Why should we find the heat capacity of any material?

First of all we consider the equipartition theorem which says that the internal energy U for each degree of freedom(DOF) is equal to (1/2)kT (where k is boltzmann const).

now, for solids and liquids we have only vibrational degrees of freedom which are two in each direction.

i.e. in monoatomic solids, there are three directions of vibration(X, Y, Z) and 2 in each direction.

so total 6 DOFs, so U=(6/2)kT=3kT and we know that (dU/dT)=molar heat capacity.

so we have C=3K.=  3R(for one mole) this means  all monoatomic solids have same molar heat capacity but different specific heat capacity which can befound out by multiplying the molar mass with C which is= 3R x MM.(you can tally the values of some metals with  experimental values of specific heats with this ; which turns out to be approximately same.

gases have the same rules but istead of one you have to find two specific heats(Cp and Cv)