Which of the following is NOT an extensive property?
Answer: B
Temperature is an intensive property as it does not depend on the quantity of substance. Volume, mass, and internal energy are extensive properties that depend on the amount of material.
Q.2Easy
According to the first law of thermodynamics, ΔU = Q - W. In this equation, W represents:
Answer: B
In the convention ΔU = Q - W, W is work done by the system. This is the IUPAC recommended convention used in most thermodynamics calculations.
Q.3Medium
Which thermodynamic potential is most useful for constant temperature and pressure processes?
Answer: C
Gibbs Free Energy (G = H - TS) is the appropriate thermodynamic potential for processes at constant T and P. ΔG = 0 at equilibrium and ΔG < 0 for spontaneous processes.
Q.4Easy
A system absorbs 500 J of heat and does 200 J of work. The change in internal energy is:
Answer: A
Using ΔU = Q - W, where Q = +500 J (absorbed) and W = +200 J (work done by system). Therefore, ΔU = 500 - 200 = 300 J.
Q.5Medium
For an ideal gas undergoing isothermal expansion, the work done is given by:
Answer: A
For isothermal process of ideal gas, W = nRTln(V₂/V₁) = nRTln(P₁/P₂). This is derived from the first law with ΔU = 0 for isothermal ideal gas process.
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Q.6Easy
The compressibility factor Z for an ideal gas is:
Answer: B
For ideal gas, Z = PV/nRT = 1 always. For real gases, Z ≠ 1 due to intermolecular forces and molecular volume.
Q.7Medium
For a process where ΔG < 0 at all temperatures, the process must be:
Answer: B
From ΔG = ΔH - TΔS, for ΔG < 0 at all T: ΔH < 0 (exothermic) and ΔS > 0 (entropy increases). This is a spontaneous process at all temperatures.
Q.8Hard
The Maxwell relation that can be derived from Gibbs free energy is:
Answer: B
From dG = -SdT + VdP, the Maxwell relation is (∂S/∂P)ₜ = -(∂V/∂T)ₚ. This relates entropy-pressure change to volume-temperature change.
Q.9Easy
In a constant pressure calorimeter, 1 kg of water is heated from 25°C to 75°C. Heat absorbed is approximately (Cₚ of water = 4.18 kJ/kg·K):
The heat of vaporization of water is 40.66 kJ/mol at 373 K. The entropy of vaporization is approximately:
Answer: C
ΔS_vap = ΔH_vap/T = 40660 J/mol / 373 K ≈ 109 J/mol·K. This follows Trouton's rule (~85-105 J/mol·K for most liquids).
Q.11Medium
For a reversible process, the Clausius inequality states:
Answer: B
For reversible processes, ΔS = Q_rev/T. For irreversible processes, ΔS > Q_irrev/T. This is the Clausius inequality: dS ≥ dQ/T.
Q.12Medium
A cyclic heat engine operates between hot reservoir at 500 K and cold reservoir at 300 K. Maximum theoretical efficiency is:
Answer: B
Maximum efficiency is Carnot efficiency: η_max = 1 - T_cold/T_hot = 1 - 500300 = 0.40 = 40%. No heat engine can exceed this efficiency.
Q.13Medium
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.14Medium
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.15Easy
Which process is represented by a horizontal line on a T-S (Temperature-Entropy) diagram?
Answer: C
On a T-S diagram, horizontal line means constant temperature (T = const), which is an isothermal process. A vertical line would represent isentropic process (S = const).
Q.16Medium
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.17Hard
The partial molar Gibbs energy at infinite dilution gives the chemical potential μ. For a component in ideal solution:
Answer: A
For ideal solutions, the chemical potential is μᵢ = μᵢ⁰ + RT ln(xᵢ), where xᵢ is the mole fraction. For non-ideal solutions, the activity aᵢ = γᵢxᵢ is used.
Q.18Hard
In a throttling process (Joule-Thomson expansion), for an ideal gas:
Answer: C
For ideal gas, enthalpy H depends only on temperature. In throttling (isenthalpic process), H = constant, so T = constant for ideal gas. For real gases, T may change based on Joule-Thomson coefficient.
Q.19Easy
A gas mixture contains N₂ (40% mole) and O₂ (60% mole) at 1 atm and 298 K. Calculate the partial pressure of O₂ in the mixture.
