Show that for an ideal gas composed of monatomic molecules the entropy change, between any two temperatures, when the pressure is kept constant is \(5 / 3\) times the corresponding entropy change when the volume is kept constant. Verify this result numerically by calculating the actual values of \((\Delta S)_{P}\) and \((\Delta S)_{V}\) per mole of an ideal gas whose temperature is raised from \(300 \mathrm{~K}\) to \(400 \mathrm{~K}\).