Govt. Exams
Efficiency η = W/Q_h = (Q_h − Q_c)/Q_h = (1000 − 600)/1000 = 400/1000 = 0.40 = 40%
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.
For diatomic gas: Cv = (5/2)R, and Cp = Cv + R = (5/2)R + R = (7/2)R. This is at room temperature where vibration is not excited.
W = P_ext × ΔV = 2 atm × (5 − 1) L = 2 × 4 = 8 atm·L = 8 × 101.325 J ≈ 810.6 J ≈ 808 J
Heat transfer between objects at different temperatures is irreversible. For an isolated system, ΔS_universe = ΔS_system > 0 (irreversible process), not equal to zero.
For monoatomic ideal gas, Cv = (3/2)R. ΔU = nCvΔT = 1 × (3/2) × 8.314 × (600 − 300) = (3/2) × 8.314 × 300 = 3,741 × 3.33 ≈ 12,471 J
COP = Tc/(Th - Tc) = 263/(303 - 263) = 263/40 ≈ 6.575 ≈ 6.5
For diatomic gas: Cv = (5/2)R. Using Cp = Cv + R, we get Cp = (5/2)R + R = (7/2)R
For isobaric process: W = nRΔT = 2 × 8.314 × (600 - 300) = 2 × 8.314 × 300 = 4988.4 ≈ 4984 J
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.
