You should consult your Physical Chemistry text for a review of the meaning of heat capacity, its thermodynamic definition, and the relationships between molecular structure and heat capacity. Carefully evaluated heat capacities have been of great value in studies of the physical properties of matter.
Heat capacities depend upon the manner in which they are measured.
We will make two very different kinds of measurements, to illustrate broad applicability of thermodynamic principles. The Method of Clement and Desormes The basic device in this method is a large glass vessel initially containing the gas of interest at a pressure slightly above atmospheric. The apparatus is in effect a very sensitive gas thermometer, but analysis of the data does not require knowledge of temperature. The vessel is first purged for a few minutes with the gas of interest, the exit tube of the vessel is then closed and gas is allowed to flow until a modest pressure is established. Success depends upon the absence of leaks and the use of not too high initial pressure.