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 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.62Medium
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.63Medium
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.64Medium
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.65Medium
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.66Medium
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).
Q.67Medium
The compressibility factor Z for a real gas at high pressure and low temperature typically shows:
Answer: B
At high P and low T, attractive intermolecular forces dominate over repulsion, making Z < 1. This indicates volume is less than ideal gas volume (PV < nRT).
Q.68Hard
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.69Medium
The second law of thermodynamics can be expressed as:
Answer: B
Second law states ΔS_univ ≥ 0 for isolated systems. Equality holds for reversible processes, inequality for irreversible processes (ΔS_univ > 0).
Q.70Easy
For a binary ideal solution, the total vapor pressure at constant T is given by:
Answer: A
Raoult's law states P_i = P_i°x_i for ideal solutions. Total pressure P = P₁°x₁ + P₂°x₂. This assumes ideal mixing behavior.
Q.71Hard
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.72Hard
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.73Medium
A heat engine operating between 800 K and 300 K has actual efficiency of 40%. Its carnot efficiency is:
Answer: A
Carnot efficiency = 1 - T_c/T_h = 1 - 800300 = 800500 = 0.625 or 62.5%. Actual efficiency (40%) is always less than Carnot efficiency.
Q.74Medium
The Gibbs phase rule F = C - P + 2 indicates that for a binary system with 2 phases:
Answer: A
F = C - P + 2 = 2 - 2 + 2 = 2, but if we consider only intensive variables at fixed P, then F = 1. Temperature alone determines composition of both phases.
Q.75Easy
During a constant volume process, the first law of thermodynamics simplifies to:
Answer: B
At constant volume, ΔV = 0, so w = -P∫dV = 0. Therefore, ΔU = q + w = q + 0 = q. All heat goes into internal energy change.
Q.76Medium
The reduced temperature T_r and reduced pressure P_r are defined using critical point parameters. A substance at T_r = 0.9 and P_r = 2.0 is classified as:
Answer: B
T_r < 1 means T < T_c (subcritical). P_r = 2 means P > 2P_c (high pressure). This combination indicates compressed liquid state.
Q.77Hard
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.78Easy
A gas undergoes an isothermal expansion from 2 L to 5 L at 298 K. If the process is reversible, what is the sign of entropy change for an ideal gas?
Answer: A
For isothermal expansion of an ideal gas, ΔS = nR ln(V_f/V_i) = nR ln(25) > 0. Volume increases, so entropy increases.
Q.79Easy
In the van der Waals equation, the term 'a' represents:
Answer: B
In (P + a/V²)(V - b) = RT, 'a' corrects for intermolecular forces reducing pressure, while 'b' corrects for molecular volume.
