Thermodynamics at work: The pressure derivative of the specific heat

Thermodynamics relates measurable quantities such as thermal coefficients and specific heats. The first law, which implies that the enthalpy is a function of state, yields a relation for the pressure derivative of the specific heat cP. The second law gives a simpler and well-known relation for this pressure derivative. We compare the values of the pressure derivative of cP obtained from the first and second laws to the values obtained from measurements for water at different pressures. The comparison illustrates the scope and methodology of thermodynamics.