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.442Medium
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.443Easy
A system absorbs 500 J of heat and does 200 J of work on surroundings. The change in internal energy is:
Answer: A
First Law: ΔU = Q - W. Q = +500 J (absorbed), W = +200 J (work by system). ΔU = 500 - 200 = 300 J. Positive indicates internal energy increases.
Q.444Medium
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.
Q.445Medium
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.
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Q.446Medium
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.447Hard
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.448Hard
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.449Hard
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.450Hard
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.451Easy
At constant temperature and pressure, which of the following represents the Gibbs free energy change for a spontaneous process?
Answer: B
For a spontaneous process at constant T and P, ΔG must be negative. ΔG = 0 indicates equilibrium, and ΔG > 0 indicates non-spontaneous process.
Q.452Easy
The Clausius-Clapeyron equation relates vapor pressure to temperature. Which statement is correct?
Answer: A
Clausius-Clapeyron equation (d ln P/dT = ΔH_vap/RT²) applies specifically to phase equilibria and shows direct relationship between vapor pressure and temperature.
Q.453Easy
For an ideal gas undergoing adiabatic compression, the entropy change is:
Answer: C
For a reversible adiabatic process, dq = 0, therefore ΔS = ∫dq_rev/T = 0. Entropy remains constant during reversible adiabatic processes.
Q.454Easy
In a constant pressure process, the heat absorbed by a system equals:
Answer: B
At constant pressure, q_p = ΔH (change in enthalpy). This is the definition of enthalpy and is a key relationship in engineering thermodynamics.
Q.455Medium
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.456Medium
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.457Medium
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.458Medium
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.459Medium
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.460Medium
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).
