# Recent questions tagged gate2014

A process with transfer function, $G_{p}=\frac{2}{s-1}$ is to be controlled by a feedback proportional controller with a gain $K_{c}$. If the transfer functions of all other elements in the control loop are unity, the which $ONE$ of the following conditions produces a stable closed loop response ? $K_{c}=0.25$ $0<K_{c}<0.25$ $0.25<K_{c}<0.5$ $K_{c}>0.5$
Consider a binary liquid mixture at equilibrium with its vapour at $25^{\circ}C$. Antoine equation for this system is given as $log_{10}\:p_{t}^{sat}=A-\frac{B}{t+C}$ where $t$ is in $^{\circ}C$ and $p$ in Torr. The Antoine constant ($A$, $B$ and $C$) ... of component $1$ in liquid phase $(x_{1})$ is $0.11$, then the mole fraction of component $1$ in vapour phase $(y_{1})$ is ____________________
In a steady and incompressible flow of a fluid (density = $1.25\: kg\: m^{-3}$), the difference between stagnation and static pressures at the same location in the flow is $30 \:mm$ of mercury (density = $13600 \:kg \:m^{-3}$). Considering gravitational acceleration as $10 \:m \:s^{-2}$ the fluid speed (in $m \:s^{-1}$) is _________________
Consider the following block diagram for a closed-loop feedback control system A proportional controller is being used with $K_{c}=-4$. If a step change in distrubance of magnitude $2$ affects the system, then the value of the offset is _____________
Match the raw materials of Group-$1$ and $2$ with the final products of Group-$3$ $\begin{array}&&\textbf{Group 1} & \textbf{Group 2} & \textbf{Group 3} \\ &\text{P$_{1}$: Ethylene} & \text{Q$_{1}$: Ammonia} &\text{R$_{1}$: Synthetic fibre}\\ &\text{P$ ...
Determine the correctness or otherwise of the following Assertion $[a]$ and Reason $[r]$ Assertion: Significant combustion of coke takes place only if it is heated at higher temperature in presence of air. Reason: $C+O_{2}{\rightarrow} CO_{2}$ is an exothermic reaction. Both $[a]$ and $[r]$ ... is not the correct reason for $[a]$ $[a]$ is correct but $[r]$ is false Both $[a]$ and $[r]$ are false
A cash flow of Rs. $12,000$ per year is received at the end year (uniform periodic payment) for $7$ consecutive years. The rate of interest is $9\%$ per year compounded annually. The present worth (in Rs.) of such cash flow at time zero is ____________
A step change of magnitude $2$ is introduced into a system having the following transfer function $G\left ( s \right )=\frac{2}{s^{2}+2s+4}$ The percent overshoot is __________
In a steady incompressible flow, the velocity distribution is given by $\bar{V}=3x\hat{i}-Py\hat{j}+5z\hat{k}$, where, $V$ is in $m/s$ and $x,y$ and $z$ are in $m$. In order to satisfy the mass conservation, the value of the constant $P$ (in $s^{-1}$) is _____________
Given below is a simplified block diagram of a feedforward control system. The transfer function of the process is $G_{p}=\frac{5}{s+1}$ and the disturbance transfer function is $G_{d}=\frac{5}{s^{2}+2s+1}$. The transfer function of the $PERFECT$ feedforward controller, $G_{f}(s)$ ... $\frac{-5}{\left ( s+1 \right )}$ $\frac{-1}{5\left ( s+1 \right )}$ $-5\left ( s+1 \right )$
A polymer plant with a production capacity of $10,000$ tons per year has an overall yield of $70\%$, on mass basis ($kg$ of product per $kg$ of raw material), The raw material costs Rs. $50,000$ per ton. A process modification is proposed to increase ... $12.5$ crore. In how many years can the invested amount be recovered with the additional profit? ________________
The bottom face of a horizontal slab of thickness $6 \:mm$ is maintained at $300^{\circ}C$. The top face is exposed to a flowing gas at $30^{\circ}C$. The thermal conductivity of the slab is $1.5 \:W\: m^{-1}\: K^{-1}$ and the convective heat transfer coefficient is $30\: W\: m^{-2}\:K^{-1}$. At steady state, the temperature (in $^{\circ}C$) of the top face is ______________
Match the following $\begin{array}&&\textbf{Group I} & \textbf{Group II} \\ &\text{P. Turbulence} & \text{I. Reciprocating pump}\\ &\text{Q.$ ... P-III, R-II, T-IV Q-V, R-II, S-III P-III, R-IV, T-II Q-III, S-V, T-IV
Two elemental gases ($A$ and $B$) are reacting to form a liquid ($C$) in a steady state process as per the reaction $A+B{\rightarrow}C$. The single-pass conversion of the reaction is only $20\%$ and hence recycle is used. The product is separated completely in pure ... in the recycle stream is $20$ mol$\%$. The amount of purge stream (in moles) per $100$ moles of the fresh feed is ___________
Match the following $\begin{array}&&\textbf{Group I} & \textbf{Group II} \\ &\text{P. Tank in series model} & \text{I. Non-isothermal reaction}\\&\text{Q. Liquid-liquid extraction} & \text{II. Mixer-settler} \\ &\text{R. Optimum temperature progression} & \text{III.$ ... Q-IV, R-I, S-III P-I, Q-II, R-III, S-IV P-III, Q-I, R-II, S-IV P-III, Q-II, R-I, S-IV
An incompressible fluid is flowing through a contraction section of length $L$ and has a $1-D$ ($x$- direction steady state velocity distribution, $u=u_{0}\left ( 1+\frac{2x}{L} \right )$. If $u_{0}=2\:m/s$ and $L=3m$, the convective acceleration (in $m/s^{2}$) of the fluid at $L$ is _________
A binary distillation column is operating with a mixed feed containing $20$ mol$\%$ vapour. If the feed quality is changed to $80$ mol$\%$ vapour, the change is the slope of the $q$-line is _______________
A vapour phase catalytic reaction $(Q+R{\rightarrow}S)$ follows Rideal mechanism ($R$ and $S$ are not absorbed). Initially, the mixture contains only the reactants in equimolar ratio. The surface reaction step is rate controlling. With constant $a$ and $b$, the initial rate of reaction $(-r_{o})$ in terms of ... $-r_{o}=\frac{aP_{T}^{2}}{\left (1+bP_{T}\right)^{2}}$
A homogenous reaction $(R{\rightarrow}P)$ occurs in a batch reactor. The conversion of the reactant $R$ is $67\%$ after $10$ minutes and $80\%$ after $20$ minutes. The rate equation for this reaction is $-r_{R}=k$ $-r_{R}=kC_{R}^{2}$ $-r_{R}=kC_{R}^{3}$ $-r_{R}=kC_{R}^{0.5}$
Carbon monoxide $(CO)$ is burnt in pressure of $200\%$ excess pure oxygen and the flame temperature achieved is $2298\:K$. The inlet streams are at $25^{\circ}$. The standard heat of formation (at $25^{\circ}C$) of $CO$ and $CO_{2}$ are $-110\:kJ\:mol^{-1}$ ... $T$ is the temperature in $K$. The heat loss (in $kJ$) per mole of $CO$ burnt Is _________________
Consider the following two normal distributions $f_{1}\left ( x \right )=exp\left ( -\pi x^{2} \right )$ $f_{2}\left ( x \right )=\frac{1}{2 \pi}exp\left \{ -\frac{1}{4\pi }\left ( x^{2}+2x+1 \right ) \right \}$ If $\mu$ and ${\rho}$ denote the mean and standard deviation, respectively, then ... $\mu _{1}>\mu _{2}\:and \:\sigma _{1}^{2}>\sigma _{2}^{2}$
A spherical ball of benzoic acid (diameter=$1.5\:cm$) is submerged in a pool of still water. The solubility and diffusively of benzoic acid in water are $0.03$ $k$mol/$m^{4}$ and $1.25 \times 10^{-9}\:m^{2}/s$ ... benzoic acid approximately is $3.54 \times 10^{-11}$ $3.54 \times 10^{-12}$ $3.54 \times 10^{-13}$ $3.54 \times 10^{-14}$
In rolling of two fair dice, the outcome of an experiments is considered to be the sum of the numbers appearing on the dice. The probability is highest for the outcome of __________________
A wet solid of $100\:kg$ is dried from a moisture content of $40\:wt\%$ to $10\:wt\%$. The critical moisture content is $15\:wt\%$ and the equilibrium moisture content is negligible. All moisture contents are on dry basis. The falling rate is considered ... . It takes $5$ hours to dry the material in the constant rate period. The duration (in hours) of the falling rate period is ________________
A brick wall of $20\:cm$ thickness has thermal conductivity of $0.7\:W\:m^{-1}\:K^{-1}$. An insulation of thermal conductivity $0.2\:W\:m^{-1}\:K^{-1}$ is to be applied on one side of the wall, so that the heat ... $cm$) of the isulation is ________________
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 __________
Which $ONE$ of the following is $CORRECT$ for an ideal gas in a closed system? $\left ( \frac{\partial U}{\partial V} \right )_{s}V=nR\left ( \frac{\partial U}{\partial S} \right )_{V}$ ... $\left ( \frac{\partial H}{\partial P} \right )_{s}P=nR\left ( \frac{\partial U}{\partial S} \right )_{V}$
Consider the following differential equation $\frac{dy}{dx}=x+In\:\left ( y \right ); y=2 \: at \: x=0$ The solution of this equation at $x=0.4$ using Euler method with a step size of $h=0.2$ is ___________________
The differential equation $\frac{d^{2}y}{dx^{2}}+x^{2}\frac{dy}{dx}+x^{3}y=e^{x}$ is a non-linear differential equation of first degree linear differential equation of first degree linear differential equation of second degree non-linear differential equation of second degree
The integrating factor for the differential equation $\frac{dy}{dx}-\frac{y}{1+x}=\left ( 1+x \right )$ is $\frac{1}{1+x}$ $(1+x)$ $x(1+x)$ $\frac{x}{1+x}$