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Recent questions tagged numerical-answers

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GATE Chemical 2013 | Question: 23
The overall rates of an isothermal catalytic reaction using spherical catalyst particles of diameters 1 mm and 2 mm are $r_A$$_1$ and $r_A$$_2$ (in mol (kg-catalyst)$^{-1...
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GATE Chemical 2013 | Question: 22
An isothermal liquid phase zero order reaction A $\rightarrow$ B (k = 0.5 mol/m$^{3}$ -s) is carried out in a batch reactor. The initial concentration of A is 2 mol/m$^{3...
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GATE Chemical 2013 | Question: 21
The exit age distribution for a reactor is given by E(t) = $\delta$(t-4), where t is in seconds. A first order liquid phase reaction (k = 0.25 s$^{-1}$) is carried out in...
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GATE Chemical 2013 | Question: 18
A hole of area 1 cm$^{2}$ is opened on the surface of a large spherical cavity whose inside temperature is maintained at 727 $^{o}$C. The value of stefan-Boltzmann consta...
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GATE Chemical 2013 | Question: 15
Taking the acceleration due to gravity to be 10 m/s$^{2}$, the separation factor of a cyclone 0.5 m in diameter and having a tangential velocity of 20m/s near the wall is...
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GATE Chemical 2013 | Question: 9
An open tank contains two immiscible liquids of densities $(800\: kg/m^{3}$ and $1000\:kg/m^{3})$ as shown in the figure. If $g = 10\: m/s^2$, under static conditions, th...
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GATE Chemical 2013 | Question: 5
A gaseous system contains H${_2}$,I${_2}$ and HI, which participate in the gas-phase reaction 2H...
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GATE Chemical 2013 | Question: 2
For two rolls of a fair die, the probability of getting a 4 in the first roll and a number less than 4 in the second roll, up to 3 digits after the decimal point, is ____...
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GATE Chemical 2018 | Question: 55
A hot liquid is to be cooled in a $1-1$ shell and tube heat exchanger from $80^{\circ}C$ to $50^{\circ}C$. Cooling water enters the tube side at $30^{\circ}C$, and exits ...
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GATE Chemical 2018 | Question: 54
In a roll crusher, rolls of diameter $1$ $m$ each are set in such a manner that minimum clearance between the crushing surfaces is $15$ $mm$. If the angle of nip is $31^{...
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GATE Chemical 2018 | Question: 53
The humidity of air at a dry-bulb temperature of $65^{\circ}\:C$ is $0.025$ $kg$ water/$kg$ dry air. The latent heat of vaporization of water at $0^{\circ}\:C$ is $2500$ ...
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GATE Chemical 2018 | Question: 52
Hydrogenation of benzene is to be carried out using $Ni$ (density = $8910$ $kg/m^{3}$) as catalyst, cast in the from of non-porous hollow cylinders, as shown below. The r...
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GATE Chemical 2018 | Question: 47
For the matrix $A=\begin{bmatrix} \cos\theta &-\sin\theta \\ \sin \theta & \cos\theta \end{bmatrix}$ if $\det$ stands for the determinant and $A^{T}$ is the transpose of ...
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GATE Chemical 2018 | Question: 46
If $y=e^{-x^{2}}$ then the value of $\underset{x\rightarrow \infty }{\lim}\frac{1}{x}\frac{dy}{dx}$ is __________
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GATE Chemical 2018 | Question: 51
A set of standard stainless steel pipes, each of internal diameter $26.65\:mm$ and $6000\:mm$ length, is used to make a plug flow reactor by joining them in series to car...
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GATE Chemical 2018 | Question: 50
In a closed piston-cylinder system, methane was observed to obey the following equation of state$$P\left ( V-nb \right )=nRT$$where $b=0.029\:m^{3}$/mol. The temperature ...
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GATE Chemical 2018 | Question: 49
The volume of liquid filled in a spherical storage tank of radius $R$ is computed from height of liquid, $h$, in the outside tube (neglecting the volume of liquid in the ...
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GATE Chemical 2018 | Question: 45
For a closed-loop system, consider the following transfer functions:process $G_{p}\left ( s \right )$, controller $G_{c}\left ( s \right )$, measuring device $G_{m}\left ...
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GATE Chemical 2018 | Question: 44
Consider the following transfer function:$$G\left ( s \right )=\frac{3}{\left ( 5s+1 \right )^{2}}$$where, the natural period of oscillation is in min. The amplitude rati...
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GATE Chemical 2018 | Question: 43
A fiberboard sheet $\left ( 1.5\:m\times 2.0\:m\times 15\:mm \right )$ is being dried by suspending it horizontally in a current of hot, dry air. The edges are insulted s...
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GATE Chemical 2018 | Question: 48
An azeotropic mixture of ethanol and water is to be separated in a distillation column using benzene as an entrainer. At the column operating conditions, two liquid phase...
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GATE Chemical 2018 | Question: 42
A binary distillation column is designed by McCabe-Thiele method to get a distillate mole fraction of $0.9$. The enriching section operating line has an intercept with $y...
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GATE Chemical 2018 | Question: 41
It is decided to extract $A$ from a feed containing $20$ mol$\%$ $A$ and $80$ mol$\%$ $B$ in two ideal cross-current stages as shown below, using equal amount of pure sol...
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GATE Chemical 2018 | Question: 40
The elementary second-order liquid phase reaction $A+B{\rightarrow}C+D$ is carried out in an isothermal plug flow reactor of $2\:m^{3}$ volume. The inlet volumetric flow ...
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GATE Chemical 2018 | Question: 39
A $CSTR$ and a $PFR$ of equal volume are connected in series as shown below to carry out a first-order, isothermal, liquid phase reaction$$A{\rightarrow}P$$The rate const...
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GATE Chemical 2018 | Question: 38
At a shear rate of $10\:s^{-1}$, the apparent viscosity of a non-Newtonian liquid was found to be $1\: Pa\:s$. At a shear rate of $100\:s^{-1}$, the apparent viscosity of...
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GATE Chemical 2018 | Question: 37
Under isothermal condition, a vertical tube of length $L=100\:m$ contains a gas of molecular weight equal to $60$. The pressure and temperature at the top of the tube are...
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GATE Chemical 2018 | Question: 36
Vapour bubbles are formed in the nucleate boiling regime at a frequency of $10$ bubbles per second per nucleation site. There are $100$ nucleation sites per $m^{2}$ of he...
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GATE Chemical 2018 | Question: 35
The wall of a pipe of radius $1\:m$ is at a uniform temperature of $200\:^{\circ}C$, and is covered by insulation of thickness $0.1\:m$. The ambient air outside the ins...
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GATE Chemical 2018 | Question: 34
An insulted storage tank contains $1000\:kg$ liquid of specific heat $10\:kJ\:kg^{-1}\:K^{-1}$. The liquid is heated by saturated steam, condensing in a helical coil at a...
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GATE Chemical 2018 | Question: 33
In a laboratory batch setup, reaction of $P$ over a catalyst was studied at various temperature. The reactions occurring are$$P\rightarrow 2Q\:;\:P\rightarrow R$$At the e...
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GATE Chemical 2018 | Question: 25
The inital water level in a tank is $4\:m$. When the value located at the bottom is opened, the rate of change of water level ($L$) with respect to time ($t$) is, $\frac{...
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GATE Chemical 2018 | Question: 24
The ammonia ($NH_{3}$) oxidation process occurs over a catalyst as$$4NH_{3}+5O_{2}\rightarrow 6H_{2}O+4NO$$Air is supplied such that oxygen ($O_{2}$) is $20\%$ in excess ...
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GATE Chemical 2018 | Question: 23
A venturi meter is installed to measure the flow rate of water in a $178\:mm$ diameter ($ID$) pipe. The throat diameter is $102\:mm$. The differential pressure measured u...
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