Apply first law of thermodynamics.
Heat added = increase in internal energy + external work done by the system
∴ dQ = du+dw
Specific heats of gases are expressed as molar specific heats which are constant pressure Cp and constant volume Cv.
From enthalpy, H = u + Pv
Relationship between specific heats for ideal gases
be written as H = u + Pv
dh = du + d(RT)
Cpdt = Cvdt + Rdt
Cp = Cv + R or R = Cp - Cv
where R is gas constant