燨n the assumption that Onnes equations meet the requirements of the relativistic covariance, virial coefficients as functions of temperature are derived by using the transformations between thermodynamic variables provided by the vector theory of relativistic thermodynamics, and result in agreement with those obtained from cluster expansions in statistics. This breaks, to some extent, the traditional ideas that the thermodynamic theory is not able to derive equations of state at all and presents a possibly simple and new way of finding theoretically the equation of state.