Specific heat is a property related to internal energy that is very important in thermodynamics. The intensive properties cv and cp are defined for pure, simple compressible substances as partial derivatives of the internal energy u(T, v) and enthalpy h(T, p), respectively:
where the subscripts v and p denote the variables held fixed during differentiation. The properties cv and cp are referred to as specific heats (or heat capacities) because under certain special conditions they relate the temperature change of a system to the amount of energy added by heat transfer. Their SI units are J/kg K or J/mol K. Two specific heats are defined for gases, one for constant volume (cv) and one for constant pressure (cp).
According to the first law of thermodynamics, for constant volume process with a monatomic ideal gas the molar specific heat will be:
Cv = 3/2R = 12.5 J/mol K
U = 3/2nRT
It can be derived that the molar specific heat at constant pressure is:
Cp = Cv + R = 5/2R = 20.8 J/mol K
This Cp is greater than the molar specific heat at constant volume Cv, because energy must now be supplied not only to raise the temperature of the gas but also for the gas to do work because in this case volume changes.