A non-extensive thermodynamic system Consider a classical gas of N weakly interacting atoms of mass m, enclosed in a container of volume V and surface area A. The interactions between the atoms are so weak that they may be neglected (ideal gas approximation). However, the interaction of the atoms with the walls of the container may NOT be neglected. Some fraction of the atoms are adsorbed onto the walls of the container in equilibrium. Your job will be to calculate the average number Nof adsorbed atoms on the walls.

A simple model for the atoms adsorbed onto the walls is to treat them as a twodimensional ideal gas. The energy of an adsorbed atom is taken to be

where p is the two-dimensional momentum and ?o is a known parameter that describes the energy of adsorption. The entire system is in equilibrium and in thermal contact with a heat reservoir at temperature T.

1. What is the classical partition function of the adsorbed atoms if N of them are adsorbed onto the walls of the container?

2. What is the chemical potential μS of the atoms adsorbed on the surface?

3. What is the chemical potential μV of the N - N atoms in the volume of the container?

4. When the atoms in the volume and those adsorbed on the walls are in equilibrium, what is the average number of atoms adsorbed as a function of the temperature?

5. What are the high- and low-temperature limits of the ratio of the number of adsorbed atoms to the total number of atoms?