Serway & Jewett — Heat Engines, Entropy, and the Second Law of Thermodynamics: Problem 39

A heat engine operates between two reservoirs at \(T_2 = 600\text{ K}\) and \(T_1 = 350\text{ K}\). It takes in \(1.00 \times 10^3\text{ J}\) of energy from the higher-temperature reservoir and performs \(250\text{ J}\) of work. Find (a) the entropy change of the Universe \(\Delta S_U\) for this process and (b) the work \(W\) that could have been done by an ideal Carnot engine operating between these two reservoirs. (c) Show that the difference between the amounts of work done in parts (a) and (b) is \(T_1 \Delta S_U\).