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

Cyclohexane (C₆H₁₂) is produced from benzene (C₆H₆) and hydrogen (H₂) according to the following reaction.
\[ C_6H_6 + 3H_2 \rightarrow C_6H_{12} \]
Consider the process flow diagram shown in the figure.

In this process, the overall and single-pass conversions are 90% and 25%, respectively. The recycle stream contains 25 mol% C₆H₆ and 75 mol% H₂. If the fresh feed contains 25% excess H₂, at steady state, the ratio of the molar flow rate of the recycle stream to that of the fresh feed is ______ (rounded off to one decimal place).

Methanol is formed by the following gas phase homogeneous reaction:

\[ \mathrm{CO(g) + 2H_2(g) \rightleftharpoons CH_3OH(g)} \]

The standard Gibbs free energies of formation at $298\ \mathrm{K}$ for CO and $\mathrm{CH_3OH}$ are $-137\ \mathrm{kJ\,mol^{-1}}$ and $-162\ \mathrm{kJ\,mol^{-1}}$, respectively. The value of the universal gas constant is $8.314\ \mathrm{J\,mol^{-1}\,K^{-1}}$. The equilibrium constant for the given reaction at $298\ \mathrm{K}$ is ______ $\times 10^4$ (rounded off to one decimal place).

Which of the following statements regarding the heat of reaction is/are CORRECT?

According to the phase rule, which one of the following is the number of degrees of freedom for pure water at its triple point?

Consider a closed system of one mole of an ideal gas undergoing a polytropic process. The process follows $ PV^n = \text{constant} $, where P is the pressure, V is the volume and n is a constant. If the process is isobaric, which one of the following is the value of n?

For a first-order irreversible reaction carried out in a batch reactor, the rate of reaction is proportional to:

Which mode of heat transfer is dominant in vacuum?

For an ideal gas, internal energy is a function of:

In distillation, relative volatility is a measure of:

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).

The residence-time distribution (RTD) function of a reactor (in min$^{-1}$) is

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

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).

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).

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).

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).

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).

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 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).

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).

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

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:

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).