Govt. Exams
Entrance Exams
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.
For reversible isothermal process: ΔS = Q/T = nR ln(Vf/Vi) since Q = nRT ln(Vf/Vi) for ideal gas isothermal expansion.
Efficiency η = (Qh - Qc)/Qh = (1000 - 600)/1000 = 400/1000 = 0.40 = 40%
Internal energy U = nCvT. Without knowing the number of moles in each sample, the ratio cannot be determined. Same temperature doesn't mean same internal energy.
In an isothermal process, temperature is constant. For an ideal gas, internal energy depends only on temperature, so ΔU = 0. Pressure and volume change according to PV = constant.