Calculation of specific heats for different gases :-

For monatomic gas:-

According to the law of equi-partition of  energy U = (F/2) k T    for one molecule

and for one mole U = (F/2) R T

C_p – C_v = R

For Triatomic gas :- for Linear Molecule

C_P – C_V­  = R

C_P = 4R