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Recent questions tagged numerical-answers
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GATE CH 2021 | Question: 55
A viscous liquid is pumped through a pipe network in a chemical plant. The annual pumping cost per unit length of ... is _______ meter (round off to $3$ decimal places).
A viscous liquid is pumped through a pipe network in a chemical plant. The annual pumping cost per unit length of pipe is given by $$C_{\text{pump}} = \dfrac{48.13\: q^2 ...
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Mar 1, 2021
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GATE Chemical 2020 | Question: 21
An irreversible gas phase reaction $2 \textbf{P} \rightarrow 4 \textbf{Q} + \textbf{R}$ is conducted in an isothermal and isobaric batch reactor. Assume ideal gas behavio...
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GATE Chemical 2020 | Question: 22
Consider two Carnot engines $C_1$ and $C_2$ as shown in the figure.The efficiencies of the engines $C_1$ and $C_2$ are $0.40$ and $0.35$, respectively. If the temperature...
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Nov 16, 2020
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GATE Chemical 2020 | Question: 23
Consider the following closed loop system with $G_p$ and $G_c$ as the transfer functions of the process and the controller, respectively.For a unit step change in the set...
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1.8k
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Nov 16, 2020
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GATE Chemical 2020 | Question: 24
The decomposition of acetaldehyde $(X)$ to methane and carbon monoxide follows four-step free radical mechanism. The overall rate of decomposition of $X$ is $$-r_X=k_2 \b...
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1.8k
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soujanyareddy13
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Nov 16, 2020
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GATE Chemical 2020 | Question: 25
Sum of the eigenvalues of the matrix $\begin{bmatrix} 2 & 4 & 6 \\ 3 & 5 & 9 \\ 12 & 1 & 7 \end{bmatrix}$ is ______ (round off to nearest integer).
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1.8k
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soujanyareddy13
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Nov 16, 2020
Linear Algebra
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numerical-answers
linear-algebra
matrices
eigen-values
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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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Nov 16, 2020
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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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Nov 16, 2020
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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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Nov 16, 2020
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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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Nov 16, 2020
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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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Nov 16, 2020
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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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Nov 16, 2020
Differential equations
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numerical-answers
differential-equations
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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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Nov 16, 2020
Numerical Methods
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numerical-answers
numerical-methods
integration-by-trapezoidal-and-simpsons-rule
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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).
Arjun
4.7k
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Arjun
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Feb 24, 2019
Linear Algebra
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numerical-answers
linear-algebra
matrices
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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...
Arjun
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Arjun
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Feb 24, 2019
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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...
Arjun
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Arjun
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Feb 24, 2019
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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 ...
Arjun
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Arjun
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Feb 24, 2019
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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 ...
Arjun
4.7k
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Arjun
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Feb 24, 2019
Calculus
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numerical-answers
calculus
vector-calculus
directional-derivatives
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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 _____...
Arjun
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Arjun
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Feb 24, 2019
Probability and Statistics
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numerical-answers
probability-and-statistics
probability
conditional-probability
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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...
Arjun
4.7k
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Arjun
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Feb 24, 2019
Numerical Methods
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numerical-answers
numerical-methods
newton-raphson-method
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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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Arjun
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Feb 24, 2019
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GATE Chemical 2019 | Question: 38
For a given binary system at constant temperature and pressure, the molar volume (in $m^{3}$/mol) is given by: $v=30x_{A}+20x_{B}+x_{A}x_{B}\left ( 15x_{A} -7x_{B}\right ...
Arjun
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Arjun
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Feb 24, 2019
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GATE Chemical 2019 | Question: 39
Consider a vessel containing steam at $180^{\circ}C$.The initial steam quality is $0.5$ and the initial volume of the vessel in $1$ $m^{3}$. The vessel loses heat at a co...
Arjun
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Arjun
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Feb 24, 2019
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GATE Chemical 2019 | Question: 40
A fractionator recovers $95$ mol $\%$ $n$-propane as the distillate from an equimolar mixture of $n$-propane and $n$-butane. The condensate is a saturated liquid at $55^{...
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Feb 24, 2019
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GATE Chemical 2019 | Question: 41
A centrifugal pump is used to pump water (density $1000$ $kg/m^{3}$) from an inlet pressure of $10^{5}$ $Pa$ to an exit pressure of $2 \times 10^{5}$ $Pa$. The exit is at...
Arjun
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Arjun
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Feb 24, 2019
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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 $10^{4}$...
Arjun
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Arjun
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Feb 24, 2019
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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...
Arjun
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Arjun
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Feb 24, 2019
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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...
Arjun
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Arjun
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Feb 24, 2019
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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...
Arjun
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Arjun
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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...
Arjun
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Arjun
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Feb 24, 2019
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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...
Arjun
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GATE Chemical 2019 | Question: 50
Two spherical camphor particles of radii $20$ $cm$ and $5$ $cm$ far away from each other, are undergiong sublimation in a stream of air. The mass transfer coefficient is ...
Arjun
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