GATE Overflow for GATE XE - Recent questions in Integral Analysis for a Control Volume

GATE XE 2026 | Question: 95

Tue, 24 Feb 2026 15:38:54 +0000

A stream of moist air enters an adiabatic saturator at $45^{\circ} \mathrm{C}$ and $101$ $\mathrm{kPa}$ and leaves as a saturated mixture at $30^{\circ} \mathrm{C}$. Make-up water to the saturator is supplied at $30^{\circ} \mathrm{C}$. The amount of make-up water (in grams per kg of dry air) supplied is $\_\_\_\_$ (rounded off to two decimal places).

Use the following data:

Specific heat capacity of water is $4.2 \mathrm{~kJ} / \mathrm{kg}-\mathrm{K}$

Specific heat capacity of air at constant pressure is $1 \mathrm{~kJ} / \mathrm{kg}-\mathrm{K}$

Saturated water properties:

At $30^{\circ} \mathrm{C}$ : specific enthalpy of saturated water vapor is $2556 \mathrm{~kJ} / \mathrm{kg}-\mathrm{K}$, specific enthalpy of saturated liquid water is $125.7 \mathrm{~kJ} / \mathrm{kg}-\mathrm{K}$, and saturation pressure is $4.25$ kPa

At $45^{\circ} \mathrm{C}$ : specific enthalpy of saturated water vapor is $2582 \mathrm{~kJ} / \mathrm{kg}-\mathrm{K}$, specific enthalpy of saturated liquid water is $188.4 \mathrm{~kJ} / \mathrm{kg}-\mathrm{K}$, and saturation pressure is $9.60$ kPa

GATE XE 2026 | Question: 137

Tue, 24 Feb 2026 15:26:29 +0000

For a given temperature difference between the top and bottom surfaces of a flat metal plate, Fourier's law of heat conduction implies that

temperature gradient increases with increase in heat transfer area
heat flux is proportional to the thermal conductivity of the metal
heat flux increases with increase in thickness of the metal plate
temperature gradient decreases with increase in thickness of the metal plate

GATE XE 2026 | Question: 146

Tue, 24 Feb 2026 15:23:02 +0000

What is the approximate value of annual-mean pH of seawater at the surface in the northern Indian Ocean?

$4.5$
$5.0$
$8.0$
$11.0$

GATE XE 2026 | Question: 187

Tue, 24 Feb 2026 15:08:22 +0000

The useful heat gain in Watt (rounded off to one decimal place) of a solar flat plate collector using Hottel-Whillier-Bliss equation is $\_\_\_\_$.

Assume:
Collector heat removal factor $=0.85$
Absorber plate area $=1.5 \mathrm{~m}^{2}$
Absorbed solar flux by the absorber plate $=600 \mathrm{Wm}^{-2}$
Overall loss coefficient $=4 \mathrm{Wm}^{-2} \mathrm{~K}^{-1}$
Water inlet temperature $=60^{\circ} \mathrm{C}$
Ambient temperature $=25^{\circ} \mathrm{C}$

GATE XE 2025 | Question: 25

Sun, 04 May 2025 19:08:18 +0000

Statement of Reynolds Transport Theorem is given below with three blanks.

The rate of change of $\_\_\_\_\_$ extensive property can be calculated by summing the rate of change of the amount of same property in the $\_\_\_\_\_$ and the rate at which the property is $\_\_\_\_\_$ the surface of the control volume.

Which one of the following options correctly fills the blanks by using its comma-separated phrases in sequence?

system, control volume, exiting
control volume, system, exiting
system, control volume, entering
control volume, control volume, entering

GATE XE 2025 | Question: 40

Sun, 04 May 2025 19:07:39 +0000

A fixed control volume has four one-dimensional boundary sections $(1,2,3$, and $4$). For a steady flow inside the control volume, the flow properties at each section are tabulated below:

$$\begin{array}{|l|l|l|l|l|l|} \hline \textbf{Boundary} & \textbf{Type} & \textbf{Density} & \textbf{Surface Normal} & \textbf{Cross-sectional} & \textbf{Specific} \\ \textbf{Section} && (\text {kg}/{m}^3) & \textbf{Velocity} & \textbf{Area} & \textbf{Energy} \\ &&& (\mathrm{m} / \mathrm{s}) & (\mathrm{m}^{2}) & (\mathrm{J} / \mathrm{kg} ) \\ \hline 1 & \text{Inlet} & 1000 & 10 & 0.5 & 200 \\ \hline 2 & \text{Inlet} & 1000 & 2 & 3.0 & 50 \\ \hline 3 & \text{Outlet} & 1000 & 5 & 1.0 & 100 \\ \hline 4 & \text{Outlet} & 1000 & 4 & 1.5 & 80 \\
\hline \end{array}$$

The rate of change of energy of the system which occupies the control volume at this instant is $E \times 10^{6} \mathrm{~J} / \mathrm{s}$. The value of $E$ (rounded off to $2$ decimal places) is $\_\_\_\_\_$

GATE XE 2024 | Question: 16

Sun, 21 Jul 2024 16:42:33 +0000

Let $\vec{r}, \vec{V}$, and $m$ be position vector, velocity vector, and mass, respectively in a control mass system. Which one of the following properties is considered as conserved extensive property in Reynolds Transport Theorem to obtain the angular momentum equation?

$\vec{r} \times m \vec{V}$
$\vec{r} \times \vec{V}$
$m \vec{V}$
$m$

GATE XE 2024 | Question: 42

Sun, 21 Jul 2024 16:42:13 +0000

The work done by a body expanding from an initial state $\text{A}$ to the final state $\text{B}$, as shown in the $\text{P-V}$ diagram below, is $\text{(in units of litre-atm)}$ __________ $\text{(rounded off to nearest integer)}$.

GATE XE 2024 | Question: 95

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

Air $\text{(assumed as an ideal gas)}$ with a mass flow rate of $2.5 \mathrm{~kg} / \mathrm{s}$ enters a horizontal nozzle at $350 \mathrm{~K}, 350 \mathrm{kPa}$ with a velocity of $3 \mathrm{~m} / \mathrm{s}$. The air exits the nozzle at a pressure of $101.5$ kPa and temperature $305$ K with a Mach number of $\frac{9}{7}$. Assuming steady state operation and constant properties given in the data, the ratio of inlet area to exit area required to satisfy the exit condition is ________ $\text{(rounded off to one decimal place)}$.

Use the following data: $\gamma=1.4, c_{p}=1.011 \mathrm{~kJ} / \mathrm{kg} . \mathrm{K}, \quad R=0.287 \mathrm{~kJ} / \mathrm{kg} . \mathrm{K}$

GATE XE 2024 | Question: 99

Sun, 21 Jul 2024 16:41:22 +0000

A piston-cylinder system contains $2$ kg of wet steam at $90^{\circ} \mathrm{C}$ with quality of $0.1$. The piston is loaded with a linear spring. The steam expands to $800$ kPa and $250^{\circ} \mathrm{C}$ on heating. The work done (in kJ ) in this process is _________ $\text{(rounded off to two decimal places)}$.

Use the following data:

At $90^{\circ} \mathrm{C}: P_{\text {sat }}=70 \mathrm{kPa}, v_{f}=0.001 \mathrm{~m}^{3} / \mathrm{kg}, v_{g}=2.4 \mathrm{~m}^{3} / \mathrm{kg}$

At $250^{\circ} \mathrm{C}$ and $800 \mathrm{kPa}: v=0.29 \mathrm{~m}^{3} / \mathrm{kg}$