Halliday, Resnick & Walker — Entropy and the Second Law of Thermodynamics: Problem 2

2. Expand 1.00 mol of an monatomic gas initially at 8.00 kPa and 600 K from initial volume \(V_i = 1.00 \text{ m}^3\) to final volume \(V_f = 2.00 \text{ m}^3\). At any instant during the expansion, the pressure \(p\) and volume \(V\) of the gas are related by \(p = 5.00 \exp[(V_i - V)/a]\), with \(p\) in kilopascals, \(V_i\) and \(V\) in cubic meters, and \(a = 1.00 \text{ m}^3\). What are the final (a) pressure and (b) temperature of the gas? (c) How much work is done by the gas during the expansion? (d) What is \(\Delta S\) for the expansion? (Hint: Use two simple reversible processes to find \(\Delta S\).)