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.
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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.
