Thermodynamic equations for the isobaric and isochoric heat capacities of pure substances at the critical point

It was proved on the assumption of a nonzero and finite slope of the elasticity curve at the critical point that the isochoric heat capacity at this point cannot be established on the basis of thermodynamics only. The critical conditions of a pure substance were derived from the differential equations of thermodynamics using a rigorous mathematical apparatus. Several indeterminate forms containing isochoric or isobaric heat capacities or their derivatives were evaluated.