The subject of this research is the second-order mixed derivatives at the critical state of a pure substance that could be constructed from the variables of thermodynamic Maxwell equations. The values of these derivatives and the indeterminate relationships formed from them are obtained by using second-order thermodynamic equations, critical conditions, and rigorous mathematical apparatus. The results of this work could be applied to any pure substance or mixture of fixed chemical composition, and to any equation of state that describes critical point. For thermal equation of state the types of the singularities for some second-order mixed derivatives were established. It was shown that values of several second-order mixed derivatives cannot be determined principally because of indeterminacy of heat capacity at constant volume at the critical point.
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