Failure of the Identity That Links Thermal Expansion and Isothermal Compressibility in the Case of Condensed Phases

In thermodynamics, there is a relation that connects the thermal expansion coefficient and the isothermal compressibility. It has been supposed that it was a universal identity. However, it is shown here that this identity is not appropriate for condensed phases. Experimental measurements confirm this conclusion. This relation is used in the derivation of Mayer's relation and the heat capacity ratio, and proceeds to produce results that significantly deviate from experimental results for condensed phases. An additional mistake is also detected in the derivation of Mayer's relation.