathrm{R}$
(b) $40 \mathrm{R}$
(c) $0.4 \mathrm{R}$
(d) $0.04 \mathrm{R}$

Ashok Prajapati

Ashok Prajapati

Numerade Educator

Problem 71

One mole of an ideal gas is taken through a cyclic process as shown in the $V-T$ diagram. Which of the following statements is correct?
(a) The magnitude of work done by the gas is $4 \mathrm{R} T_{0} \ln 2$
(b) Work done by the gas is $\mathrm{R} T_{0} \ln 2$.
(c) Net work done by the gas is zero.
(d) Work done by the gas is $2 \mathrm{R} T_{0} \ln 2$.

Ashok Prajapati

Ashok Prajapati

Numerade Educator

Problem 72

Pressure $P$, volume $V$ and temperature $T$ for a certain gas are related by $P=\frac{X T-Y T^{2}}{V}$, where $X$ and $Y$ are
constants. The work done by the gas as its temperature change from $T_{1}$ to $T_{2}$ with pressure remaining constant is:
(a) $X-Y\left(T_{2}-T_{1}\right)$
(b) $X\left(T_{2}^{2}-T_{1}^{2}\right)-Y\left(T_{2}-T_{1}\right)$
(c) $X\left(T_{2}-T_{1}\right)-Y\left(T_{2}^{2}-T_{1}^{2}\right)$
(d) $(X-Y)\left(T_{2}^{2}-T_{1}^{2}\right)$

Ashok Prajapati

Ashok Prajapati

Numerade Educator

Problem 73

When the state of a gas adiabatically changed from an equilibrium state $X$ to another equilibrium state $Y$, an amount of work done on the system is $35 \mathrm{~J}$. If the gas is taken from state $X$ to $Y$ via process in which the net heat absorbed by the system is 12 calorie, then the net work done by the system is: ( 1 calorie $=4.2 \mathrm{~J}$ )
(a) $13.6 \mathrm{~J}$
(b) $15.4 \mathrm{~J}$
(c) $14.6 \mathrm{~J}$
(d) $1.26 \mathrm{~J}$

Ashok Prajapati

Ashok Prajapati

Numerade Educator

Problem 74

If a gas is compressed adiabatically by doing work of $250 \mathrm{~J}$, the change in internal energy of the gas is:
(a) $150 \mathrm{~J}$
(b) $250 \mathrm{~J}$
(c) 0
(d) $2500 \mathrm{~J}$

Ashok Prajapati

Ashok Prajapati

Numerade Educator

Problem 75

In changing the state of a gas adiabatically from equilibrium state $X$ to another equilibrium state $Y$ an amount of work equal to $19.3 \mathrm{~J}$ is done on the system. If the gas is taken from state $X$ to $Y$ via a process in which the net heat absorbed by the system is $9.35$ calorie then the net work done by the system in latter case is: (Take l calorie $=4.2 \mathrm{~J}$ )
(a) $20 \mathrm{~J}$
(b) $58.6 \mathrm{~J}$
(c) $40 \mathrm{~J}$
(d) $80 \mathrm{~J}$

Ashok Prajapati

Ashok Prajapati

Numerade Educator

Problem 76

A monatomic gas is compressed adiabatically to onethird of its original volume, the final pressure of gas in terms of initial pressure $P$ is:
(a) $6.24 \mathrm{PJ}$
(b) $108 \mathrm{PJ}$
(c) $9.08 \mathrm{PJ}$
(d) $62.4 P \mathrm{~J}$

Ashok Prajapati

Ashok Prajapati

Numerade Educator

Problem 77

If at $60^{\circ} \mathrm{C}$ and $70 \mathrm{~cm}$ of mercury pressure, a definite mass of a gas is compressed slowly, then the final pressure of the gas if the final volume is half of the initial volume $(\gamma=3 / 2)$ is:
(a) $120 \mathrm{~cm}$ of $\mathrm{Hg}$
(b) $140 \mathrm{~cm}$ of $\mathrm{Hg}$
(c) $160 \mathrm{~cm}$ of $\mathrm{Hg}$
(d) $180 \mathrm{~cm}$ of $\mathrm{Hg}$

Ashok Prajapati

Ashok Prajapati

Numerade Educator

Problem 78

During an isothermal expansion, a confined ideal gas does $-350 \mathrm{~J}$ of work against its surroundings. This implies that
(a) $350 \mathrm{~J}$ of heat has been removed from the gas.
(b) $350 \mathrm{~J}$ of heat has been added to the gas.
(c) no heat is transferred because the process is isothermal.
(d) $700 \mathrm{~J}$ of heat has been added to the gas.

Ashok Prajapati

Ashok Prajapati

Numerade Educator

Problem 79

According to Kelvin-Planck's statement of second law of thermodynamics:
(a) it is impossible to construct an engine working on a non-cyclic process, whose sole purpose is to convert heat energy into work.
(b) it is possible to construct an engine working on a cyclic process, whose sole purpose is to convert the heat energy into work.
(c) it is impossible to construct a device which while working in a cyclic process produces no effect other than the transfer of heat from a colder body to a hotter body.
(d) None of the above

Ashok Prajapati

Ashok Prajapati

Numerade Educator

Problem 80

Second law of efficiency is defined as:
(a) actual energy intake/minimum energy intake.
(b) minimum energy intake/actual energy intake.
(c) actual energy intake/maximum energy intake.
(d) maximum energy intake/minimum energy intake.

Ashok Prajapati

Ashok Prajapati

Numerade Educator

Problem 81

The change of entropy, when heat is absorbed by the gas is:
(a) positive.
(b) negative.
(c) positive or negative.
(d) Data is insufficient.

Ashok Prajapati

Ashok Prajapati

Numerade Educator

Problem 82

A process is said to be reversible if
(a) the surroundings return to their original states.
(b) both the system as well as the surroundings return to their original states.
(c) the system returns to their original states.
(d) neither systems nor surroundings return to their original states.

Ashok Prajapati

Ashok Prajapati

Numerade Educator

Problem 83

Which of the following processes described below is irreversible?
(a) Work done against friction
(b) Joule's heating effect
(c) Diffusion of gases into another
(d) All of the above

Ashok Prajapati

Ashok Prajapati

Numerade Educator

Problem 84

A heat engine has an efficiency, $\eta$. Temperatures of source and sink are each decreased by $200 \mathrm{~K}$. The efficiency of the engine:
(a) Decreases
(b) Increases
(c) No change
(d) Data is insufficient.

Ashok Prajapati

Ashok Prajapati

Numerade Educator

Problem 85

An engine has an efficiency of $0.25$ when temperature of sink is reduced by $48^{\circ} \mathrm{C}$, if its efficiency is doubled then the temperature of the source is:
(a) $192^{\circ} \mathrm{C}$
(b) $292^{\circ} \mathrm{C}$
(c) $96^{\circ} \mathrm{C}$
(d) $100^{\circ} \mathrm{C}$

Ashok Prajapati

Ashok Prajapati

Numerade Educator

Problem 86

If a steam engine delivers $8.0 \times 10^{8} \mathrm{~J}$ of work per minute and absorbs $7 \times 10^{9} \mathrm{~J}$ of heat per minute from its boiler then the efficiency of the engine is:
(a) $11.4 \%$
(b) $12.4 \%$
(c) $15.4 \%$
(d) $116.4 \%$

Ashok Prajapati

Ashok Prajapati

Numerade Educator

Problem 87

In a heat engine, the temperature of the source and sink are $500 \mathrm{~K}$ and $375 \mathrm{~K}$. If the engine consumes $5 \times 10^{5} \mathrm{~J}$ per cycle, the work done per cycle is:
(a) $5 \times 10^{5} \mathrm{~J}$
(b) $5 \times 10^{6} \mathrm{~J}$
(c) $1.25 \times 10^{5} \mathrm{~J}$
(d) $1.25 \times 10^{6} \mathrm{~J}$

Ashok Prajapati

Ashok Prajapati

Numerade Educator

Problem 88

When the door of a refrigerator is kept open, then the room temperature starts
(a) first hot up then cool down.
(b) first cool down then hot up.
(c) hot up.
(d) neither cool down nor hot up.

Dheeraj Sharma

Numerade Educator

Problem 89

A refrigerator is to maintain eatables kept inside at $9^{\circ} \mathrm{C}$. The coefficient of performance of refrigerator if room temperature is $28^{\circ} \mathrm{C}$ is:
(a) $15.2$
(b) $14.8$
(c) $13.8$
(d) $12.8$

Ashok Prajapati

Ashok Prajapati

Numerade Educator

Problem 90

The co-efficient of performance of refrigerator, whose efficiency is $20 \%$ is:
(a) 1
(b) 2
(c) 3
(d) 4

Ashok Prajapati

Ashok Prajapati

Numerade Educator

Problem 91

If the co-efficient of performance of a refrigerator is 5 and operates at the room temperature $25^{\circ} \mathrm{C}$, the temperature inside the refrigerator is:
(a) $240 \mathrm{~K}$
(b) $248 \mathrm{~K}$
(c) $250 \mathrm{~K}$
(d) $252 \mathrm{~K}$

Ashok Prajapati

Ashok Prajapati

Numerade Educator

Problem 92

The temperature inside a refrigerator is $t_{\mathrm{B}}{ }^{\circ} \mathrm{C}$ and the room temperature is $t_{\mathrm{A}}{ }^{\circ} \mathrm{C}$. The amount of heat deliv= ered to the room for each joule of electrical energy consumed ideally will be:
(a) $\frac{t_{A}-273}{t_{A}-t_{B}}$
(b) $\frac{t_{B}+273}{t_{A}-t_{B}}$
(c) $\frac{t_{A}+273}{t_{A}-t_{B}}$
(d) $\frac{t_{B}-273}{t_{A}-t_{B}}$

Ashok Prajapati

Ashok Prajapati

Numerade Educator

Problem 93

The freezer in a refrigerator is located at the top section so that:
(a) the entire chamber of the refrigerator is cooled quickly due to convection.
(b) the motor is not heated.
(c) the heat gained from the environment is high.
(d) the heat gained from the environment is low.

Ashok Prajapati

Ashok Prajapati

Numerade Educator

Problem 94

Carnot engine is
(a) operating between two temperatures $T_{1}$ (source) and $T_{2}$ (sink) have maximum efficiency.
(b) consisting of two isothermal processes connected by two adiabatic processes.
(c) irreversible engine.
(d) Both (a) and (b) options are correct

Ashok Prajapati

Ashok Prajapati

Numerade Educator