  In this paper we introduce the Isotherm Length-Work theorem using the
Helmholtz potential metric and the virial expansion of pressure in inverse
power of molar volume. The theorem tells us what length of a thermodynamical
system described by equation of state through virial expansion along isotherms
actually is with such a metric. We also give explicit solutions for
thermodynamic length along isotherms in the case of first, second and third
order expansion.
