Chemical Engineering GATE 2024 Questions with Answer

Ques 14 Chemical Engineering

A first-order heterogenous reaction A → B is carried out using a porous spherical catalyst. Assume isothermal conditions, and that intraphase diffusion controls the reaction rate. At a bulk A concentration of 0.3 mol L⁻¹, the observed reaction rate in a 3 mm diameter catalyst particle is 0.2 mol s⁻¹ L⁻¹ catalyst volume. At a bulk A concentration of 0.1 mol L⁻¹, the observed reaction rate, in mol s⁻¹ L⁻¹ catalyst volume, in a 6 mm diameter catalyst particle, is ______

Ques 15 Chemical Engineering

A first-order liquid phase reaction A → B is carried out in two isothermal plug flow reactors (PFRs) of volume 1 m³ each, connected in series. The feed flow rate and concentration of A to the first reactor are 10 m³ h⁻¹ and 1 kmol m⁻³, respectively. At steady-state, the concentration of A at the exit of the second reactor is 0.2 kmol m⁻³. If the two PFRs are replaced by two equal-volume continuously stirred tank reactors (CSTRs) to achieve the same overall steady-state conversion, the volume of each CSTR, in m³, is ______

Ques 16 Chemical Engineering

The residence time distribution, E, for a non-ideal flow reactor is given in the figure. A first-order liquid phase reaction with a rate constant 0.2 min⁻¹ is carried out in the reactor. For an inlet reactant concentration of 2 mol L⁻¹, the reactant concentration (in mol L⁻¹) in the exit stream is

Ques 17 Chemical Engineering

For the block diagram shown in the figure, the correct expression for the transfer function G_d = y₁(s) / d(s) is

Ques 18 Chemical Engineering

For purchasing a batch reactor, three alternatives P, Q and R have emerged, as summarized in the table. For a compound interest rate of 10% per annum, choose the correct option that arranges the alternatives, in order, from the least expensive to the most expensive.

Ques 19 Chemical Engineering

Methane combusts with air in a furnace as CH₄ + 2O₂ → CO₂ + 2H₂O. The heat of reaction ΔH_rxn = −880 kJ per mol CH₄ and is assumed to be constant. The furnace is well-insulated and no other side reactions occur. All components behave as ideal gases with a constant molar heat capacity of 44 J mol⁻¹ °C⁻¹. Air may be considered as 20 mol% O₂ and 80 mol% N₂. The air-fuel mixture enters the furnace at 50 °C. The methane conversion X varies with the air-to-methane mole ratio, r, as X = 1 − 0.1 e^{−2(r−r_s)} with 0.9 r_s ≤ r ≤ 1.1 r_s, where r_s is the stoichiometric air-to-methane mole ratio. For r = 1.05 r_s, the exit flue gas temperature in °C, rounded off to 1 decimal place, is ______

Ques 20 Chemical Engineering

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 m² 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 m³. 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, in K, of the gas in compartment A, rounded off to 1 decimal place, is _________

Ques 21 Chemical Engineering

Ethylene obeys the truncated virial equation-of-state:
(PV) / (RT) = 1 + (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 cm³ mol⁻¹K⁻¹. At 340 K, the slope of the compressibility factor vs. pressure curve is −3.538 × 10⁻³ bar⁻¹. Let G^R denote the molar residual Gibbs free energy. At these conditions, the value of (∂G^R/∂P)_T, in cm³ mol⁻¹, rounded off to 1 decimal place, is _________

Ques 22 Chemical Engineering

A metallic spherical particle of density 7001 kg m⁻³ and diameter 1 mm is settling steadily due to gravity in a stagnant gas of density 1 kg m⁻³ and viscosity 10⁻⁵ kg m⁻¹ s⁻¹. Take g = 9.8 m s⁻². Assume that the settling occurs in the regime where the drag coefficient C_D is independent of the Reynolds number, and equals 0.44. The terminal settling velocity of the particle, in m s⁻¹, rounded off to 2 decimal places, is ______

Ques 23 Chemical Engineering

A chemostat with cell recycle is shown in the figure. The feed flow rate and culture volume are F = 75 L h⁻¹ and V = 200 L, respectively. The glucose concentration in the feed C_S0 = 15 g L⁻¹. Assume Monod kinetics with specific cell growth rate μ_g = (1/C_C) (dC_C/dt) = μ_m C_S / (K_S + C_S), where μ_m = 0.25 h⁻¹ and K_S = 1 g L⁻¹. Assume maintenance and death rates to be zero, input feed to be sterile (C_C0 = 0), and steady-state operation. The glucose concentration in the recycle stream, C_S1, in g L⁻¹, rounded off to 1 decimal place, is _________.

Ques 24 Chemical Engineering

Consider the surge drum in the figure. Initially the system is at steady-state with a hold-up V̅ = 5 m³, which is 50% of full tank capacity, V_full, and volumetric flow rates F̅_in = F̅_out = 1 m³ h⁻¹. The high hold-up alarm limit V_high = 0.8 V_full while the low hold-up alarm limit V_low = 0.2 V_full. A proportional (P-only) controller manipulates the outflow to regulate the hold-up V as F_out = K_c(V − V̅) + F̅_out. At t = 0, F_in increases as a step from 1 m³ h⁻¹ to 2 m³ h⁻¹. Assume linear control valves and instantaneous valve dynamics. Let K_cmin be the minimum controller gain that ensures V never exceeds V_high. The value of K_cmin, in h⁻¹, rounded off to 2 decimal places, is _________

Ques 25 Chemical Engineering

A PD controller with transfer function G_c is used to stabilize an open-loop unstable process with transfer function G_p, where

G_c = K_c [(τ_Ds + 1) / ((τ_D/20)s + 1)],   G_p = 1 / [(s − 1)(10s + 1)]

and time is in minutes. From the necessary conditions for closed-loop stability, the maximum feasible value of τ_D, in minutes, rounded off to 1 decimal place, is _________

Ques 26 Chemical Engineering

Consider a tray-column of diameter 120 cm. Each downcomer has a cross-sectional area of 575 cm². For a tray, the percentage column cross-sectional area not available for vapour flow due to the downcomers, rounded off to 1 decimal place, is _____________