List of top Process Calculations and Thermodynamics Questions asked in GATE CH

Methanol is produced by the reversible, gas-phase hydrogenation of carbon monoxide: \[ {CO} + 2{H}_2 \rightleftharpoons {CH}_3{OH} \] CO and H$_2$ are charged to a reactor, and the reaction proceeds to equilibrium at 453 K and 2 atm. The reaction equilibrium constant, which depends only on the temperature, is 1.68 at the reaction conditions. The mole fraction of H$_2$ in the product is 0.4. Assuming ideal gas behavior, the mole fraction of methanol in the product is ____________ (rounded off to 2 decimal places).

An adiabatic pump of efficiency 40% is used to increase the water pressure from 200 kPa to 600 kPa. The flow rate of water is 600 L/min. The specific heat of water is 4.2 kJ/(kg°C). Assuming water is incompressible with a density of 1000 kg/m\(^3\), the maximum temperature rise of water across the pump is ________°C (rounded off to 3 decimal places).

An ideal monoatomic gas is contained inside a cylinder-piston assembly connected to a Hookean spring as shown in the figure. The piston is frictionless and massless. The spring constant is 10 kN/m. At the initial equilibrium state (shown in the figure), the spring is unstretched. The gas is expanded reversibly by adding 362.5 J of heat. At the final equilibrium state, the piston presses against the stoppers. Neglecting the heat loss to the surroundings, the final equilibrium temperature of the gas is _________ K (rounded off to the nearest integer).


 

Consider moist air with absolute humidity of 0.02 (kg moisture)/(kg dry air) at 1 bar pressure. The vapor pressure of water is given by the equation: \[ \ln P_{{sat}} = 12 - \frac{4000}{T - 40} \] where \( P_{{sat}} \) is in bar and \( T \) is in K. The molecular weight of water and dry air are 18 kg/kmol and 29 kg/kmol, respectively. The dew temperature of the moist air is ____________ ℃ (rounded off to the nearest integer).

A hot plate is placed in contact with a cold plate of a different thermal conductivity as shown in the figure. The initial temperature (at time $t = 0$) of the hot plate and cold plate are $T_h$ and $T_c$, respectively. Assume perfect contact between the plates. Which one of the following is an appropriate boundary condition at the surface $S$ for solving the unsteady state, one-dimensional heat conduction equations for the hot plate and cold plate for $t>0$?


 

The residence-time distribution (RTD) function of a reactor (in min−1) is:

\[ E(t) = \begin{cases} 1 - 2t, & \text{if } t \leq 0.5\ \text{min} \\ 0, & \text{if } t > 0.5\ \text{min} \end{cases} \]

The mean residence time of the reactor is _____ min (rounded off to 2 decimal places).

Oil is extracted from mustard seeds having 20 wt% oil and 80 wt% solids, using hexane as a solvent. After extraction, the hexane-free residual cake contains 1 wt% oil. Assuming negligible dissolution of cake in hexane, the percentage oil recovery in hexane is ___________ % (rounded off to the nearest integer).

Ideal nonreacting gases A and B are contained inside a perfectly insulated chamber, separated by a thin partition, as shown in the figure. The partition is removed, and the two gases mix till final equilibrium is reached. The change in total entropy for the process is \( \_\_ \) J/K (rounded off to 1 decimal place).

Given: Universal gas constant \( R = 8.314 \) J/(mol K), \( T_A = T_B = 273 \) K, \( P_A = P_B = 1 \) atm, \( V_B = 22.4 \) L, \( V_A = 3V_B \).

The following data is given for a ternary \(ABC\) gas mixture at 12 MPa and 308 K:

\(y_i\): mole fraction of component \(i\) in the gas mixture
\(\hat{\phi}_i\): fugacity coefficient of component \(i\) in the gas mixture at 12 MPa and 308 K
The fugacity of the gas mixture is _________ MPa (rounded off to 3 decimal places).

Consider an enzymatic reaction that follows Michaelis-Menten kinetics. Let \( K_M \), \( S \), and \( V_{max} \) denote the Michaelis constant, substrate concentration, and maximum reaction rate, respectively. Which of the following statements is/are TRUE?

Choose the option that correctly matches the items in Group 1 with those in Group 2.


 

Choose the CORRECT statement that describes the dependence of the variance (\( \sigma^2_\Theta \)) of the residence time distribution (RTD) with respect to the number of tanks (\( n \)) in the Tanks-in-Series model of non-ideal reactors.
The boundary of a system does not allow exchange of either mass or energy (in the form of heat and/or work) with the surroundings. The system is termed
The number of independent intensive variables that need to be specified to determine the thermodynamic state of a ternary mixture at vapor-liquid-liquid equilibrium is:
A zero-order gas phase reaction \(A \to B\) with rate \((-r_A) = k = 100\) mol/(L min) is carried out in a mixed flow reactor of volume 1 L. Pure \(A\) is fed to the reactor at a rate of 1 mol/min. At time \(t = 0\), the outlet flow is stopped while the inlet flow rate and reactor temperature remain unchanged. Assume that the reactor was operating under steady state before the flow was stopped (\(t<0\)). The rate of consumption of \(A\), \(-\frac{dC_A}{dt}\), in mol/(L min), at \(t = 1\) min is:
An isolated system consists of two perfectly sealed cuboidal compartments A and B separated by a movable rigid wall of cross-sectional area 0.1 m\(^2\) as shown in the figure. Initially, the movable wall is held in place by latches L1 and L2 such that the volume of compartment A is 0.1 m\(^3\). Compartment A contains a monoatomic ideal gas at 5 bar and 400 K. Compartment B is perfectly evacuated and contains a massless Hookean spring of force constant 0.3 N m\(^{-1}\) at its equilibrium length (stored elastic energy is zero). The latches L1 and L2 are released, the wall moves to the right by 0.2 m, where it is held at the new position by latches L3 and L4. Assume all the walls and latches are massless. The final equilibrium temperature of the gas in compartment A, in K, rounded off to 1 decimal place, is ______.
two perfectly sealed cuboidal compartments
Consider a vapour-liquid mixture of components A and B that obeys Raoult's law. The vapour pressure of A is half that of B. The vapour phase concentrations of A and B are 3 mol m\(^{-3}\) and 6 mol m\(^{-3}\), respectively. At equilibrium, the ratio of the liquid phase concentration of A to that of B is:
Heat is available at a rate of 2 kW from a thermal reservoir at 400 K. A two-stage process harnesses this heat to produce power. Stages 1 and 2 reject heat at 360 K and 300 K, respectively. Stage 2 is driven by the heat rejected by Stage 1. If the overall process efficiency is 50% of the corresponding Carnot efficiency, the power delivered by the process, in kW, rounded off to 2 decimal places, is ____.
Ethylene obeys the truncated virial equation-of-state \( \frac{PV}{RT} = 1 + \frac{BP}{RT} \) where \( P \) is the pressure, \( V \) is the molar volume, \( T \) is the absolute temperature, and \( B \) is the second virial coefficient. The universal gas constant \( R = 83.14 \) bar cm\(^3\) mol\(^{-1}\) K\(^{-1}\). At 340 K, the slope of the compressibility factor (\( Z \)) vs. pressure curve is \( -3.538 \times 10^{-3} \) bar\(^{-1}\). Let \( G_R \) denote the molar residual Gibbs free energy. At these conditions, the value of \( \left( \frac{\partial G_R}{\partial P} \right)_T \), in cm\(^3\) mol\(^{-1}\), rounded off to 1 decimal place, is _____.
The Newton-Raphson method is used to solve \( f(x) = 0 \), where \( f(x) = e^x - 5x \). Starting with an initial guess \( x^{(0)} = 1.0 \), the value of the next iterate \( x^{(1)} \), rounded off to 2 decimal places, is _____
Consider a binary mixture of components A and B at temperature \( T \) and pressure \( P \). Let \( \vec{V}_A \) and \( \vec{V}_B \) be the partial molar volumes of A and B, respectively. At a certain mole fraction of A, \( X_A \):
\[ \left( \frac{\partial \vec{V}_A}{\partial X_A} \right)_{T,P} = 22 \text{ cm}^3 \text{ mol}^{-1} \quad \text{and} \quad \left( \frac{\partial \vec{V}_B}{\partial X_A} \right)_{T,P} = -18 \text{ cm}^3 \text{ mol}^{-1} \]
The value of \( X_A \), rounded off to 2 decimal places, is ____.