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