Abstract <p>The paper presents approaches for constructing thermodynamic relationships for a mixture of noninteracting substances without resorting to labor-intensive molecular modeling. The main practically applicable approximations are the requirements of thermodynamic equilibrium (<i>pT</i>-approximation) and mechanical equilibrium (<i>p</i>-approximation). It is assumed that the motion of the components is described by a single velocity. For these approximations, the corresponding systems of nonlinear equations and approaches for solving them are presented. Using the example of solving a Riemann problem at the contact interface between two substances with significantly different properties, it is demonstrated that the requirement of temperature equilibrium between components is not always justified and can lead to incorrect results.</p>