Equations of State for Gas and Liquid

To illustrate the technique, consider an ideal gas of N spherical, point-like, nrai-interacting particles or molecules without internal degrees of freedom. The partitirai 

k states of energy Zk belong to an individual particle and the summation should be made over all these states. Since particles do not interact, the statistic sum for N independent particles is a product of N sums calculated for each particle. As explained above, to exclude identical sum corresponding to the same state of the gas, the number of permutation N is introduced in the denominator. 

The translational motion of a particle is classic and the kinetic energy of one molecule is kiPx Py Pz) = (pI+pI+ Therefore, the summation may be 

Note that, in the triple integral, each integral with respect to p, with limits 

50) integrating is made over N-dimensional coordinate space of volume V. Then, the free energy (6.47) reads  

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