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.222Medium
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.223Medium
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.224Medium
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.225Medium
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.
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Q.226Medium
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.227Medium
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.228Medium
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.229Medium
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.230Medium
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.231Medium
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.232Medium
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.233Medium
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.234Medium
The work done by a system during expansion against constant external pressure P_ext is:
Answer: B
For constant external pressure, work is W = P_ext × ΔV. This is path-dependent work for irreversible processes.
Q.235Medium
In a throttling process (Joule-Thomson expansion), which property remains constant?
Answer: B
Throttling through a valve occurs at constant enthalpy (isenthalpic process). This explains cooling of real gases during expansion.
Q.236Medium
For a spontaneous adiabatic process in an isolated system, entropy must:
Answer: C
Second law: dS_universe ≥ 0. For isolated systems, dS_system ≥ 0. Equality holds for reversible adiabatic processes.
Q.237Medium
The Maxwell relation derived from dG = -SdT + VdP is:
Answer: B
From dG = -SdT + VdP, cross derivatives give (∂S/∂P)_T = -(∂V/∂T)_P, a Maxwell relation.
Q.238Medium
In an adiabatic compression process for an ideal gas, which statement is correct?
Answer: B
For adiabatic process, Q = 0, so ΔU = W (first law). Temperature increases during compression.
Q.239Medium
The Joule-Thomson coefficient μ_JT is negative for most gases at room temperature. This means:
Answer: A
μ_JT = (∂T/∂P)_H. Negative coefficient means T increases with pressure drop (cooling requires very low T or high P).
Q.240Medium
For a binary ideal solution, Raoult's law states that:
Answer: A
Raoult's law: P_i = x_i × P_i° for ideal solutions. Both statements A and C are equivalent for ideal solutions.
