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.42Medium
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.43Medium
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.44Medium
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.45Medium
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.
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Q.46Easy
In a constant volume process, the heat added to the system equals:
Answer: A
For constant volume: W = 0, so Q = ΔU from first law (ΔU = Q - W). This is isochoric process where all heat goes to internal energy change.
Q.47Medium
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.48Medium
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.49Easy
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.50Medium
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.51Medium
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.52Medium
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.53Hard
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.54Hard
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.55Hard
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.56Hard
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.57Easy
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.58Easy
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.59Easy
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.60Easy
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.
