List of top Questions asked in GATE CH- 2021

In a solvent regeneration process, a gas is used to strip a solute from a liquid in a countercurrent packed tower operating under isothermal condition. Pure gas is used in this stripping operation. All solutions are dilute and Henry's law, $y^ = mx$, is applicable. Here, $y^$ is the mole fraction of the solute in the gas phase in equilibrium with the liquid phase of solute mole fraction $x$, and $m$ is the Henry's law constant. Let $x_1$ be the mole fraction of the solute in the leaving liquid, and $x_2$ be the mole fraction of solute in the entering liquid. When the value of the ratio of the liquid-to-gas molar flow rates is equal to $m$, the overall liquid phase Number of Transfer Units, NTU$_{OL$, is given by}

Which of the following is NOT a necessary condition for a process under closed-loop control to be stable?

The van der Waals equation in reduced form is \[ P_r = \frac{8T_r}{3v_r - 1} - \frac{3}{v_r^2}. \] If \(v_r = 3\) and \(T_r = \frac{4}{3}\), compute the compressibility factor \(Z\) (rounded to 2 decimals).

Consider a steady flow of an incompressible Newtonian fluid through a smooth circular pipe. For turbulent flow, the kinetic energy correction factor is \[ \alpha_{turbulent} = \left(\frac{V_0}{\overline{V}}\right)^3 \frac{2n^2}{(3+n)(3+2n)} \] and the ratio of average velocity to centerline velocity is \[ \frac{\overline{V}}{V_0} = \frac{2n^2}{(n+1)(2n+1)}. \] For n = 7, the value of \(\frac{\alpha_{turbulent}}{\alpha_{laminar}}\) is \(\underline{\hspace{1cm}}\) (round to 2 decimals).

The molar heat capacity of n-pentane is \[ \frac{C_p}{R} = 2.46 + 45.4 \times 10^{-3}T - 14.1 \times 10^{-6}T^2. \] At 1000 K, the rate of change of molar entropy at constant pressure is \(\underline{\hspace{1cm}}\) J mol\(^{-1}\) K\(^{-2}\).

A company invests in a recovery unit to separate valuable metals from effluent streams. The capital investment is Rs. 10 lakhs. The recovered metals generate Rs. 4 lakhs per year. If the annual return on this investment is 15%, the annual operating costs should be \(\underline{\hspace{3cm}}\) lakhs of rupees (correct to 1 decimal place).

Let $A$ be an $n \times n$ square matrix ($n>1$) with elements \[ a_{ij} = \begin{cases} i \times j, & \text{if } i \ge j \\ 0, & \text{if } i < j \end{cases} \] The determinant of $A$ is:

A principal amount is charged a nominal annual interest rate of 10%. If interest is compounded continuously, what happens to the final amount after one year?

A source placed at the origin of a circular sample holder (radius \(r = 1\) m) emits particles uniformly in all directions. A detector of length \(l = 1\) cm is placed on the perimeter. During the experiment the detector registers 14 particles. The total number of particles emitted is \(\underline{\hspace{2cm}}\).

In reverse osmosis, the hydraulic pressure and osmotic pressure at the feed side of the membrane are $P_1$ and $\pi_1$, respectively. The corresponding values are $P_2$ and $\pi_2$ at the permeate side. The membrane, feed, and permeate are at the same temperature. For equilibrium to prevail, the general criterion that should be satisfied is:

Which of the following is NOT a standard to transmit measurement and control signals?

A feedforward controller can be used only if:

Turnover ratio is defined as:

The heat of combustion of methane, carbon monoxide and hydrogen are \(P\), \(Q\) and \(R\) respectively. For the reaction
\[ CH_4 + H_2O \longrightarrow CO + 3H_2 \] the heat of reaction is given by

Heat transfer coefficient for a vapor condensing as a film on a vertical surface is given by