Halliday, Resnick & Walker — Entropy and the Second Law of Thermodynamics: Problem 35

35 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) \( \Delta S \)?