# Recent activity An oil with a flow rate of $1000\:kg/h$ is to be cooled using water in a double-pipe counter-flow heat exchanger from a temperature of $70^{\circ}C$ to $40^{\circ}C$. Water enters the exchanger at $25^{\circ}C$ and leaves at $40^{\circ}C$. The specific heats of oil ... coefficient is $0.2\:kW\:m^{-2}\:K^{-1}$. The minimum heat exchanger area (in $m^{2}$) required for this operation is __________
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)
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. $Y$ and $Y_{sp}$ are the response and its set point, respectively. For a gain margin of $1.6$, the design value of $K_c$ is __________ (correct up to one decimal place)
Consider the gas phase reaction $N_2O_4 \rightleftarrows 2NO_2$ occuring in an isothermal and isobaric reactor maintained at $298 K$ and $1.0$ bar. The standard Gibbs energy change of the reaction at $298 K$ is $\Delta G^\circ_{298}=5253 \; J\;mol^{-1}.$ The standard ... initially charged to the reactor, the fraction of $N_2O_4$ that decomposes into $NO_2$ at equilibrium is $0$ $0.17$ $0.38$ $1$
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 proportional to $1\sqrt{r\left ( t \right )}$, where $r(t)$ is the radius of the sphere at ... $cm$ and $5$ $cm$ camphor particles, respectively, the ratio $t_{1}/t_{2}$ is _________________ (rounded off to one decimal place).
A taxi-car is bought for $Rs\: 10$ lakhs. Its salvage value is zero. The expected yearly income after paying all expenses and applicable taxes is $Rs$ $3$ lakhs. The compound interest rate is $9\%$ per annum The discounted payback period (in years), is ____________________ (rounded off to the next higher integer).
Consider two competing equipment $A$ and $B$. For a compound interest rate of $10\%$ per annum, in order for equipment $B$ to be the economically cheaper option, its minimum life (in years) is _____________ (rounded off to the next higher integer). $\begin{array}{cc}\ &\text{$Equipment$} & \text{$ ...
Consider the reactor-separator-recycle process operating under steady state conditions as shown in the figure. The reactor is an ideal Continuous-Stirred Tank Reactor ($CSTR$), where the reaction $A+B\rightarrow C$ occurs. Assume that there is no impurity in the ... in the reactor that minimizes the recycle rate is ____________________________ (rounded off to two decimal places).
A binary mixture with components $A$ and $B$ is to be separated in a distillation column to obtain $95$ mol$\%$ $A$ as the top product. The binary mixture has a constant relative volatility $\alpha _{AB}=2$. The column feed is a ... constant molal overflow, negligible heat loss, ideal trays, the minimum reflux ratio for this separation is _______________ (rounded off to one decimal place).
A countercurrent absorption tower is designed to remove $95\%$ of component $A$ from an incoming binary gas mixture using pure solvent $B$. The mole ratio of $A$ in the inlet gas is $0.02$. The carrier gas flow rate is $50$ $k$mol/$h$ The equilibrium ... at twice the minimum solvent flow rate, the mole ratio of $A$ in the exit liquid stream is ____________ (rounded off to three decimal places).
For the closed loop system shown in figure, the phase margin (in degrees) is ____________ (rounded off to one decimal place).
The elementary irreversible gas-phase reaction $A\rightarrow B+C$ is carried out adiabatically in an ideal $CSTR$ (Continuous-Stirred Tank Reactor) operating at 10 $atm$. Pure $A$ enters the $CSTR$ at a flow rate of 10 mol/$s$ and a temperature of $450$ ... referenced to $273 \:K$. The reactor volume (in Liters) for $75\%$conversion is __________________ (rounded off to the nearest integer).
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 ideal $CSTR$(Continuous-Stirred Tank Reactor). Pure $A$ is fed to the reactor at a ... , is ________________ (rounded off to the nearest integer).
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 following reactor arrangement comprising an ideal $CSTR$ (Continuous-Stirred Tank Reactor) and two ideal ... From the information in the figure, the volume of the $CSTR$ (in Liters) is ______________ (rounded off to the nearest integer).
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 measured in a tracer experiment is shown in the figure, where $C(t)$ is the ... $2$ mol/Liter. Using the segregated model, the percentage conversion in the reactor is ___________________ (rounded off to the nearest integer)
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 nuclear fission at a spatially uniform rate of $10^{4}\:W/kg$. The heat from ... and azimuthal dependence, the maximum temperature (in $^{\circ}C$) in the pellet at steady state is ________________ (rounded off to the nearest integer).
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 heat exchanger having a heat transfer area of $8$ $m^{2}$. The cold stream $B$ ... $A$ (in $kg/s$), is _____________________ (rounded off to two decimal places).
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 $10^{4}$ $kg/m^{3}$ and the specific heat capacity is $500\;J/(kg\:K)$. The density of the gas ... $95^{\circ}\:C$ is ______________ (rounded off to the nearest integer)
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 an elevation of $10$ $m$ ... $g=10$ $m/s^{2}$. Neglecting losses in the system, the power (in Watts) delivered by the pump is __________ (rounded off to the nearest integer).
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 $55^{\circ}\:C$ ... Assuming Raoult's law, the condenser pressure (in bar) is _________________ (rounded off to one decimal place).
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 constant rate $q$ under isobaric conditions so that the quality of steam reduces to $0.1$ after $10$ ... 21kJ/kg$.}\\ \\ \end{array}$ The rate of heat loss $q$ (in $kJ$/hour) is _____________ (rounded off to the nearest integer).
For a given binary system at constant temperature and pressure, the molar volume (in $m^{3}$/mol) is given by: $v=30x_{A}+20x_{B}+x_{A}x_{B}\left ( 15x_{A} -7x_{B}\right )$, where $x_{A}$ and $x_{B}$ are the mole fraction of components $A$ and $B$, respectively. The volume change of mixing $\Delta v_{mix}$ (in $m{3}$/mol) at $x_{A}=0.5$ is _______________ (rounded off to one decimal place).
Carbon monoxide $(CO)$ reacts with hydrogen sulphide $(H_2S)$ at a constant temperature of $800\:K$ and a constant pressure of 2 bar as: $CO+H_2S\leftrightharpoons COS+H_2$ The Gibbs free energy of the reaction ${\Delta g^\circ}_{rxn}=22972.3\:J/mol$ and ... only $4\:mol$ of CO are present, the extent of the reaction (in mol) at equilibrium is _________ (rounded off to two decimal places).
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 iterations is _______ (rounded off to three decimal places).
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 ____________ (rounded off to two decimal places).
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 $u\left ( x,y,z \right )=x^{2}-3yz$ at the point $\left ( 2,0,-4 \right )$ in the direction $\left ( i+j-2k \right )/\sqrt{6}$_____________ (rounded off to two decimal places).
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 the ideal gas law. The liquid phase in the bottle contains $CO_{2}$ ... $CO_{2}$ dissolved in $H_{2}O$ is __________________ (rounded off to three decimal places).
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 of the liquid is $0.8$, then the valve coefficient, $C_{V}$, in gal/(min $psi^{0.5}$) is _________________ (rounded off to two decimal places).
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 force of $100 \:N$ is ____________________ (rounded off to two decimal places).
The product of the eigenvalues of the matrix $\begin{pmatrix} 2 &3 \\ 0& 7 \end{pmatrix}$ is ______________________ (rounded off to one decimal place).
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 at $45^{\circ}C$. The properties of the liquids are constant ... percentage saving in heat transfer area for counter-current option with respect to the area of co-current option is __________ (rounded off to third decimal place).
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 $31^{\circ}$, the maximum diameter of the particle (in $mm$) which can be crushed is ___________ (rounded off to third decimal place).
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 $2500$ $kJ/kg$. The psychrometric ratio of air is $0.95$ $kJ$ ($kg$ dry ... , the enthalpy of air (in $kJ/kg$) at its adiabatic saturation temperature of $35^{\circ}\:C$ is ____________________ (rounded off to two decimal places).
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 reaction occurs on all the surfaces of the hollow cylinder. During an experiment, one such cylinder ... rate of reaction in mol($kg$ of catalyst)$^{-1}$ min$^{-1}$ is ________________________ (rounded off to three decimal places).
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 carry out degradation of polyethylene. Seven such pipes are required to obtain a ... pipes of the same internal diameter to be procured for obtaining at least $66\%$ conversion under the same reaction condition is _______________.
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 and volume are $500 \:^{\circ}C$ and $5\:m^{3}$ respectively for $100$ moles of ... system, the isobaric rate of change of temperature with volume (in $^{\circ}C\:/m^{3}$) is ________________ (rounded off to second decimal place).
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 outside tube) as $V=\pi h^{2}\frac{\left ( 3R-h \right )}{3}$. The estimate of ... of Secant method, using $1\:m$ and $3\:m$ as tow initial guesses of liquid height is _________________ (rounded off to second decimal place).
If $y=e^{-x^{2}}$ then the value of $\underset{x\rightarrow \infty }{lim}\frac{1}{x}\frac{dy}{dx}$ is __________
For a closed-loop system, consider the following transfer functions: process $G_{p}\left ( s \right )$, controller $G_{c}\left ( s \right )$, measuring device $G_{m}\left ( s \right )$, and final control element $G_{f}\left ( s \right )$ ... The offset in the closed loop response due to a unit step change introduced in the set point of the output variable is ___________.
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 ratio at a frequency of $0.5$ rad/min is ________________ (rounded off to second decimal place).