Chemical Engineering questions for GATE and PSU exams are built on a handful of core subjects applied in many ways. Practice spans fluid mechanics, heat transfer, mass transfer, chemical reaction engineering, thermodynamics, process control and instrumentation, and plant design economics. Numerical solutions carry the assumptions written out, because the assumption is usually what separates a correct answer from a plausible one.
The Maxwell relation that can be derived from Gibbs free energy is:
Answer: B
From dG = -SdT + VdP, the Maxwell relation is (∂S/∂P)ₜ = -(∂V/∂T)ₚ. This relates entropy-pressure change to volume-temperature change.
Q.2Hard
The partial molar Gibbs energy at infinite dilution gives the chemical potential μ. For a component in ideal solution:
Answer: A
For ideal solutions, the chemical potential is μᵢ = μᵢ⁰ + RT ln(xᵢ), where xᵢ is the mole fraction. For non-ideal solutions, the activity aᵢ = γᵢxᵢ is used.
Q.3Hard
In a throttling process (Joule-Thomson expansion), for an ideal gas:
Answer: C
For ideal gas, enthalpy H depends only on temperature. In throttling (isenthalpic process), H = constant, so T = constant for ideal gas. For real gases, T may change based on Joule-Thomson coefficient.
Q.4Hard
The Maxwell relation derived from Gibbs free energy (G = H - TS) is:
Answer: B
From dG = -SdT + VdP, the Maxwell relation is: (∂V/∂T)_P = -(∂S/∂P)_T
Q.5Hard
For a non-ideal binary mixture, the activity coefficient (γᵢ) deviates from unity when:
Answer: B
Activity coefficients account for non-ideal behavior due to intermolecular forces and molecular size differences
Q.6Hard
The Clausius-Clapeyron equation relates vapor pressure to temperature. Which assumption is NOT required for its derivation?
Answer: D
Clausius-Clapeyron requires phase equilibrium, constant ΔH_vap, ideal gas approximation, but works for closed systems
Q.7Hard
The osmotic pressure of a dilute solution is given by van't Hoff equation: π = iMRT. What does 'i' represent?
Answer: A
The van't Hoff factor i accounts for ionic dissociation in solution. For non-electrolytes i ≈ 1; for electrolytes i > 1 (e.g., NaCl: i ≈ 2). Essential for colligative property calculations.
Q.8Hard
When CO₂ gas at 1 atm is cooled below the sublimation temperature (~195 K), it directly converts to dry ice without passing through liquid phase. This phenomenon is explained by:
Answer: A
CO₂ triple point is at 5.1 atm and 216.6 K. At 1 atm, cooling solid CO₂ cannot reach liquid phase because pressure is insufficient. Sublimation occurs directly solid→gas.
Q.9Hard
For a real gas obeying virial equation PV/nRT = 1 + B/V̄, the internal energy change with volume at constant T is:
Answer: D
For real gases, (∂U/∂V)_T ≠ 0. From thermodynamic relations: (∂U/∂V)_T = T(∂P/∂T)_V - P. Using virial equation gives (∂U/∂V)_T = T(dB/dT)/V̄². Non-ideal behavior affects internal energy.
Q.10Hard
In a Joule-Thomson expansion of real gas at 298 K, a positive μ_JT (inversion coefficient) means:
Answer: B
μ_JT = (∂T/∂P)_H > 0 means temperature decreases with pressure drop during isenthalpic expansion. For most gases at room temp (except H₂ and He), μ_JT > 0, enabling gas cooling for liquefaction.
Q.11Hard
In a steam power plant, the Rankine cycle efficiency increases when:
Answer: C
Rankine cycle efficiency η = 1 - T_c/T_h improves with higher boiler temperature/pressure and lower condenser temperature, following Carnot efficiency limits.
Q.12Hard
The chemical potential μᵢ of a component in a mixture relates to partial molar properties by:
Answer: D
All statements define chemical potential from different perspectives. μᵢ is the partial molar Gibbs energy and equals (∂G/∂nᵢ)_{T,P,n_j}.
Q.13Hard
For a spontaneous process in an isolated system, the entropy production σ satisfies:
Answer: B
Entropy production σ = ΔS_total ≥ 0 for isolated systems. σ > 0 for irreversible spontaneous processes; σ = 0 for reversible processes (equilibrium).
Q.14Hard
For a reversible process at constant T and P, the minimum work required (excluding PV work) is:
Answer: B
Useful work (non-PV) available = -ΔG at constant T,P. This represents maximum useful work for spontaneous process or minimum work needed for non-spontaneous process.
Q.15Hard
For a polytropic process PV^n = constant, if n = γ (heat capacity ratio), the process is:
Answer: B
For adiabatic process of ideal gas, PV^γ = constant where γ = Cp/Cv. This is the defining equation for adiabatic polytropic process.
Q.16Hard
An engineer needs to liquefy natural gas (primarily methane). The gas must be cooled below the inversion temperature because:
Answer: A
Above inversion temperature (for methane ≈ 625 K), μ_JT < 0 (heating on expansion). Below it, μ_JT > 0 (cooling on expansion), enabling liquefaction.
Q.17Hard
For a binary ideal solution at constant T and P, if we mix 1 mole of component A and 1 mole of component B, the entropy of mixing is:
In a desalination plant using reverse osmosis, work must be applied because:
Answer: A
Desalination (salt separation) is non-spontaneous: ΔG > 0. External work must be supplied to drive the process. This applies to RO and most separation processes.
