Abstract: The 2nd virial coefficient of the hard sphere potential, rectangular potential well and LennardJones＇ potential are obtained for classical non-ideal gases in any dimension. The method of calculating higher virial coefficient is given. It is explicated that the 2nd virial coefficient converges for Lennard-Jones＇ potential, when the dimension n is smaller than 6.

Key words: any dimension, non-ideal gas, virial coefficient, statistical thermodynamics