Halliday, Resnick & Walker — Entropy and the Second Law of Thermodynamics: Problem 19

Suppose 1.00 mol of a monatomic ideal gas is taken from initial pressure \(p_1\) and volume \(V_1\) through two steps: (1) an isothermal expansion to volume \(2.00V_1\) and (2) a pressure increase to \(2.00p_1\) at constant volume. What is \(Q/p_1V_1\) for (a) step 1 and (b) step 2? What is \(W/p_1V_1\) for (c) step 1 and (d) step 2? For the full process, what are (e) \(\Delta E_{\text{int}}/p_1V_1\) and (f) \(\Delta S\)? The gas is returned to its initial state and again taken to the same final state but now through these two steps: (1) an isothermal compression to pressure \(2.00p_1\) and (2) a volume increase to \(2.00V_1\) at constant pressure. What is \(Q/p_1V_1\) for (g) step 1 and (h) step 2? What is \(W/p_1V_1\) for (i) step 1 and (j) step 2? For the full process, what are (k) \(\Delta E_{\text{int}}/p_1V_1\) and (l) \(\Delta S\)?