GATE Overflow for GATE XE - Recent questions in First Law of Thermodynamics

GATE XE 2026 | Question: 37

Tue, 24 Feb 2026 15:47:32 +0000

The plot shows three different paths ($1,2,$ and $3$) connecting the initial equilibrium state $\text{X}$ to the final equilibrium state $\text{Y}$ in a thermodynamic process. Which of the following statements is/are correct?

The change in internal energy is the same for all three paths.
The work done is the same for all three paths.
The heat exchange will differ depending on the path taken.
The first law of Thermodynamics is violated if work differs along the paths.

GATE XE 2026 | Question: 78

Tue, 24 Feb 2026 15:42:20 +0000

Consider any substance whose mass specific heat capacity at constant pressure and mass specific heat capacity at constant volume are $c_{P}$ and $c_{V}$, respectively. If the gas constant is $R$, which ONE of the following relations is CORRECT for the substance at all conditions?

$c_{P}=c_{V}$
$c_{P}-c_{V}=R$
$c_{P} \geq c_{V}$
$c_{P} > c_{V}$

GATE XE 2026 | Question: 80

Tue, 24 Feb 2026 15:41:43 +0000

In a mixing chamber hot water enters at a temperature of $80^{\circ} \mathrm{C}$ with a flowrate of $0.5 \mathrm{~kg} / \mathrm{s}$. From another entry, cold water enters the chamber at $20^{\circ} \mathrm{C}$. The desired temperature after mixing at the exit of the chamber is $40^{\circ} \mathrm{C}$. There is no water leakage and the mixing happens at adiabatic conditions. Assume the specific heat capacity of water is $4.2 \mathrm{~kJ} / \mathrm{kg}-\mathrm{K}$. For a steady state operation, the mass flow rate (in $\mathrm{kg} / \mathrm{s}$) of the cold-water stream is

$2.0$
$1.5$
$1.0$
$0.5$

GATE XE 2026 | Question: 82

Tue, 24 Feb 2026 15:41:09 +0000

A mixture of carbon-dioxide ( $\mathrm{CO}_{2}$ ), nitrogen ( $\mathrm{N}_{2}$ ) and oxygen ( $\mathrm{O}_{2}$ ) are introduced in a rigid and impermeable tank containing only liquid water $\left(\mathrm{H}_{2} \mathrm{O}\right)$. Assume that the components are non-reacting and un-dissociated. The system is kept isolated till an equilibrium is achieved, where only two phases are present. The degrees-of-freedom of the equilibrium mixture, as obtained from the phase rule, is

GATE XE 2026 | Question: 85

Tue, 24 Feb 2026 15:40:22 +0000

A house looses heat at a rate of $150$ $\mathrm{MJ}$ per hour. The temperature outside the house is $-3{ }^{\circ} \mathrm{C}$. The minimum power (in $\mathrm{kW}$) required to maintain the temperature inside the house at $25^{\circ} \mathrm{C}$ using a heat pump is $\_\_\_\_$ (rounded off to two decimal places).

GATE XE 2026 | Question: 91

Tue, 24 Feb 2026 15:39:04 +0000

An adiabatic rigid and impermeable tank of volume $10 \mathrm{~m}^{3}$ contains air at $800$ $\mathrm{kPa}$ and $70^{\circ} \mathrm{C}$. The air is allowed to leave the tank until the pressure is one-fourth of its original value. During the process, the air in the tank is maintained at $70^{\circ} \mathrm{C}$ using an electrical heater. Assume that the air behaves as an ideal gas having gas constant and ratio of specific heat capacities as $287 \mathrm{~J} / \mathrm{kg}-\mathrm{K}$ and $1.4$, respectively. The total electrical energy (in $\mathrm{MJ}$) supplied by the heater is $\_\_\_\_\_\_$ (rounded off to two decimal places).

GATE XE 2026 | Question: 92

Tue, 24 Feb 2026 15:39:01 +0000

Two $\mathrm{kg}$ of a gas is compressed in a process. Pressure $(P)$ and mass specific volume $(v)$ of the gas during the process follows: $P v^{1.2}=$ constant. The temperature of the gas before and after compression is $300$ $\mathrm{K}$ and $600$ $\mathrm{K}$, respectively. Assume that the gas behaves as an ideal gas with gas constant and ratio of specific heat capacities equal to $287 \mathrm{~J} / \mathrm{kg}-\mathrm{K}$ and $1.4$, respectively. The heat rejected (in $\mathrm{kJ}$) during the process is $\_\_\_\_$ (rounded off to two decimal places).

GATE XE 2026 | Question: 98

Tue, 24 Feb 2026 15:38:51 +0000

A mixture of helium $\text{(He)}$ and nitrogen ($\mathrm{N}_{2}$) expands in a turbine from $800$ $\mathrm{kPa}$ to $100$ $\mathrm{kPa}$. The mixture composition is $40\% ~\mathrm{He}$ and $60 \% \mathrm{~N}_{2}$ by mass. The turbine inlet temperature is $1000$ $\mathrm{K}$. The temperature (in $\mathrm{K}$) at the turbine exit is $\_\_\_\_$ (rounded off to two decimal places).

Assume:

The process is isentropic. Kinetic and potential energy changes in the process are negligible. $\mathrm{He}$ and $\mathrm{N}_{2}$ behaves as ideal gases. Specific heat capacities are constant.

Use the following data:

Ratio of specific heat capacities for $\mathrm{He}$ and $\mathrm{N}_{2}$ are $1.67$ and $1.4$, respectively.

Specific heat capacities at constant pressure for $\mathrm{He}$ and $\mathrm{N}_{2}$ are $5.19 \mathrm{~kJ} / \mathrm{kg}-\mathrm{K}$ and $1.04 \mathrm{~kJ} / \mathrm{kg}-\mathrm{K}$, respectively.

GATE XE 2025 | Question: 89

Sun, 04 May 2025 19:06:05 +0000

A cylinder of volume $0.1 \mathrm{~m}^{3}$ is filled with nitrogen at $10 \: \mathrm{MPa}$ and $300 \: \mathrm{K}$. Consider nitrogen to be an ideal gas. The cylinder develops a leak and nitrogen escapes to atmosphere which is at $0.1 \: \mathrm{MPa}$. After sometime, the pressure in the cylinder reduces to $5 \: \mathrm{MPa}$. Assuming the cylinder and the leaked gas temperature remains constant at $300 \: \mathrm{K}$, the work done (in $\mathrm{MJ}$) by nitrogen gas is

$0.1$
$1$
$0.5$
$10$

GATE XE 2025 | Question: 90

Sun, 04 May 2025 19:06:03 +0000

A closed system undergoes a process $1-2$ in which it absorbs $150 \: \mathrm{kJ}$ of energy as heat and does $90 \: \mathrm{kJ}$ of work. Then it follows another process $2-3$ in which $80 \: \mathrm{kJ}$ of work is done on it while it rejects $60\: \mathrm{ kJ}$ as heat. If it is desired to restore the system to the initial state (state $1$) by an adiabatic path, the work interaction (in $\mathrm{kJ}$) in this process will be

$80$
$100$
$50$
$70$

GATE XE 2025 | Question: 91

Sun, 04 May 2025 19:06:01 +0000

The inlet and outlet temperatures of the flowing fluid during a steady state flow process are the same as that of the surroundings. If the changes in kinetic and potential energies are neglected, the maximum power that can be obtained is equal to

the rate of increase in enthalpy of the flowing fluid
the rate of decrease in Helmholtz energy of the flowing fluid
the rate of decrease in Gibbs free energy of the flowing fluid
the rate of decrease in internal energy of the flowing fluid

GATE XE 2025 | Question: 99

Sun, 04 May 2025 19:05:44 +0000

Consider a gas obeying the relation $P(v-b)=R T$, where $b$ and $R$ are constants. Which of the following statement(s) is/are CORRECT about the specific heat capacity at constant pressure?

It is independent of temperature
It is a function of pressure
It is a function of temperature
It is independent of both specific volume and pressure

GATE XE 2025 | Question: 103

Sun, 04 May 2025 19:05:38 +0000

A stream of superheated steam ( $2 \mathrm{MPa}, \: 300^{\circ} \mathrm{C}$) mixes with another stream of superheated steam $\left(2 \mathrm{MPa}, \: 400^{\circ} \mathrm{C}\right)$ through a steady-state adiabatic process. The flow rates of the streams are $3 \mathrm{~kg} / \mathrm{min}$ and $2 \mathrm{~kg} / \mathrm{min}$, respectively. This mixture then expands in an adiabatic nozzle to a saturated mixture with quality of $0.77$ and $1\: \mathrm{kPa}$. Neglect the velocity at the nozzle entrance and the change in potential energies. The velocity at the nozzle exit (in $\mathrm{m} / \mathrm{s}$ ) is $\_\_\_\_\_\_\_$ (rounded off to two decimal places).

Use the following data:

At $2 \: \mathrm{MPa}, \: 300^{\circ} \mathrm{C}$ : Specific enthalpy of superheated steam $=3024.2 \mathrm{~kJ} / \mathrm{kg}$

At $2 \mathrm{MPa}, 400^{\circ} \mathrm{C}$ : Specific enthalpy of superheated steam $=3248.4 \mathrm{~kJ} / \mathrm{kg}$

At $1 \: \mathrm{kPa}$ : Specific enthalpy of saturated water $=29.3 \mathrm{~kJ} / \mathrm{kg}$

At $1 \: \mathrm{kPa}$ : Specific enthalpy of saturated vapour $=2513.7 \mathrm{~kJ} / \mathrm{kg}$

GATE XE 2025 | Question: 108

Sun, 04 May 2025 19:05:28 +0000

A particular temperature scale is obtained according to the relation:

$$t=a e^{\alpha}+b$$

where $a$ and $b$ are constants, and $t$ is in ${ }^{\circ} \mathrm{C}$.

The thermometric property as measured by the thermometer is $\alpha$. The values of $\alpha$ at ice point and steam point are $6$ and $9$, respectively. The temperature (in ${ }^{\circ} \mathrm{C}$ ) which gives $\alpha=7$ is $\_\_\_\_\_\_\_$ (rounded off to two decimal places).

GATE XE 2025 | Question: 170

Sun, 04 May 2025 15:26:32 +0000

One kg of dry air at $15^{\circ} \mathrm{C}$ is isothermally compressed to one-tenth of its initial volume. The work done on the system is $\_\_\_\_\_\_ \: \mathrm{kJ}$. (Round off to the nearest integer.)

[Assume that the gas constant for dry air is $287 \times 10^{5} \mathrm{~J} \mathrm{~K}^{-1} \mathrm{~kg}^{-1}$.]

GATE XE 2024 | Question: 80

Sun, 21 Jul 2024 16:41:39 +0000

The temperature of $10$ g of liquid water $\left(c_{p}=4.2 \mathrm{~J} / \mathrm{g} . \mathrm{K}\right)$ in an insulated container is raised by $5$ K by stirring. The amount of heat transferred to the water $\text{(in J)}$ is

$210$
$420$
$0$
$105$

GATE XE 2024 | Question: 83

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

A closed system containing an unknown substance undergoes an adiabatic process governed by the relation $P V^{\gamma}=$ constant, where $P$ is pressure, $V$ is volume, and $\gamma$ is the ratio of specific heats. For this scenario, which of the following statements is/are always TRUE?

The substance is an ideal gas and process is reversible
The substance is a liquid and process is reversible
The substance is a non-ideal gas and process is reversible
The substance is an ideal gas and process is NOT reversible

GATE XE 2024 | Question: 94

Sun, 21 Jul 2024 16:41:26 +0000

An ideal gas undergoes a series of reversible steady state, steady flow processes between states $1,2$, and $3$. Process $1 \rightarrow 2$ satisfies the relation $P+800 v=900$, where pressure, $P$ is in kPa and specific volume, $v$ is in $\mathrm{m}^{3} / \mathrm{kg}$. Process $2 \rightarrow 3$ is isochoric. Given that $v_{1}=0.5 \mathrm{~m}^{3} / \mathrm{kg}, v_{2}=v_{3}=1 \mathrm{~m}^{3} / \mathrm{kg}, \frac{P_{3}}{P_{2}}=4$, the total work done per unit mass $\text{(in $\mathrm{kJ} / \mathrm{kg}$ )}$ in the series of processes $1 \rightarrow 2 \rightarrow 3$ is ________ $\text{(rounded off to the nearest integer)}$.

GATE XE 2024 | Question: 96

Sun, 21 Jul 2024 16:41:25 +0000

The melting point of a substance at $1$ bar is $273$ K . The following property data is available for this substance at $1$ bar.

Density of the solid phase	$900 \mathrm{~kg} / \mathrm{m}^{3}$
Density of the liquid phase	$1000 \mathrm{~kg} / \mathrm{m}^{3}$
Latent heat for melting	$300 \mathrm{~kJ} / \mathrm{kg}$

Assuming that the above properties are constant, the melting point $\text{(in K)}$ of the substance at $101$ bar is ________ $\text{(rounded off to two decimal places)}$.

GATE XE 2024 | Question: 98

Sun, 21 Jul 2024 16:41:23 +0000

A rigid insulated tank containing an ideal gas at $300$ K and $1$ bar is being filled from an external pressurized line supplying the same gas at $300$ K and $10$ bar. When the mass of gas inside the tank has doubled, its temperature (in K ) is _________ $\text{(rounded off to the nearest integer)}$.

Assume ratio of specific heats to be constant for this process and equal to $1.4$.

GATE XE 2023 | Question: 53

Wed, 14 Feb 2024 18:09:32 +0000

Q. 63 Two moles of a monoatomic ideal gas at 10 atm and $300 \mathrm{~K}$ is expanded isothermally and reversibly to a pressure of $2 \mathrm{~atm}$. The absolute value of work done by the system is (in $\mathrm{kJ}$ ) (rounded off to two decimal places) Given: $\mathrm{R}=8.31 \mathrm{~J} \mathrm{~mol}^{-1} \mathrm{~K}^{-1}, 1 \mathrm{~atm}=101 \mathrm{kPa}$

GATE XE 2023 | Question: 87

Wed, 14 Feb 2024 18:08:58 +0000

\begin{tabular}{|c|c|}
\hline Q. 97 & \begin{tabular}{l}
A rigid closed tank having a volume of $2 \mathrm{~m}^{3}$ contains $0.1 \mathrm{~m}^{3}$ of saturated liquid \\
water and $1.9 \mathrm{~m}^{3}$ of saturated water vapor at $100 \mathrm{kPa}$. Heat is transferred to the \\
tank until the final tank pressure reaches $2 \mathrm{MPa}$. \\
Following data for water is given: \\
$\qquad$\begin{tabular}{rll}
At $100 \mathrm{kPa}:$ & $v_{f}=0.001043 \mathrm{~m}^{3} / \mathrm{kg}$, & $v_{g}=1.694 \mathrm{~m}^{3} / \mathrm{kg}$, \\
$u_{f}=417.33 \mathrm{~kJ}^{2} / \mathrm{kg}$, & $u_{g}=2506.06 \mathrm{~kJ} / \mathrm{kg}$ \\
At $2 \mathrm{MPa}: \quad v_{f}=0.001177 \mathrm{~m}^{3} / \mathrm{kg}$, & $v_{g}=0.09963 \mathrm{~m}^{3} / \mathrm{kg}$, \\
$u_{f}=906.42 \mathrm{~kJ} / \mathrm{kg}$, & $u_{g}=2600.26 \mathrm{~kJ} / \mathrm{kg}$
\end{tabular}
\end{tabular} \\
\hline & The magnitude of heat transfer in this process is \\
\hline

& $34670 \mathrm{~kJ}$ \\
\hline
& $55842 \mathrm{~kJ}$ \\
\hline
& $67906 \mathrm{~kJ}$ \\
\hline
& $77470 \mathrm{~kJ}$ \\
\hline
\end{tabular}

GATE XE 2023 | Question: 91

Wed, 14 Feb 2024 18:08:54 +0000

Q. 101
A piston-cylinder device initially contains $1 \mathrm{~m}^{3}$ of air at $200 \mathrm{kPa}$ and $25^{\circ} \mathrm{C}$. Air expands at constant pressure while a heater of $250 \mathrm{~W}$ is switched on for 10 minutes. There is a heat loss of $4 \mathrm{~kJ}$ during this process. Assuming air as an ideal gas, the final temperature of air is ${ }^{\circ} \mathrm{C}$ (rounded off to one decimal place).

Use the following data for air: $\quad R=0.287 \mathrm{~kJ} / \mathrm{kg}-\mathrm{K}, c_{p}=1.005 \mathrm{~kJ} / \mathrm{kg}-\mathrm{K}$

GATE XE 2023 | Question: 92

Wed, 14 Feb 2024 18:08:53 +0000

Q. 102
Steam at $2 \mathrm{MPa}$ and $300^{\circ} \mathrm{C}$ steadily enters a nozzle of inlet diameter of $20 \mathrm{~cm}$. Steam leaves the nozzle with a velocity of $300 \mathrm{~m} / \mathrm{s}$. The mass flow rate of steam through the nozzle is $10 \mathrm{~kg} / \mathrm{s}$. Assume no work interaction and no change in potential energy. If the heat loss from the nozzle per $\mathrm{kg}$ of steam is $3 \mathrm{~kJ}$, the exit enthalpy per $\mathrm{kg}$ of steam is $\mathrm{kJ}$ (rounded off to nearest integer).

Use the following data for steam:
At $2 \mathrm{MPa}$ and $300{ }^{\circ} \mathrm{C}: v=0.12551 \mathrm{~m}^{3} / \mathrm{kg}, h=3024.2 \mathrm{~kJ} / \mathrm{kg}$