GATE Overflow for GATE XE - Recent questions and answers in Mass Transfer

GATE XE 2026 | Question: 49

Tue, 24 Feb 2026 15:45:51 +0000

Which of the following statements is/are applicable to Fick's second law:

Concentration changes with time
Steady state condition prevails
Diffusion is time dependent
Concentration profile is linear

GATE XE 2026 | Question: 130

Tue, 24 Feb 2026 15:29:39 +0000

A wet solid, fed to a dryer at a rate of $5 \mathrm{~kg} / \mathrm{s}$, is dried using hot air. In this process its moisture content is reduced from $25 \%$ to $15 \%$. The rate of moisture removal is $\_\_\_\_$ $\mathrm{kg/s}$. (Round off to two decimal places)

GATE XE 2025 | Question: 64

Sun, 04 May 2025 19:06:56 +0000

At $873 \: \mathrm{K}$ , hydrogen diffuses under steady state condition through a $5\: \mathrm{mm}$ thick palladium sheet with a cross-sectional area of $0.3 \mathrm{~m}^{2}$. The concentrations of hydrogen at high and low pressure ends of the sheet are $3 \mathrm{~kg} \mathrm{~m}^{-3}$ and $0.5 \mathrm{~kg} \mathrm{~m}^{-3}$, respectively. The amount of hydrogen (in $\mathrm{kg}$ per day) passing through the sheet is (rounded off to two decimal places) $\_\_\_\_\_\_$

Given: At $873 \: \mathrm{K}$, diffusivity of hydrogen $=1.8 \times 10^{-8} \mathrm{~m}^{2} \mathrm{~s}^{-1}$

GATE XE 2025 | Question: 152

Sun, 04 May 2025 15:30:16 +0000

A fruit juice is concentrated using an ultrafiltration membrane. A feed stream at $10 \mathrm{~kg} / \mathrm{min}$ with $6 \%$ total solids (by weight) is increased to $20 \%$ total solids (by weight). The membrane tube has $10 \: \mathrm{cm}$ inside diameter and the pressure difference across the membrane is $2000 \: \mathrm{ kPa}$. If the permeability constant of the membrane is $5 \times 10^{-5} \mathrm{~kg} \text{ water} / ( \mathrm{m}^{2} \: \mathrm{kPa} \: \mathrm{s}$ ), the length of membrane tube (in $\mathrm{m}$ ) is $\_\_\_\_\_\_$ (rounded off to $2$ decimal places)

GATE XE 2025 | Question: 171

Sun, 04 May 2025 15:26:31 +0000

In hot weather, a human body cools by the evaporation of sweat from its skin. The amount of water that must evaporate to cool the body by $1^{\circ} \mathrm{C}$ is $\_\_\_\_\_\_\_$ $\%$ of the body mass. (Round off to two decimal places.)

[Assume that latent heat of vaporization of water is $2.25 \times 10^{6} \mathrm{~J} \mathrm{~kg}^{-1}$ and specific heat capacities of both human body and liquid water is $4.2 \times 10^{3} \mathrm{~J} \mathrm{~K}^{-1} \mathrm{~kg}^{-1}$.]

GATE XE 2024 | Question: 53

Sun, 21 Jul 2024 16:42:04 +0000

A $2$ mm thick palladium sheet of $1000 \mathrm{~mm}^{2}$ cross section is used as a diffusional membrane to purify hydrogen. The hydrogen concentration is maintained at a steady state with $\boldsymbol{c}_{\boldsymbol{h}}=1.5 \mathrm{~kg} \mathrm{~m}^{-3}$ and $\boldsymbol{c}_{\boldsymbol{l}}=0.3 \mathrm{~kg} \mathrm{~m}^{-3}$ on the two sides of the membrane as shown in the figure below.

The rate of hydrogen purification is $\text{(in units of $\mathrm{kg} \mathrm{hr}^{-1}$ )}$ _________ $\times 10^{-6}$ $\text{(rounded off to one decimal place)}$.

Given: The diffusion coefficient of hydrogen in palladium is $1.0 \times 10^{-8} \mathrm{~m}^{2} \mathrm{~s}^{-1}$

GATE XE 2024 | Question: 97

Sun, 21 Jul 2024 16:41:24 +0000

$100$ moles of moist air at $70 \%$ relative humidity is cooled from $70^{\circ} \mathrm{C}$ to $50^{\circ} \mathrm{C}$ at a constant pressure of $1$ bar . The vapour pressures of water are given in the table. The number of moles of water left in the moist air at the end of this process is _________ $\text{(rounded off to two decimal places)}$.

Temperature $\left({ }^{\circ} \mathbf{C}\right)$	Vapour Pressure (kPa)
$50$	$12.34$
$70$	$31.16$

GATE XE 2024 | Question: 143

Sun, 21 Jul 2024 16:40:49 +0000

A tubular bowl centrifuge is used to separate an aqueous phase from an oil phase. The radii of outlets of the light and heavy liquids are set at $4.5$ cm and $4.6$ cm, respectively. The radius in cm of the neutral zone in the centrifuge is ________ $\text{(round off to 2 decimal places)}$. Assume the density of the aqueous phase is $950 \mathrm{~kg} \cdot \mathrm{m}^{-3}$ and that of oil is $900 \mathrm{~kg} \cdot \mathrm{m}^{-3}$.

GATE XE 2023 | Question: 139

Wed, 14 Feb 2024 18:08:09 +0000

\begin{tabular}{l|l}
Q.149 & Identify the correct pair(s) of governing law with respective process operation. \\
\hline

& Stoke's law - Mass transfer \\
\hline
& Kirchhoff's law - Radiation heat transfer \\
\hline
& Fourier's law - Conduction heat transfer \\
& Fick's law - Molecular diffusion
\end{tabular}

GATE XE 2022 | Question: 51

Fri, 17 Feb 2023 06:51:58 +0000

It is known that component A diffuses into a solid to a depth of $10 \mu \mathrm{m}$ in 1 hour at $300 \mathrm{~K}$. Treat diffusion in one dimension. The time taken for A to diffuse to the same depth at $600 \mathrm{~K}$ _________ is seconds.

$\text{(Round off to 1 decimal)}$.

Diffusivity of $\mathrm{A}$ in the solid is given by
\[
D_{A}=D_{A}^{0} \exp \left(-\frac{E_{a}}{k_{B} T}\right)
\]
$D_{A}^{0}$ : Diffusivity coefficient
$E_{a}:$ Activation energy $=0.3 \mathrm{eV}$
$k_{B}$ : Boltzmann's constant $=8.62 \times 10^{-5} \mathrm{eV} / \mathrm{K}$
$T:$ Absolute temperature