The entropy change for a reversible isothermal process is given by:
Answer: C
For reversible isothermal process: ΔS = Q/T = nR ln(Vf/Vi) since Q = nRT ln(Vf/Vi) for ideal gas isothermal expansion.
Q.122Medium
Which process would result in the maximum work output from an ideal gas expansion between two fixed pressures?
Answer: A
For expansion between fixed initial and final states, isothermal process yields maximum work because the gas maintains maximum pressure throughout the expansion compared to adiabatic or other processes.
Q.123Medium
A cylinder with a movable piston contains 2 moles of ideal gas at 300 K and 1 atm. When heated at constant pressure to 600 K, what is the work done by the gas? (R = 8.314 J/mol·K)
If a reversible process occurs in an isolated system, the entropy of the system:
Answer: C
For a reversible process in an isolated system, ΔS_total = ΔS_sys + ΔS_surr = 0 (no heat exchange with surroundings). Therefore entropy remains constant at its initial value.
Q.127Hard
An ideal gas undergoes a process where PV^n = constant. If n = 1, this process is _____ and if n = γ, this process is _____
Answer: A
When n = 1: PV = constant (isothermal). When n = γ = Cp/Cv: PV^γ = constant (adiabatic process).
Q.128Hard
Consider a system where entropy decreases by 50 J/K. Which statement must be true?
Answer: B
By second law, ΔS_total ≥ 0. If ΔS_sys = -50 J/K, then ΔS_surr ≥ +50 J/K to maintain ΔS_total ≥ 0.
Q.129Hard
A polytropic process with polytropic index n = 1.3 is performed on 1 mole of air (diatomic). The work done when volume changes from 1 m³ to 0.5 m³ at initial pressure 100 kPa is:
Answer: A
For polytropic process: W = [P₁V₁ - P₂V₂]/(n-1). Using PVⁿ = const: P₂ = 100 × (01.5)^1.3 ≈ 245.7 kPa. W = [100×1 - 245.7×0.5]/0.3 ≈ 81.2 kJ
Q.130Hard
For a van der Waals gas with equation (P + a/V²m)(Vm - b) = RT, at the critical point, which relationship is valid?
Answer: A
At the critical point, both first and second derivatives of pressure with respect to volume (at constant T) are zero: (∂P/∂V)T = 0 and (∂²P/∂V²)T = 0. This defines the critical point.
Q.131Easy
A system absorbs 500 J of heat and performs 200 J of work on the surroundings. What is the change in internal energy of the system?
Answer: A
By first law of thermodynamics: ΔU = Q − W = 500 − 200 = 300 J
Q.132Easy
An ideal gas undergoes an adiabatic process. If the gas is compressed, which of the following is true?
Answer: B
In adiabatic compression (Q = 0), work is done on the gas (W < 0). By first law: ΔU = Q − W = 0 − W > 0. Since ΔU ∝ ΔT for ideal gas, temperature increases.
Q.133Easy
What is the efficiency of a Carnot engine operating between 400 K and 300 K?
Two identical blocks of metal at different temperatures are brought into thermal contact in an isolated system. The process is:
Answer: C
Heat transfer between objects at different temperatures is irreversible. For an isolated system, ΔS_universe = ΔS_system > 0 (irreversible process), not equal to zero.
Q.136Medium
A gas expands from 1 L to 5 L against a constant external pressure of 2 atm. The work done by the gas is approximately:
The molar heat capacity of a diatomic ideal gas at constant pressure is (R = 8.314 J/mol·K):
Answer: B
For diatomic gas: Cv = (25)R, and Cp = Cv + R = (25)R + R = (27)R. This is at room temperature where vibration is not excited.
Q.138Medium
A cyclic process ABCA is shown on a P-V diagram where AB is isothermal expansion, BC is adiabatic compression, and CA is isochoric process. Which statement is correct?
Answer: A
In a complete cycle returning to initial state, ΔU = 0, so Q = W. For expansion-dominated processes in a typical cycle, W > 0 and Q > 0.
Q.139Medium
A heat engine absorbs 1000 J from a hot reservoir and rejects 600 J to a cold reservoir in one cycle. Its efficiency is:
A reversible heat engine operates between two thermal reservoirs. If the temperature of the cold reservoir decreases while hot reservoir temperature remains constant, the maximum efficiency:
Answer: A
Carnot efficiency η = 1 − (T_c/T_h). As T_c decreases while T_h remains constant, the ratio T_c/T_h decreases, so η increases.
