List of practice Questions

A single-effect evaporator with a heat transfer area of 70 m$^{2}$ concentrates a salt solution using steam. The salt solution feed rate and temperature are 10000 kg h$^{-1}$ and 40$^\circ$C, respectively. The saturated steam feed rate and temperature are 7500 kg h$^{-1}$ and 150$^\circ$C, respectively. The boiling temperature of the solution in the evaporator is 80$^\circ$C. The average specific heat is 0.8 kcal kg$^{-1}$ K$^{-1}$. The latent heat of vaporization is 500 kcal kg$^{-1}$. If the steam-economy is 0.8, the overall heat transfer coefficient is $\underline{\hspace{2cm}}$ kcal h$^{-1}$ m$^{-2}$ K$^{-1}$ (rounded off to the nearest integer).

An equimolar binary mixture is to be separated in a simple tray-distillation column. The feed rate is 50 kmol min$^{-1}$. The mole fractions of the more volatile component in the top and bottom products are 0.90 and 0.01, respectively. The feed and the reflux stream are saturated liquids. On application of the McCabe-Thiele method, the operating line for the stripping section is obtained as \[ y = 1.5x - 0.005 \] where $y$ and $x$ are the mole fractions of the more volatile component in the vapor and liquid phases, respectively. The reflux ratio is $\underline{\hspace{2cm}}$ (rounded off to two decimal places).

The dry-bulb temperature of air in a room is 30 °C. The Antoine equation for water is \[ \ln P^{sat} = 12.00 - \frac{4000}{T - 40} \] where $T$ is in K and $P^{sat}$ is in bar. The latent heat of vaporization is 2000 kJ kg$^{-1}$, humid heat is 1.0 kJ kg$^{-1}$ K$^{-1}$, and the molecular weights of air and water are 28 and 18 kg kmol$^{-1}$. If absolute humidity is $Y'$ kg moisture per kg dry air, then for a wet-bulb depression of 9 °C, $1000\,Y' =$ $\underline{\hspace{2cm}}$ (rounded to one decimal place).

In the tank-level control system shown, the tank cross-sectional area is $A$. The flow controllers are perfect. The level controller (LC) is PI. For an integral time $\tau_I$, the controller gain $K_c$ is tuned for critical damping. The value of $\dfrac{K_c\tau_I}{A}$ is $\underline{\hspace{2cm}}$ (rounded off to nearest integer).

In the block diagram shown in the figure, the transfer function $G=\dfrac{K}{(\tau s+1)}$ with $K>0$ and $\tau>0$. The maximum value of $K$ below which the system remains stable is $\underline{\hspace{2cm}}$ (rounded off to two decimal places).

Consider a single-input-single-output (SISO) system with the transfer function \[ G_p(s)=\frac{2(s+1)}{\left(\frac{1}{2}s+1\right)\left(\frac{1}{4}s+1\right)} \] where the time constants are in minutes. The system is forced by a unit step input at time $t=0$. The time at which the output response reaches its maximum is $\underline{\hspace{2cm}}$ minutes (rounded off to two decimal places).

Information for a proposed greenfield project is provided in the table. The discounted cash flow for the fourth year is Rs $\underline{\hspace{1cm}}$ crores (rounded off to one decimal place).

Consider the process in the figure. The liquid-phase elementary reactions \[ A + B \rightarrow P -r_{B1} = k_1 x_A x_B \] \[ P + B \rightarrow S -r_{B2} = k_2 x_P x_B \] \[ S + A \rightarrow 2P -r_{S3} = k_3 x_S x_A \] occur in the continuous stirred tank reactor (CSTR). All fresh feeds, exit streams and recycle streams are pure. At steady state, the net generation of the undesired product $S$ in the CSTR is zero. Let $q = x_A/x_B$ in the reactor. For 90% single-pass conversion of $B$ and fixed product rate, determine the value of $q$ that minimizes the sum of the molar flow rates of the A and S recycle streams (rounded to one decimal place).

An elementary irreversible liquid-phase reaction, $2A \rightarrow B$, is carried out under isothermal conditions in a 1 m$^{3}$ ideal plug flow reactor (PFR) as shown. The volumetric flow rate of fresh A is $v_{1}=10$ m$^{3}$ h$^{-1}$ and its concentration is $C_{A1}=2$ kmol m$^{-3}$. For a recycle ratio $R=0$, the conversion of A at location 2 with respect to fresh feed (location 1) is 50%. For $R\rightarrow\infty$, the corresponding conversion of A is $\underline{\hspace{1cm}}$% (rounded off to one decimal place).

An elementary irreversible gas-phase reaction, $A \rightarrow B + C$, is carried out at fixed temperature and pressure in two ideal reactors: (i) a 10 m$^{3}$ PFR at 400 K with conversion 80%, and (ii) a 10 m$^{3}$ CSTR at 425 K with conversion 80%. Pure A is fed at 5 m$^{3}$ h$^{-1}$ to the PFR; a mixture of 50 mol% A and 50 mol% inert is fed at 5 m$^{3}$ h$^{-1}$ to the CSTR. Assume Arrhenius kinetics. Estimate activation energy (rounded to 1 decimal place).

An elementary irreversible liquid-phase reaction, $2P \xrightarrow{k}Q$, with rate constant $k = 2\ \text{L mol}^{-1}\text{min}^{-1}$, occurs in an isothermal non-ideal reactor. Pure $P$ (2 mol L$^{-1}$) is fed. The $E$-curve from a tracer test is triangular from $t=0$ to $t=0.5$ min, rising linearly from 1 to 2 min$^{-1}$. Using the segregated model, the percentage conversion of $P$ at the reactor exit is $\underline{\hspace{2cm}}$% (rounded to the nearest integer).

The molar excess Gibbs free energy ($g^E$) of a liquid mixture of $A$ and $B$ is given by \[ \frac{g^E}{RT} = x_A x_B [C_1 + C_2(x_A - x_B)] \] where $x_A$ and $x_B$ are the mole fraction of $A$ and $B$, respectively, the universal gas constant, $R = 8.314$ J K$^{-1}$ mol$^{-1}$, $T$ is the temperature in K, and $C_1, C_2$ are temperature-dependent parameters. At 300 K, $C_1 = 0.45$ and $C_2 = -0.018$. If $\gamma_A$ and $\gamma_B$ are the activity coefficients of $A$ and $B$, respectively, the value of \[ \int_{0}^{1} \ln\left(\frac{\gamma_A}{\gamma_B}\right)\,dx_A \] at 300 K and 1 bar is $\underline{\hspace{2cm}}$ (rounded off to the nearest integer).

Two large parallel planar walls are maintained at 1000 K and 500 K. Parallel radiation shields are to be installed between the two walls. Assume emissivities of walls and shields are equal. If the melting temperature of the shields is 900 K, the maximum number of shield(s) that can be installed between the walls is (are)

Saturated steam condenses on a vertical plate maintained at a constant wall temperature. If $x$ is the vertical distance from the top edge of the plate, then the local heat transfer coefficient $h(x) \propto \Gamma(x)^{-1/3}$, where $\Gamma(x)$ is the local mass flow rate of the condensate per unit plate width. The ratio of the average heat transfer coefficient over the entire plate to the heat transfer coefficient at the bottom of the plate is

A process described by the transfer function \[ G_p(s) = \frac{10s + 1}{5s + 1} \] is forced by a unit step input at time $t = 0$. The output value immediately after the step input (at $t = 0^+$) is $\underline{\hspace{2cm}}$ (rounded off to the nearest integer).

The partial differential equation
\[ \frac{\partial u}{\partial t} = \frac{1}{\pi^2} \frac{\partial^2 u}{\partial x^2} \]
where $t \ge 0$ and $x \in [0,1]$, is subjected to the following initial and boundary conditions:
\[ u(x,0) = \sin(\pi x) \]
\[ u(0,t) = 0 \]
\[ u(1,t) = 0 \]
The value of $t$ at which \[ \frac{u(0.5,t)}{u(0.5,0)} = \frac{1}{e} \] is

The reaction A → B is carried out isothermally on a porous catalyst. The intrinsic reaction rate is $k C_A^2$, where $k$ is the rate constant and $C_A$ is the concentration of A. If the reaction is strongly pore-diffusion controlled, the observed order of the reaction is

Consider turbulent flow in a pipe under isothermal conditions. Let r denote the radial coordinate and z denote the axial flow direction. On moving away from the wall towards the center of the pipe, the rz-component of the Reynolds stress

Consider two stationary spherical pure water droplets of diameters $ d_1 $ and $ 2d_1 $. CO$_2$ diffuses into the droplets from the surroundings. If the rate of diffusion of CO$_2$ into the smaller droplet is $ W_1 $ mol s$^{-1}$, the rate of diffusion of CO$_2$ into the larger droplet is

In soap manufacturing, the triglycerides present in oils and fats are hydrolyzed to mainly produce

The chemical formula of Glauber's salt, used in the Kraft process, is

In injection blow molding of plastic beverage bottles, the blowing is accomplished by

Match the therblig symbols with their meanings.

Matrix A as a product of two other matrices is given by \[ A=\begin{bmatrix} 3 \\ 2 \end{bmatrix} \begin{bmatrix} 1\;\;4 \end{bmatrix}. \] The value of det(A) is $\underline{\hspace{3cm}}$ (round off to nearest integer).

In a slider–crank mechanism, the crank rotates at 60 rpm. The crank radius is 30 mm and the connecting rod length is 120 mm. The average speed (in mm/s) of the piston over one revolution of the crank is $\underline{\hspace{2cm}}$ (round off to nearest integer).