GATE Overflow for GATE XE - Recent questions and answers in Second Law of Thermodynamics

GATE XE 2026 | Question: 88

Tue, 24 Feb 2026 15:40:16 +0000

$M \mathrm{~kg}$ of a liquid at a temperature $T_{1}$ is mixed with $M \mathrm{~kg}$ of the same liquid at another temperature $T_{2}$ in an isolated tank at constant pressure. The mass specific heat capacity at constant pressure of the liquid is $c_{P}$, which is a constant. The total entropy change in the process is

$M c_{P} \ln \left(\dfrac{T_{1}+T_{2}}{2\sqrt{T_{1} T_{2}}}\right)$
$2 M c_{P} \ln \left(\dfrac{T_{1}+T_{2}}{\sqrt{T_{1} T_{2}}}\right)$
$M c_{P} \ln \left(\dfrac{T_{1}+T_{2}}{\sqrt{T_{1} T_{2}}}\right)$
$2 M c_{P} \ln \left(\dfrac{T_{1}+T_{2}}{2 \sqrt{T_{1} T_{2}}}\right)$

GATE XE 2025 | Question: 93

Sun, 04 May 2025 19:05:56 +0000

Let $T_{H}$ and $T_{L}$ denote the absolute temperatures of high and low temperature reservoirs, respectively. The coefficient of performance of a reversible refrigerator operating between these two reservoirs is

$\frac{1}{\frac{T_{H}}{T_{L}}-1}$
$\frac{1}{1-\frac{T_{H}}{T_{L}}}$
$\frac{1}{\frac{T_{L}}{T_{H}}-1}$
$\frac{1}{\frac{T_{L}}{T_{H}}+1}$

GATE XE 2025 | Question: 95

Sun, 04 May 2025 19:05:52 +0000

A heat engine having thermal efficiency of $40 \%$ receives heat from a source at $600 \: \mathrm{K}$ and rejects heat to a sink at $300 \: \mathrm{K}$. The second-law efficiency (in $\%$) of this engine is $\_\_\_\_\_\_\_$ (answer in integer).

GATE XE 2025 | Question: 105

Sun, 04 May 2025 19:05:34 +0000

Air enters a hair dryer at $22^{\circ} \mathrm{C}$ and $100 \: \mathrm{kPa}$ with a velocity of $3.7 \mathrm{~m} / \mathrm{s}$, and leaves the dryer at $83{ }^{\circ} \mathrm{C}$ and $100 \: \mathrm{kPa}$ with a velocity of $9.1 \mathrm{~m} / \mathrm{s}$. The exit area of the dryer is $18.7 \mathrm{~cm}^{2}$, and the ambient temperature is $22^{\circ} \mathrm{C}$. The air is an ideal gas with gas constant $R=0.287 \mathrm{~kJ} / \mathrm{kg}-\mathrm{K}$ and isobaric specific heat $c_{p}=1.005 \mathrm{~kJ} / \mathrm{kg}-\mathrm{K}$. If the change in potential energy is neglected, the second law efficiency (in $\%$) of the dryer is $\_\_\_\_\_\_\_$ (rounded off to one decimal place).

GATE XE 2025 | Question: 107

Sun, 04 May 2025 19:05:30 +0000

Two Carnot heat engines ($\text{E1}$ and $\text{E2}$) are operating in series as shown in figure. Engine $\text{E1}$ receives heat from a reservoir at $T_{H}=1600 \mathrm{~K}$ and does work $\mathrm{W}_{1}$. Engine $\text{E2}$ receives heat from an intermediate reservoir at $T$, does work $\mathrm{W}_{2}$ and rejects the rest to a reservoir at $T_{L}=400 \mathrm{~K}$. Both the engines have identical thermal efficiencies. The temperature $T$ (in $\mathrm{K}$ ) of the intermediate reservoir is $\_\_\_\_\_\_\_$ (answer in integer).

GATE XE 2025 | Question: 109

Sun, 04 May 2025 19:05:27 +0000

In a piston cylinder assembly, one $\mathrm{kmol}$ of an ideal gas is compressed from an initial state of $200 \: \mathrm{kPa}$ and $400 \:\mathrm{ K}$ to a final state of $1 \: \mathrm{MPa}$ and $400\: \mathrm{ K}$. If the surroundings are at $400 \: \mathrm{K}$, the minimum amount of work (in $\mathrm{kJ} / \mathrm{kmol}$) required for the compression process is $\_\_\_\_\_\_\_$ (rounded off to two decimal places).

Use: Universal gas constant $\left(R_{u}\right)=8.314 \mathrm{~kJ} / \mathrm{kmol}-\mathrm{K}$

GATE XE 2024 | Question: 78

Sun, 21 Jul 2024 16:41:41 +0000

A heat source at temperature $T_{H}$ transfers the same amount of heat to a sink under the following situations:

Case A: Sink is at temperature $T_{L, 1}$

Case B: Sink is at temperature $T_{L, 2}$

If $T_{L, 1} < T_{L, 2}$, which one of the following statements is TRUE?

The reversibility is the same, and the entropy generation is greater than zero for Cases A and B
Case B is less reversible with the entropy generation greater than zero
Case B is more reversible with the entropy generation greater than zero
Case B is more reversible with the entropy generation equal to zero

GATE XE 2024 | Question: 84

Sun, 21 Jul 2024 16:41:36 +0000

Two rigid, impermeable containers $A$ and $B$ are filled with an ideal gas. They are allowed to exchange heat only with each other and not with the surroundings. $P, V, N$, and $T$ represent the pressure, total volume, number of moles, and temperature, respectively. At equilibrium, which of the following conditions is/are necessarily satisfied?
$\text{(Subscripts $A$ and $B$ represent properties of the gas in the respective containers.)}$

$\quad P_{A}=P_{B}$
$\quad T_{A}=T_{B}$
$\frac{P_{A} V_{A}}{N_{A}}=\frac{P_{B} V_{B}}{N_{B}}$
$\frac{P_{A}}{V_{A}}=\frac{P_{B}}{V_{B}}$

GATE XE 2024 | Question: 89

Sun, 21 Jul 2024 16:41:31 +0000

Match each quantity in Column $\mathbf{M}$ with the appropriate relation from Column $\mathbf{N}$. Here, $\psi$ is Helmholtz function, $P$ is pressure, $v$ is specific volume, $T$ is temperature, $h$ is specific enthalpy, and $s$ is specific entropy.

$\text{M1-N5, M2-N1, M3-N4, M4-N7}$
$\text{M1-N6, M2-N2, M3-N3, M4-N8}$
$\text{M1-N5, M2-N1, M3-N4, M4-N8}$
$\text{M1-N8, M2-N1, M3-N4, M4-N5}$

GATE XE 2024 | Question: 91

Sun, 21 Jul 2024 16:41:29 +0000

A Carnot engine operates between two temperatures $T_{1}$ and $T_{2}$ such that $T_{1}>T_{2}$. If the thermal efficiency of the engine is to be increased by changing one of the temperatures by a constant amount $\Delta T>0$, which one of the following cases will give the highest increase in efficiency?

Increasing $T_{1}$ by $\Delta T$ while keeping $T_{2}$ constant
Decreasing $T_{1}$ by $\Delta T$ while keeping $T_{2}$ constant
Increasing $T_{2}$ by $\Delta T$ while keeping $T_{1}$ constant
Decreasing $T_{2}$ by $\Delta T$ while keeping $T_{1}$ constant

GATE XE 2023 | Question: 89

Wed, 14 Feb 2024 18:08:56 +0000

\begin{tabular}{l|l}
Q. 99 & \begin{tabular}{l}
A $5 \mathrm{~kg}$ metal block $\left(c_{p}=0.5 \mathrm{~kJ} / \mathrm{kg}-\mathrm{K}\right)$ at $373 \mathrm{~K}$ is submerged into $10 \mathrm{~kg}$ of water \\
$\left(c_{p}=4.2 \mathrm{~kJ} / \mathrm{kg}-\mathrm{K}\right)$ at $293 \mathrm{~K}$ in an insulated rigid container without spilling. \\
Assuming thermal equilibrium is reached, the approximate entropy change of the \\
universe is
\end{tabular} \\
\hline

& $-0.565 \mathrm{~kJ} / \mathrm{K}$ \\
\hline
& $0.073 \mathrm{~kJ} / \mathrm{K}$ \\
\hline
& $0.642 \mathrm{~kJ} / \mathrm{K}$ \\
\hline
& $0.963 \mathrm{~kJ} / \mathrm{K}$
\end{tabular}

GATE XE 2023 | Question: 99

Wed, 14 Feb 2024 18:08:47 +0000

Q. 109
In a liquid-vapour phase change process, $\left(\frac{\mathrm{d} P}{\mathrm{~d} T}\right)_{\text {sat }}$ at $100{ }^{\circ} \mathrm{C}$ for saturated water is $3750 \mathrm{~Pa} / \mathrm{K}$. If the resulting change in specific volume $\left(v_{g}-v_{f}\right)$ is $1.672 \mathrm{~m}^{3} / \mathrm{kg}$, the enthalpy of vaporization $\left(h_{f g}\right)$ will be $\mathrm{kJ} / \mathrm{kg}$ (in integer).

GATE XE 2023 | Question: 98

Wed, 14 Feb 2024 18:08:47 +0000

Q. 108 An office uses a heat pump to receive $500 \mathrm{~kJ} /$ day heat in winter to maintain its temperature at $300 \mathrm{~K}$. The ambient temperature is $280 \mathrm{~K}$. If the COP of the heat pump is $60 \%$ of its theoretical maximum value, the ratio of actual work input to the minimum theoretical work input to the heat pump is (rounded off to one decimal place).