A system consists of Nā molecules of type I at temperature Tā and Nā molecules of type 2 at temperature Tā confined within a box of volume Vā and Vā respectively. The two systems are separated by a diathermic wall. The molecules are supposed to interact very weakly so that they constitute an ideal gas mixture.
a) Estimate the total number of microstates Q(E) in the range between E and E+5E as a function of V, E, and Nā. You may treat the problem classically.
b) Obtain the expression for entropy before and after the thermal interaction.
c) Use this result to find the equation of state of this system, i.e., to find its mean pressure as a function of V and T.