A 1.00-mol sample of an ideal gas expands isothermally, doubling in volume. (a) Show that the work it does in ex- panding is W = RT ln 2. (b) Because the internal energy Eint 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. Why does this conversion not violate the second law?