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GATE Chemical 2024 | Question: 26
Consider a steady, fully-developed, uni-directional laminar flow of an incompressible Newtonian fluid (viscosity $\mu$ ) between two infinitely long horizonta...
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GATE Chemical 2024 | Question: 27
The temperatures of two large parallel plates of equal emissivity are $900 \mathrm{~K}$ and $300 \mathrm{~K}$. A reflection radiation shield of low emis...
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GATE Chemical 2024 | Question: 28
Hot oil at $110{ }^{\circ} \mathrm{C}$ heats water from $30^{\circ} \mathrm{C}$ to $70{ }^{\circ} \mathrm{C}$ in a counter-current double-pipe heat exchang...
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GATE Chemical 2024 | Question: 29
A solid slab of thickness $H_{1}$ is initially at a uniform temperature $T_{0}$. At time $t=0$, the temperature of the top surface at $y=H_{1}$ is increase...
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GATE Chemical 2024 | Question: 30
A gas stream containing $95 \mathrm{~mol} \% \mathrm{CO}_{2}$ and $5 \mathrm{~mol} \%$ ethanol is to be scrubbed with pure water in a counter-current, i...
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GATE Chemical 2024 | Question: 31
Sulfur dioxide $\left(\mathrm{SO}_{2}\right)$ gas diffuses through a stagnant air-film of thickness $2 \mathrm{~mm}$ at 1 bar and $30^{\circ} \mathrm{C}$. ...
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GATE Chemical 2024 | Question: 32
A simple distillation column separates a binary mixture of $A$ and $B$. The relative volatility of $A$ with respect to $B$ is $2$. The steady-state composi...
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GATE Chemical 2024 | Question: 33
Alumina particles with an initial moisture content of $5 \mathrm{~kg}$ per $\mathrm{kg}$ dry solid are dried in a batch dryer. For the first two hours, the measu...
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GATE Chemical 2024 | Question: 34
A first-order heterogenous reaction $A \rightarrow B$ is carried out using a porous spherical catalyst. Assume isothermal conditions, and that intraphase diffusion contro...
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GATE Chemical 2024 | Question: 35
A first-order liquid phase reaction $A \rightarrow B$ is carried out in two isothermal plug flow reactors (PFRs) of volume $1 \mathrm{~m}^{3}$ each, con...
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GATE Chemical 2024 | Question: 36
The residence time distribution, $E$, for a non-ideal flow reactor is given in the figure. A first-order liquid phase reaction with a rate constant $0.2 \math...
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GATE Chemical 2024 | Question: 37
Let $r$ and $\theta$ be the polar coordinates defined by $x=r \cos \theta$ and $y=r \sin \theta$. The area of the cardioid $r=a(1-\cos \theta), 0 \leq \...
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GATE Chemical 2024 | Question: 38
For the block diagram shown in the figure, the correct expression for the transfer function $G_{d}=\frac{y_{1}(s)}{d(s)}$ is$\frac{-G_{p 1} G_{c 2}}{\le...
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GATE Chemical 2024 | Question: 39
For purchasing a batch reactor, three alternatives $\mathrm{P}, \mathrm{Q}$ and $\mathrm{R}$ have emerged, as summarized in the table. For a compound inter...
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GATE Chemical 2024 | Question: 40
The Newton-Raphson method is used to solve $f(x)=0$, where $f(x)=e^{x}-5 x$.If the initial guess $x^{(0)}=1.0$, the value of the next iterate, $x^{(1)}$, rounded off to $...
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GATE Chemical 2024 | Question: 41
Consider the line integral $\int_{C} \boldsymbol{F}(\boldsymbol{r}) \cdot d \boldsymbol{r}$, with $\boldsymbol{F}(\boldsymbol{r})=x \hat{\boldsymbol{\imath}}+y \hat{\bold...
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GATE Chemical 2024 | Question: 42
Consider the ordinary differential equation $x^{2} \frac{d^{2} y}{d x^{2}}-x \frac{d y}{d x}-3 y=0$, with the boundary conditions $y(x=1)=2$ and $y(x=2)=17 / 2$. The solu...
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GATE Chemical 2024 | Question: 43
Consider the function $f(x, y, z)=x^{4}+2 y^{3}+z^{2}$. The directional derivative of the function at the point $P(-1,1,-1)$ along $(\hat{\boldsymbol{\imath}}+\hat{\bolds...
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GATE Chemical 2024 | Question: 44
Consider the process in the figure for manufacturing $B$. The feed to the process is $90 \mathrm{~mol} \% A$ and a close-boiling inert component $I$. At a particular stea...
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GATE Chemical 2024 | Question: 45
Methane combusts with air in a furnace as $\mathrm{CH}_{4}+2 \mathrm{O}_{2} \rightarrow \mathrm{CO}_{2}+2 \mathrm{H}_{2} \mathrm{O}$. The heat of reaction $\Delta H_{r x ...
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GATE Chemical 2024 | Question: 46
An isolated system consists of two perfectly sealed cuboidal compartments $A$ and $B$ separated by a movable rigid wall of cross-sectional area $0.1 \mathrm{~m}^{2}$ as s...
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GATE Chemical 2024 | Question: 47
Ethylene obeys the truncated virial equation-of-state\[\frac{P V}{R T}=1+\frac{B P}{R T}\]where $P$ is the pressure, $V$ is the molar volume, $T$ is the absolute temperat...
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GATE Chemical 2024 | Question: 48
A metallic spherical particle of density $7001 \mathrm{~kg} \mathrm{~m}^{-3}$ and diameter $1 \mathrm{~mm}$ is settling steadily due to gravity in a stagnant gas of densi...
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GATE Chemical 2024 | Question: 49
Water of density $1000 \mathrm{~kg} \mathrm{~m}^{-3}$ is pumped at a volumetric flow rate of $3.14 \times 10^{-2} \mathrm{~m}^{3} \mathrm{~s}^{-1}$, through a pipe of inn...
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GATE Chemical 2024 | Question: 50
A Venturi meter with a throat diameter $d=2 \mathrm{~cm}$ measures the flow rate in a pipe of diameter $D=6 \mathrm{~cm}$, as shown in the figure. A U-tube manometer is c...
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GATE Chemical 2024 | Question: 51
Heat is available at a rate of $2 \mathrm{~kW}$ from a thermal reservoir at $400 \mathrm{~K}$. A two-stage process harnesses this heat to produce power. Stages $1$ and $2...
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GATE Chemical 2024 | Question: 52
A chemostat with cell recycle is shown in the figure. The feed flow rate and culture volume are $F=75 \mathrm{~L} \mathrm{~h}^{-1}$ and $V=200 \mathrm{~L}$, respectively....
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GATE Chemical 2024 | Question: 53
Consider the surge drum in the figure. Initially the system is at steady-state with a hold-up $\bar{V}=5 \mathrm{~m}^{3}$, which is $50 \%$ of full tank capacity, $V_{f u...
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GATE Chemical 2024 | Question: 54
A $\text{PD}$ controller with transfer function $G_{c}$ is used to stabilize an open-loop unstable process with transfer function $G_{p}$, where\[G_{c}=K_{c} \frac{\tau_{...
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GATE Chemical 2024 | Question: 55
Consider a tray-column of diameter $120 \mathrm{~cm}$. Each downcomer has a cross-sectional area of $575 \mathrm{~cm}^{2}$. For a tray, the percentage column cross-sectio...
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GATE CH 2023 | Question: 12
The vector $\overrightarrow{\boldsymbol{v}}$ ... $0$ $3$ $14$ $13$
The vector $\overrightarrow{\boldsymbol{v}}$ is defined as$$\overrightarrow{\boldsymbol{v}}=z x \hat{\imath}+2 x y \hat{\jmath}+3 y z \hat{k} .$$Which one of the followin...
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GATE CH 2023 | Question: 13
Given that $F=\frac{\left|z_1+z_2\right|}{\left|z_1\right|+\left|z_2\right|},$ where $z_1=2+3 i$ and $z_2=-2+3 i$ ... $\text{CORRECT}$? $F<0$ $F<1$ $F>1$ $F=1$
Given that$$F=\frac{\left|z_1+z_2\right|}{\left|z_1\right|+\left|z_2\right|},$$where $z_1=2+3 i$ and $z_2=-2+3 i$ with $i=\sqrt{-1}$, which one of the following options i...
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GATE CH 2023 | Question: 14
For a two-dimensional plane, the unit vectors, $\left(\hat{e}_r, \hat{e}_\theta\right)$ ... $-\hat{e}_{r}+\hat{e}_{\theta}$
For a two-dimensional plane, the unit vectors, $\left(\hat{e}_r, \hat{e}_\theta\right)$ of the polar coordinate system and $(\hat{\imath}, \hat{\jmath})$ of the cartesian...
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GATE CH 2023 | Question: 15
Which one of the following statements related to octane number is NOT correct? Linear alkanes with higher carbon ... Gasoline quality is measured in terms of octane number.
Which one of the following statements related to octane number is NOT correct?Linear alkanes with higher carbon number have higher octane number.Branching in linear alkan...
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GATE CH 2023 | Question: 16
Which one of the following options represents the major components of oleum? Sulfuric acid and nitric acid ... acid and hydrochloric acid Sulfuric acid and sulfur trioxide
Which one of the following options represents the major components of oleum?Sulfuric acid and nitric acidConcentrated sulfuric acid and petroleum jellySulfuric acid and h...
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GATE CH 2023 | Question: 17
For a reversible endothermic chemical reaction with constant heat of reaction over the operating temperature range, $K$ is ... $K$ on temperature $T$?
For a reversible endothermic chemical reaction with constant heat of reaction over the operating temperature range, $K$ is the thermodynamic equilibrium constant. Which o...
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GATE CH 2023 | Question: 18
Nitrile rubber is manufactured via polymerization process. Which one of the following options is the ... and butadiene Butadiene and styrene Butadiene and isoprene
Nitrile rubber is manufactured via polymerization process. Which one of the following options is the $\text{CORRECT}$ pair of monomers used in this process?Acrylonitrile ...
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GATE CH 2023 | Question: 19
John and Jane independently performed a thermodynamic experiment, in which $\mathbf{X}$ and $\mathbf{Y}$ represent the ...
John and Jane independently performed a thermodynamic experiment, in which $\mathbf{X}$ and $\mathbf{Y}$ represent the initial and final thermodynamic states of the syste...
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GATE CH 2023 | Question: 20
For a packed-bed comprising of uniform-sized spherical particles of diameter $D_{\mathrm{p}}$, the pressure drop across the bed is given ... exponent $n$? $2$ $-1$ $-2$ $1$
For a packed-bed comprising of uniform-sized spherical particles of diameter $D_{\mathrm{p}}$, the pressure drop across the bed is given by the Kozeny-Carman equation whe...
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GATE CH 2023 | Question: 21
Match the quantities in Group $1$ with their units in Group $2$ ... $\text{P-IV, Q-I, R-III, S-II}$
Match the quantities in Group $1$ with their units in Group $2$ listed in the table below.$$\begin{array}{|l|l|} \hline \qquad \qquad \qquad \textbf{Group 1} & \textbf{Gr...
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