Thermodynamic relations for the critical point of a pure substance

At the critical point of a pure substance, arbitrary-order derivatives of pressure, with respect to temperature at constant internal energy, Helmholtz energy, and enthalpy, were shown to equal the derivatives of the same order of the elasticity curve. This assertion was proved with the use of formal expressions similar in structure to the Maxwell rule for phase equilibria of pure substances. The obtained relations were used to remove some thermodynamic function indeterminacies that arise at the critical point.