Various ways of thermodynamic evaluations can yield different results, contradicting to one another. Such a case is considered a paradox, with the attempts to solve it. This is because thermodynamics is thought to be the science established on solid conceptual ground, with accurate mathematical evaluations. Recently, we faced similar problem, when the relationship between heat capacity and pressure is described by two different equations, predicting opposite behavior. Both equations are free of evident errors. In searching for the reason of the discrepancy, we found out that it is common practice in thermodynamic evaluations to tune the mathematical operations in order to receive the necessary result. It is typical of empirical science, but inappropriate for the fundamental knowledge based on axiomatic background. Short historical survey on experimental data and theoretical concepts dealing with the relation between heat capacity and pressure proves that the thermodynamics is very flexible and effective tool for the solution of the problems in the field of relationships among P–V–T parameters and thermophysical properties of matter. One should not consider the solutions as the universal laws.
1. Caratheodory, C1909Untersuchungen über die Grundlagen der Thermodynamik. Math Ann67:355–386.