List of top Mass Transfer Questions asked in GATE CH

A slab of thickness $L$, as shown in the figure, has cross-sectional area $A$ and constant thermal conductivity $k$. $T_1$ and $T_2$ are the temperatures at $x=0$ and $x=L$, respectively. Which one of the following options is the CORRECT expression of the thermal resistance for steady-state one-dimensional heat conduction?

Consider steady-state diffusion in a binary A-B liquid at constant temperature and pressure. The mole-fraction of A at two different locations is 0.8 and 0.1. Let $N_{A1}$ be the diffusive flux of A calculated assuming B to be non-diffusing, and $N_{A2}$ be the diffusive flux of A calculated assuming equimolar counter-diffusion. The quantity $\frac{(N_{A1} - N_{A2})}{N_{A1}} \times 100$ is $\underline{\hspace{2cm}}$ (rounded off to one decimal place).

Consider interphase mass transfer of a species S between two immiscible liquids A and B. The interfacial mass transfer coefficient of S in liquid A is twice of that in liquid B. The equilibrium distribution of S between the liquids is given by $y_S^A = 0.5 y_S^B$, where $y_S^A$ and $y_S^B$ are the mole-fractions of S in A and B, respectively. The bulk phase mole-fraction of S in A and B is 0.10 and 0.02, respectively. If the steady-state flux of S is estimated to be 10 kmol h$^{-1}$ m$^{-2}$, the mass transfer coefficient of S in A is $\underline{\hspace{2cm}}$ kmol h$^{-1}$ m$^{-2}$ (rounded off to one decimal place).

A wet solid containing 20% (w/w) moisture (based on mass of bone-dry solid) is dried in a tray-dryer. The critical moisture content of the solid is 10% (w/w). The drying rate (kg m$^{-2}$ s$^{-1}$) is constant for the first 4 hours, and then decreases linearly to half the initial value in the next 1 hour. At the end of 5 hours of drying, the percentage moisture content of the solid is $\underline{\hspace{2cm}}$ % (w/w) (rounded off to one decimal place).

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).

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

As shown in the figure below, air flows in parallel to a freshly painted solid surface of width 10 m, along the z-direction. The equilibrium vapor concentration of the volatile component A in the paint, at the air-paint interface, is $ C_{A,i} $. The concentration $ C_A $ decreases linearly from this value to zero along the y-direction over a distance $ \delta $ of 0.1 m in the air phase. Over this distance, the average velocity of the air stream is 0.033 m s$^{-1}$ and its velocity profile $ v_z(y) $ is given by \[ v_z(y) = 10 y^2 \] where $ y $ is in meter. Let $ C_{A,m} $ represent the flow averaged concentration. The ratio of $ C_{A,m} $ to $ C_{A,i} $ is $\underline{\hspace{1cm}}$ (round off to 2 decimal places).

Feed solution F is contacted with solvent B in an extraction process. Carrier liquid in the feed is A and the solute is C. The ternary diagram depicting a single ideal stage extraction is given below. The dashed lines represent the tie-lines.

The CORRECT option(s) is/are

A distillation column handling a binary mixture of A and B is operating at total reflux. It has two ideal stages including the reboiler. The mole fraction of the more volatile component in the residue ($x_w$) is 0.1. The average relative volatility $\alpha_{AB}$ is 4. The mole fraction of A in the distillate ($x_D$) is $\underline{\hspace{1cm}}$ (round off to 2 decimal places).

In a batch drying experiment, a solid with a critical moisture content of 0.2 kg H$_2$O/kg dry solid is dried from an initial moisture content of 0.35 kg H$_2$O/kg dry solid to a final moisture content of 0.1 kg H$_2$O/kg dry solid in 5 hours. In the constant rate regime, the rate of drying is 2 kg H$_2$O/(m$^2$·h). The entire falling rate regime is assumed to be uniformly linear. The equilibrium moisture content is assumed to be zero. The mass of the dry solid per unit area is $\underline{\hspace{1cm}}$ kg/m$^2$ (round off to nearest integer).

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}

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: