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
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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.
