In the 19th century, German chemist and physicist Julius von Mayer derived a relation between the molar heat capacity at constant pressure and the molar heat capacity at constant volume for an ideal gas.
Mayer's relation states that
where CP,m is the molar heat at constant pressure, CV,m is the molar heat at constant volume and R is the gas constant.
For more general homogeneous substances, not just ideal gases, the difference takes the form,
(see relations between heat capacities), where
is the thermal expansion coefficient and
From this latter relation, several inferences can be made:[1]