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.202Medium
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.203Medium
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.204Medium
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.210Medium
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.211Medium
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.212Medium
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.213Medium
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.214Medium
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.
Q.215Medium
The residual property in thermodynamics is defined as the difference between:
Answer: A
Residual properties (M^R) account for non-ideal behavior: M^R = M_real - M_ideal at same T and P. Essential for calculating properties of real gases and mixtures.
Q.216Medium
A process where temperature and pressure both increase is most likely:
Answer: A
In polytropic compression with n between 1 and γ, both T and P increase as volume decreases. Isentropic expansion decreases T and P. Throttling and isothermal keep T constant.
Q.217Medium
The compressibility factor Z for a real gas at high pressures typically:
Answer: D
At low T, attractive forces dominate (Z < 1). At high T, repulsive forces dominate (Z > 1). The Boyle temperature is where Z ≈ 1. Pressure and temperature both influence Z significantly.
Q.218Medium
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.219Medium
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.220Medium
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.
