One mole of an ideal gas undergoes the following cyclic process: (i) Isochoric heating from (P1, V1, — Thermodynamics and Thermochemistry Chemistry Question
Question
One mole of an ideal gas undergoes the following cyclic process: (i) Isochoric heating from (P1, V1, T1) to double temperature. (ii) Isobaric expansion to double volume. (iii) Linear expansion (on P-V curve) to (P1, 8 V1). (iv) Isobaric compression to initial state. If T1 = 300 K, the magnitude of net work done by the gas in the cyclic process is
💡 Solution & Explanation
Trace states: 1 = (P1, V1, T1). Isochoric heating to 2 T1 => 2 = (2 P1, V1). Isobaric expansion to 2 V1 => 3 = (2 P1, 2 V1). Linear expansion to (P1, 8 V1) => 4 = (P1, 8 V1). Isobaric compression to (P1, V1) => 1. Net work is sum of areas under P-V curves: W_12 = 0. W_23 = 2P1 * (2V1 - V1) = 2P1 V1. W_34 = 0.5 * (2P1 + P1) * (8V1 - 2V1) = 9 P1 V1. W_41 = P1 * (V1 - 8V1) = -7 P1 V1. Net work done BY gas = 2P1 V1 + 9P1 V1 - 7P1 V1 = 4 P1 V1 = 4 R T1 = 1200 R. In calories (R = 2 cal/mol-K), Net Work = 2400 cal.