Which thermodynamic potential is most useful for constant temperature and pressure processes?
Answer: C
Gibbs Free Energy (G = H - TS) is the appropriate thermodynamic potential for processes at constant T and P. ΔG = 0 at equilibrium and ΔG < 0 for spontaneous processes.
Q.2Medium
For an ideal gas undergoing isothermal expansion, the work done is given by:
Answer: A
For isothermal process of ideal gas, W = nRTln(V₂/V₁) = nRTln(P₁/P₂). This is derived from the first law with ΔU = 0 for isothermal ideal gas process.
Q.3Medium
For a process where ΔG < 0 at all temperatures, the process must be:
Answer: B
From ΔG = ΔH - TΔS, for ΔG < 0 at all T: ΔH < 0 (exothermic) and ΔS > 0 (entropy increases). This is a spontaneous process at all temperatures.
Q.4Medium
The heat of vaporization of water is 40.66 kJ/mol at 373 K. The entropy of vaporization is approximately:
Answer: C
ΔS_vap = ΔH_vap/T = 40660 J/mol / 373 K ≈ 109 J/mol·K. This follows Trouton's rule (~85-105 J/mol·K for most liquids).
Q.5Medium
For a reversible process, the Clausius inequality states:
Answer: B
For reversible processes, ΔS = Q_rev/T. For irreversible processes, ΔS > Q_irrev/T. This is the Clausius inequality: dS ≥ dQ/T.
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Q.6Medium
A cyclic heat engine operates between hot reservoir at 500 K and cold reservoir at 300 K. Maximum theoretical efficiency is:
Answer: B
Maximum efficiency is Carnot efficiency: η_max = 1 - T_cold/T_hot = 1 - 500300 = 0.40 = 40%. No heat engine can exceed this efficiency.
Q.7Medium
The heat capacity at constant pressure Cₚ is always greater than heat capacity at constant volume Cᵥ because:
Answer: B
Cₚ - Cᵥ = R (for ideal gas). At constant P, supplied heat does both internal energy and expansion work. At constant V, all heat goes to internal energy only.
Q.8Medium
For a real gas with van der Waals equation, the constants 'a' and 'b' represent:
Answer: B
In van der Waals equation (P + a/V²)(V - b) = RT, 'a' accounts for intermolecular attractive forces and 'b' represents excluded molecular volume. Both are positive constants.
Q.9Medium
For a spontaneous process at constant T and P, which condition must be satisfied?
Answer: C
At constant T and P, spontaneity is determined by Gibbs free energy: ΔG < 0 for spontaneous process, ΔG = 0 for equilibrium, ΔG > 0 for non-spontaneous process.
Q.10Medium
A reversible adiabatic process for an ideal gas follows PVᵞ = constant. If γ = 1.4 and initial pressure is 1 atm with volume 1 L, what is the final pressure when volume becomes 0.5 L?
For ideal gases, f = P (fugacity equals pressure), so φ = f/P = 1. Real gases have φ ≠ 1
Q.16Medium
For a spontaneous process occurring at constant temperature and pressure, which condition must be satisfied?
Answer: B
For spontaneity at constant T and P: ΔG = ΔH - TΔS must be negative (ΔG < 0)
Q.17Medium
A throttle valve is used in a refrigeration cycle. This is an example of a(n) _____ process.
Answer: C
Throttling is an adiabatic (Q=0) but irreversible process with no work done, causing entropy increase
Q.18Medium
A gas mixture at 298 K contains H₂ and N₂. If the mixture obeys Amagat's law and the partial volumes are equal, what is the mole fraction of H₂?
Answer: A
Amagat's law: V_total = V_H₂ + V_N₂. If partial volumes are equal, each is 50%, so x_H₂ = 0.5
Q.19Medium
At the critical point of a substance, which of the following is true?
Answer: A
At the critical point, surface tension between liquid and gas phases vanishes because the distinction between phases disappears. The critical compressibility factor Zc ≈ 0.27 (not 1).
Q.20Medium
For an ideal gas undergoing isothermal expansion from V₁ to V₂, the entropy change is:
Answer: A
For isothermal process: dS = dq_rev/T = nR dV/V, integrating gives ΔS = nR ln(V₂/V₁). Temperature is constant, so entropy change depends only on volume change.
