Two moles of helium gas undergoes a cyclic process as shown in the figure. Assuming ideal behaviour — Thermodynamics and Thermochemistry Chemistry Question

💡 Solution & Explanation

Path is A -> B -> C -> D -> A on a P-T plot. A = (300 K, 1 atm), B = (300 K, 2 atm), C = (400 K, 2 atm), D = (400 K, 1 atm). Work done BY gas: Isothermal compression A->B: W_AB = -nRT1 ln(P2/P1) = -600 R ln 2. Isobaric heating B->C: W_BC = nR dT = 200 R. Isothermal expansion C->D: W_CD = -nRT2 ln($P_4$/P3) = -800 R ln(1/2) = 800 R ln 2. Isobaric cooling D->A: W_DA = nR dT = -200 R. Net work done BY gas = -600 R ln 2 + 200 R + 800 R ln 2 - 200 R = 200 R ln 2 = 100 R ln 4.