Thermodynamics and the Equation of State

Results for two simple cases can be obtained immediately. First, if U(R) = 0—i.e., no interactions between the particles—then 

The second simple case is for hard rods, i.e., for particles interacting through a pair potential of the form 

This power series converges for po- 1. Clearly, when pa 1, the average length per particle p Ms smaller than a, and this is impossible in this system. 

The terms in the square brackets in Eq. (4.5.24) give the successive corrections to the ideal gas pressure due to interactions between pairs, triplets, etc., of particles. This expansion is the virial expansion of the pressure for the one-dimensional system. 

We note that the slope of P/kT versus p curve is always positive, i.e.. 

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No assumption is made thermodynamically about the specific heat of a perfect gas. Some results concerning it follow from thermodynamics and the equation of state, however. We have already seen that... 

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