On the basis of second-order differential equations of thermodynamics two relationships between the thermal state variables are derived. They may be considered as the equations of state in differential forms, obtained strictly from thermodynamics. The validity of these dependencies was confirmed by testing with the ideal gas law and the van der Waals equation of state. For the van der Waals equation, applied to the critical point of a pure substance, the equivalence of obtained relations is demonstrated. These relations could be recommended to obtain and to analyze general thermodynamic characteristics of pure substances and mixtures of fixed chemical composition.
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