Serway & Jewett — Heat Engines, Entropy, and the Second Law of Thermodynamics: Problem 45

A sample of an ideal gas expands isothermally, doubling in volume. (a) Show that the work done on the gas in expanding is \( W = -nRT \ln 2 \). (b) Because the internal energy \( E_{\text{int}} \) of an ideal gas depends solely on its temperature, the change in internal energy is zero during the expansion. It follows from the first law that the energy input to the gas by heat during the expansion is equal to the energy output by work. Does this process have 100% efficiency in converting energy input by heat into work output? (c) Does this conversion violate the second law? Explain.