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 partial molar volume of a component in solution is:
Answer: B
Partial molar volume V̄ᵢ = (∂V/∂nᵢ)T,P represents the actual volume increase when 1 mole of i is added. It varies with composition and differs from pure component molar volume.
Q.442Medium
For a binary ideal solution at constant T and P, the Gibbs energy of mixing is:
Answer: D
For ideal solutions: ΔH_mix = 0 and ΔS_mix = -R(x₁ ln x₁ + x₂ ln x₂), so ΔG_mix = -TΔS_mix = RT(x₁ ln x₁ + x₂ ln x₂) < 0, making mixing spontaneous.
Q.443Easy
A system absorbs 500 J of heat and does 200 J of work on surroundings. The change in internal energy is:
Answer: A
First Law: ΔU = Q - W. Q = +500 J (absorbed), W = +200 J (work by system). ΔU = 500 - 200 = 300 J. Positive indicates internal energy increases.
Q.444Medium
The virial equation of state truncated after second term is: PV = nRT(1 + B(T)P/RT). What does B(T) represent?
Answer: D
B(T) is the second virial coefficient that accounts for molecular interactions. It corrects ideal gas behavior and is temperature-dependent, directly representing non-ideality.
Q.445Medium
For a reversible process in an isolated system, the entropy change is:
Answer: C
For reversible processes: dS = dq_rev/T. In an isolated system, dq = 0 (no heat transfer), therefore dS = 0. Entropy remains constant for reversible isolated processes.
Q.446Medium
An engineering application of throttling includes:
Answer: D
Throttling is isenthalpic (ΔH = 0) and occurs in expansion valves, regulators, and orifices. Used in refrigeration, HVAC systems. Entropy increases (irreversible) while enthalpy remains constant.
Q.447Hard
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.448Hard
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.449Hard
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.450Hard
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.451Easy
At constant temperature and pressure, which of the following represents the Gibbs free energy change for a spontaneous process?
Answer: B
For a spontaneous process at constant T and P, ΔG must be negative. ΔG = 0 indicates equilibrium, and ΔG > 0 indicates non-spontaneous process.
Q.452Easy
The Clausius-Clapeyron equation relates vapor pressure to temperature. Which statement is correct?
Answer: A
Clausius-Clapeyron equation (d ln P/dT = ΔH_vap/RT²) applies specifically to phase equilibria and shows direct relationship between vapor pressure and temperature.
Q.453Easy
For an ideal gas undergoing adiabatic compression, the entropy change is:
Answer: C
For a reversible adiabatic process, dq = 0, therefore ΔS = ∫dq_rev/T = 0. Entropy remains constant during reversible adiabatic processes.
Q.454Easy
In a constant pressure process, the heat absorbed by a system equals:
Answer: B
At constant pressure, q_p = ΔH (change in enthalpy). This is the definition of enthalpy and is a key relationship in engineering thermodynamics.
Q.455Medium
The Maxwell relations are derived from which mathematical principle?
Answer: B
Maxwell relations originate from the equality of mixed partial derivatives of thermodynamic potentials (∂²F/∂x∂y = ∂²F/∂y∂x), combined with Legendre transformations.
Q.456Medium
In a throttling process (Joule-Thomson expansion), for an ideal gas, the enthalpy change is:
Answer: C
For an ideal gas, h depends only on temperature. Since throttling is isenthalpic (h constant), temperature remains constant, making ΔH = 0.
Q.457Medium
The fugacity coefficient φ for a pure component relates to which thermodynamic property?
Answer: A
Fugacity coefficient φ = f/P measures deviation from ideality. For ideal gas, φ = 1. It depends on both T and P and accounts for non-ideal intermolecular forces.
Q.458Medium
For a system at constant T and P, which statement about activity coefficient γ is true?
Answer: A
By definition, γ = 1 for ideal solutions. Activity coefficient accounts for non-ideal behavior. γ > 1 indicates positive deviation (activity > mole fraction).
Q.459Medium
The Legendre transformation from U(S,V) to F(T,V) replaces which variable pair?
Answer: A
Helmholtz free energy F = U - TS is the Legendre transform of U with respect to entropy S, replacing it with conjugate variable T, while V remains unchanged.
Q.460Medium
For an isothermal reversible expansion of 2 moles of ideal gas from 10 L to 50 L at 300 K:
Answer: C
W = -∫PdV = -nRT ln(V_f/V_i) = -2×8.314×300×ln(5) ≈ -12.88 kJ. Work done by system is negative (work done on surroundings).
