Halliday, Resnick & Walker — Entropy and the Second Law of Thermodynamics: Problem 62

Suppose 2.00 mol of a diatomic gas is taken reversibly around the cycle shown in the T-S diagram of Fig. 20.17, where \( S_1 = 6.00 \text{ J/K} \) and \( S_2 = 8.00 \text{ J/K} \). The molecules do not rotate or oscillate. What is the energy transferred as heat \( Q \) for (a) path 1 → 2, (b) path 2 → 3, and (c) the full cycle? (d) What is the work \( W \) for the isothermal process? The volume \( V_1 \) in state 1 is \( 0.200 \text{ m}^3 \). What is the volume in (e) state 2 and (f) state 3? What is the change \( \Delta E_{\text{int}} \) for (g) path 1 → 2, (h) path 2 → 3, and (i) the full cycle? (j) What is the work \( W \) for the adiabatic process?