Answer
a. It stays the same.
b. It increases.
Work Step by Step
a. If a gas expands adiabatically, then Q=0. By equation 15-8, $\Delta S = \frac{Q}{T}$, the change in entropy will be zero.
b. If a gas expands isothermally, its internal energy U doesn’t change as the gas expands, i.e., does work W on its surroundings. By the first law of thermodynamics, $\Delta U = Q-W$, there must be heat flow Q into the gas.
By equation 15-8, $\Delta S = \frac{Q}{T}$, the change in entropy will be positive. The entropy of the gas increases.
