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Recent questions tagged numerical-answers

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GATE Chemical 2020 | Question: 37
A feed stream containing pure species $L$ flows into a reactor, where $L$ is partly converted to $M$ as shown in the figure.The mass flow rate of the recycle stream is $2...
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GATE Chemical 2020 | Question: 41
A fluid is heated from $40^{\circ}C$ to $60^{\circ} C$ in a countercurrent, double pipe heat exchanger. Hot fluid enters at $100^{\circ}C$ and exits at $70^{\circ}C$. The...
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GATE Chemical 2020 | Question: 42
Consider an infinitely long rectangular fin exposed to a surrounding fluid at a constant temperature $T_a=27^{\circ}C$.The steady state one dimensional energy balance on ...
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GATE Chemical 2020 | Question: 43
Liquid water is pumped at a volumetric flow rate of $0.02 \: m^3 s^{-1}$ from Tank $I$ to Tank $II$, as shown in the figure.Both the tanks are open to the atmosphere. The...
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GATE Chemical 2020 | Question: 44
An elementary liquid phase reversible reaction $P \leftrightarrows Q$ is carried out in an ideal continuous stirred tank reactor (CSTR) operated at steady state. The rate...
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GATE Chemical 2020 | Question: 45
An aqueous suspension at $60^{\circ}C$ is fed to the first effect of a double effect forward feed evaporator with a mass flow rate of $1.25 \: kg \: s^{-1}$. The sum of t...
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GATE Chemical 2020 | Question: 46
A vertically held packed bed has a height of $1 \: m$, and void fraction of $0.1$, when there is no flow through the bed. The incipient (minimum) fluidization is set in b...
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GATE Chemical 2020 | Question: 47
Two ideal cross-current stages operate to extract $P$ from a feed containing $P$ and $Q$, as shown below.The mass flow rates of $P$ and $Q$ fed to Stage $1$ are $1,000 \:...
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GATE Chemical 2020 | Question: 48
Consider a vertically falling film of water over an impermeable wall. The film is in contact with a static pool of an non-reactive pure gas. The gas diffuses into the wat...
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GATE Chemical 2020 | Question: 49
An exothermic, aqueous phase, irreversible, first order reaction, $Y \rightarrow Z$ is carried out in an ideal continuous stirred tank reactor (CSTR) operated adiabatical...
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GATE Chemical 2020 | Question: 50
The liquid phase irreversible reactions, $P \xrightarrow[]{k_1} Q$ and $P \xrightarrow[]{k_2} R$, are carried out in an ideal continuous stirred tank reactor (CSTR) opera...
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GATE Chemical 2020 | Question: 51
A catalytic gas phase reaction $P \rightarrow Q$ is conducted in an isothermal packed bed reactor operated at steady state. The reaction is irreversible and second order ...
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GATE Chemical 2020 | Question: 52
Flow of water thorough an equal percentage valve is $900 \text{ litre } h^{-1}$ at $30 \%$ opening, and $1080 \text{ litre } h^{-1}$ at $35 \%$ opening. Assume that the p...
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GATE Chemical 2020 | Question: 53
Consider the following closed loop system.$G_c, G_f$ , and $G_p$ are the transfer functions of the controller, the final control element and the process, respectively. $Y...
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GATE Chemical 2020 | Question: 54
Given $\dfrac{dy}{dx}=y-20$, and $y \mid_{x=0}=40$, the value of $y$ at $x=2$ is _________ (round off to nearest integer)
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GATE Chemical 2020 | Question: 55
Consider the following dataset.$$\begin{array}{|c|c|c|c|c|c|} \hline x & 1 & 3 & 5 & 15 & 25 \\ \hline f(x) & 6 & 8 & 10 & 12 & 5 \\ \hline \end{array}$$The value of the ...
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GATE Chemical 2020 | Question: 5
In a constant-pressure cake filtration with an incompressible cake layer, volume of the filtrate $(V)$ is measured as a function of time $t$. The plot of $t/V$ versus $V$...
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GATE Chemical 2020 | Question: 10
Consider a batch distillation process for an equimolar mixture of benzene and toluene at atmospheric pressure. The mole fraction of benzene in the distillate collected af...
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GATE Chemical 2020 | Question: 15
Annual capacity of a plant producing phenol is $100$ metric tons. Phenol sells at INR $200$ per kg, and its production cost is INR $50$ per kg. The sum of annual fixed ch...
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GATE Chemical 2020 | Question: 16
A rigid spherical particle undergoes free settling in a liquid of density $750 \: kg \: m^{-3}$ and viscosity $9.81 \times 10^{-3} \: Pa \: s$. Density of the particle is...
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GATE Chemical 2019 | Question: 3
Consider a rigid, perfectly insulated, container partitioned into two unequal parts by a thin membrane (see figure). One part contains one mole of an ideal gas at pressur...
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GATE Chemical 2019 | Question: 13
The correct expression for the Colburn $j$-factor for mass transfer that relates Sherwood number ($Sh$), Reynolds number ($Re$) and Schmidt number ($Sc$) is$\frac{Sh}{\le...
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GATE Chemical 2019 | Question: 22
The product of the eigenvalues of the matrix $\begin{pmatrix} 2 &3 \\ 0& 7 \end{pmatrix}$ is ____________ (rounded off to one decimal place).
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GATE Chemical 2019 | Question: 23
For a hydraulic lift with dimensions shown in figure, assuming $g=10\:m/s^{2}$, the maximum diameter $D_{left}$ (in $m$) that lifts a vehicle of mass $1000 \:kg$ using a...
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GATE Chemical 2019 | Question: 24
The liquid flow rate through an equal percentage control valve, when fully open, is $150$ gal/min and the corresponding pressure drop is $50$ psi. If the specific gravity...
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GATE Chemical 2019 | Question: 25
Consider a sealed rigid bottle containing $CO_{2}$ and $H_{2}O$ at $10$ bar and ambient temperature. Assume that the gas phase in the bottle is pure $CO_{2}$ and follows ...
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GATE Chemical 2019 | Question: 28
An incompressible Newtonian fluid flows in a pipe of diameter $D_{1}$ at volumetric flow rate $Q$. Fluid with same properties flows in another pipe of diameter $D_{2}=D_...
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GATE Chemical 2019 | Question: 29
A disk turbine is used to stir a liquid in a baffled tank. To design the agitator, experiments are performed in a lab-scale model with a turbine diameter of $0.05 \:m$ an...
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GATE Chemical 2019 | Question: 30
Consider two non-interacting tanks-in-series as shown in figure. Water enters $TANK$ $1$ at $q$ $cm^{3}/s$ and drains down to $TANK$ $2$ by gravity at a rate $k\sqrt{h_{1...
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GATE Chemical 2019 | Question: 32
$100$ $kg$ of a feed containing $50$ $wt.\%$ of a solute $C$ is contacted with $80$ $kg$ of a solvent containing $0.5$ $wt.\%$ of $C$ is a mixer-settler unit. From the op...
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GATE Chemical 2019 | Question: 34
If $x,y$ and $z$ are directions in a Cartesian coordinate system and $i$, $j$ and $k$ are the respective unit vectors, the directional derivative of the function $u\left ...
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GATE Chemical 2019 | Question: 35
Two unbiased dice are thrown. Each dice can show any number between $1$ and $6$. The probability that the sum of the outcomes of the two dice is divisible by $4$ is _____...
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GATE Chemical 2019 | Question: 36
The Newton-Raphson method is used to determine the root of the equation $f(x)=e^{-x}-x$. If the initial guess for the root is 0, the estimate of the root after two iterat...
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GATE Chemical 2019 | Question: 37
Carbon monoxide $(CO)$ reacts with hydrogen sulphide $(H_2S)$ at a constant temperature of $800\:K$ and a constant pressure of 2 bar as:$$CO+H_2S\leftrightharpoons COS+H_...
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GATE Chemical 2019 | Question: 42
A solid sphere of radius $1$ $cm$ and initial temperature of $25^{\circ}\:C$ is exposed to a gas stream at $100^{\circ}\:C$. For the solid sphere, the density is $10^{4}$...
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GATE Chemical 2019 | Question: 43
Stream $A$ with specific heat capacity $C_{PA}=2000\:J/\left ( kg\:K \right )$ is cooled from $90^{\circ}C$ to $45^{\circ}C$ in a concentric double pipe counter current...
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GATE Chemical 2019 | Question: 44
A $20$ $cm$ diameter cylindrical solid pellet of a nuclear fuel with density $6000\: kg/m^{3}$ and conductivity of $300\:W/\left ( m\:K \right )$ generates heat by nucle...
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GATE Chemical 2019 | Question: 45
The elementary, irreversible liquid-phase, parallel reactions, $2A\rightarrow D$ and $2A\rightarrow U$, take place in an isothermal non-ideal reactor. The $C$-curve measu...
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GATE Chemical 2019 | Question: 46
A first-order irreversible liquid phase reaction $A\rightarrow B\left ( k=0.1\:min^{-1} \right )$ is carried out under isothermal, steady state conditions in the followin...
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GATE Chemical 2019 | Question: 47
The elementary liquid-phase irreversible reactions$A\overset{k_{1}=0.4\: min^{-1}}{\rightarrow}B\overset{k_{2}=0.1\:min^{-1}}{\rightarrow}C$take place in an isothermal id...
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