Virial equations of state for pure gases

In later chapters of this book there will be occasion to apply thermodynamic derivations to virial equations of state of a pure gas or gas mixture. These formulas accurately describe the gas at low and moderate pressures using empirically determined, temperature-dependent parameters. The equations may be derived from statistical mechanics, so they have a theoretical as well as empirical foundation. There are two forms of virial equations for a pure gas one a series in powers of 1/ Fm  

The parameters 5, C,. .. are called the second, third,. .. virial coefficients, and the parameters Bp, Cp,. .. are a set of pressure virial coefficients. Their values depend on the substance and are functions of temperature. (The first virial coefficient in both power series is 1, because pV must approach RT as 1/Fm or p approach zero at constant T) Coefficients beyond the third virial coefficient are small and rarely evaluated. 

The values of the virial coefficients for a gas at a given temperature can be determined from the dependence of p on Fm at this temperature. The value of the second virial coefficient B depends on pairwise interactions between the atoms or molecules of the gas, and in some cases can be calculated to good accuracy from statistical mechanics theory and a realistic intermolecular potential function. 

Thermodynamics and Chemistry, second ad iiion,version 3 by Howard DeVoe. Latest version www.chem.umd.edu/themobook 

Then we equate coefficients of equal powers of 1/Fm in Eqs. 2.2.2 and 2.2.5 (since both equations must yield the same value of pV a for any value of 1/ Fm)  

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