In Sec. 9.1 we considered the changes in thermodynamic properties on forming an ideal gas mixture from a collection of ideal gases at the same temperature and pressure. A second, less common way of forming an ideal gas mixture is to start with a collection of pure ideal gases, each at the temperature T and volume V , and mix and compress the mixture to produce an ideal gas mixture at temperature T and volume V.

a. Show that the mixing process described here is mixing at constant partial pressure of each component. 

b. Derive each of the entries in the following table.