In a heat bath, there is a box with which experiments on gases can be carried out. Both the heat bath and the gases in the box are now kept at 298.15K. In the box, there is an air-sealed diathermic partition. On one side of the partition, there are 0.4 moles of oxygen, whose pressure is 0.4 bar; on the other side, there are 0.8 moles of nitrogen, with a pressure of 0.8 bar. Both gases can be treated as an ideal gas. When the experiment begins, the partition is removed. The processes undergone by both gases can be viewed as isothermal free expansion. When the equilibrium is reached, the two gases mix homogeneously. If there is a kind of machinery in the box that can reversibly separate the mixed gases back to their initial state (as one system), then a) What entropy change S and Gibbs energy change G of the two-gas system during this reversible separation process? b) What are the input thermal energy Q and input work W for the two-gas system during the reversible gas-separation process? c) Explain the meaning of the relation between W and W according to the second law of thermodynamics