Correlation between the derivatives of thermodynamic functions at the critical point of a pure substance

The use of differential equations of thermodynamics and indefinite forms at this critical point makes it possible to reveal correlations between different derivatives of thermodynamic functions that do not depend on the kind of matter or on the model of the equation of state used. It is known that the result will be common both for a real substance and for any model of the equation of state if it is obtained based on the differential relations of thermodynamics. The relations for the derivatives of thermal quantities analyzed in this paper at fixed values of a number of calorimetric properties have been derived based on factual assumptions concerning the slope of the elasticity curve at the critical point, differential thermodynamics equations, and a rigorous mathematical apparatus. Therefore, they are valid for a real pure substance or for any model of the analytical UEOS describing its critical state.