A real gas deviates from ideal behavior. Which condition favors ideal behavior?
Answer: B
At low pressure, molecules are far apart (negligible intermolecular forces), and at high temperature, kinetic energy dominates, making gases behave ideally
Q.63Medium
An open system differs from a closed system in that:
Answer: A
An open system allows both mass and energy exchange with surroundings (e.g., a boiling kettle), while a closed system allows only energy exchange
Q.64Hard
Three moles of ideal gas undergo polytropic process with n = 1.5. If temperature increases from 300 K to 450 K, the work done by gas is:
Answer: B
W = nR(T₂-T₁)/(1-n) = 3 × 8.314 × 150/(1-1.5) = 3,741/(-0.5) = -3,741 J (compression), |W| ≈ 3,372 J accounting for polytropic work formula
Q.65Hard
A heat engine operates between 600 K and 300 K reservoirs. It absorbs 5000 J from hot reservoir. For a Carnot engine operating between same temperatures, maximum work output would be:
For a van der Waals gas, the critical point is characterized by:
Answer: A
At critical point, both first and second derivatives of pressure with respect to volume are zero, marking the boundary of liquid-gas phase transition
Q.67Medium
The heat capacity at constant pressure Cp is greater than heat capacity at constant volume Cv for ideal gases because:
Answer: A
At constant P: Q = ΔU + PΔV, so more heat is needed to produce same temperature rise. Relation: Cp - Cv = R
Q.68Hard
A reversible process has entropy change ΔS_sys = -100 J/K. The entropy change of universe is:
Answer: C
For reversible process: ΔS_universe = ΔS_sys + ΔS_surr = 0. Since ΔS_sys = -100, ΔS_surr = +100, making total change zero
Q.69Easy
A system absorbs 4000 J of heat and does 1500 J of work. Change in internal energy is:
Answer: A
First law: ΔU = Q - W = 4000 - 1500 = 2500 J (where W is work done by system)
Q.70Hard
In a free expansion of ideal gas into vacuum, the entropy change of system is:
Answer: B
Free expansion is irreversible with ΔU = 0 and W = 0, so Q = 0. Volume increases, so S = nR ln(V_f/V_i) > 0
Q.71Medium
Two identical containers of ideal gas are connected by a tube with a valve. Initially, container A has pressure 2P and volume V at temperature T, while container B has pressure P and volume V at the same temperature. When the valve is opened and the system reaches equilibrium, what is the final pressure?
Answer: A
Using conservation of moles: n_A = 2PV/RT, n_B = PV/RT. Total moles = 3PV/RT. Final pressure = (3PV/RT)RT/(2V) = 1.5P
Q.72Hard
A monatomic ideal gas undergoes a cyclic process ABCA where: A→B is isothermal expansion, B→C is isochoric process, C→A is adiabatic compression. If at point A, P = 1 atm, V = 1 L, and T = 300 K, and the volume doubles from A to B, find the heat absorbed during the isothermal process.
Answer: C
For isothermal process of ideal gas: Q = nRT ln(V_f/V_i) = W. n = PV/RT = (101325 × 0.001)/(8.314 × 300) ≈ 0.0405 mol. Q = nRT ln(2) = 0.0405 × 8.314 × 300 × ln(2) ≈ 600 ln(2) J
Q.73Medium
For a Carnot heat engine operating between reservoirs at temperatures T_h = 500 K and T_c = 300 K, if the engine absorbs 5000 J per cycle from the hot reservoir, how much work is done per cycle?
