Govt. Exams
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.
W = PΔV. Here W = 400 J, P = 2 × 101325 = 202650 Pa. So ΔV = W/P = 400/202650 ≈ 0.00197 m³
Using first law: ΔU = Q - W = 300 - 500 = -200 J (internal energy decreases)
Van der Waals equation (P + a/V²)(V - b) = RT accounts for molecular volume (b term) and intermolecular attractive forces (a term)
For reversible cycle: Q_h/T_h = Q_c/T_c. 100/400 = Q_c/300. Q_c = (100 × 300)/400 = 75 J
For isothermal expansion against constant pressure: W = PₑₓₜΔV = 1 × (10-1) = 9 L·atm = 9 × 101.325 = 910.125 J
The polytropic equation PVⁿ = constant covers isothermal (n=1), adiabatic (n=γ), isobaric (n=0), and isochoric (n=∞) processes as special cases
