A constant-volume encasement vessel surrounds a liquidnitrogen bath that has cooled \(1.00 \mathrm{~mol}\) of a monatomic ideal gas to \(77.2 \mathrm{~K}\). This system is initially in thermal equilibrium at this temperature, but over time the liquid nitrogen evaporates, and then the ideal gas and the nitrogen gas are in equilibrium in the encasement vessel at room temperature, \(297 \mathrm{~K}\).

(a) What is the change in entropy of the ideal gas as it undergoes this temperature change?

(b) The nitrogen gas is then condensed and again cools the ideal gas. What is the entropy change for the ideal gas as it returns to \(77.2 \mathrm{~K}\) ?

(c) Where in this process did entropy increase, as required by the second law of thermodynamics for an irreversible process?