A rigid, thermally insulated container of total volume 4.0L is divided into two equal compartments by a thin impermeable partition. The left compartment contains 2.0mol of an ideal monatomic gas at 300 K and the right compartment is evacuated (a vacuum). The partition is suddenly removed, allowing the gas to expand freely until it uniformly fills the entire container.
(a) Determine the numerical value and sign of the change in entropy of the gas after equilibrium is reached.
(b) Explain how your result in part (a) is consistent with the predicted spontaneous direction of change for an isolated system.