Constructing an Equation of State for a Diatomic Gas

In the interest of better understanding systems of interacting particles in equilibrium, the canonical partition function for a diatomic gas at low temperatures (below 100 degrees kelvin) is computed using a modification of the Lennard-Jones potential to model molecular interactions. This is then used to find a correction to the ideal gas law by calculating the second virial coefficient. An expression for the chemical potential is found as well. This allows us to construct an equation of state which is checked by referring to empirical measurements of the pressure, temperature, and volume of diatomic nitrogen and diatomic oxygen. Moreover, a Monte Carlo Simulation of a diatomic gas is generated to which our results are compared.