Sir (du)_p=du(due to temperature change)+F(v) where f(v) is change in u due to change in volume

du_p=nc_vdt+f(v), nc_pdt- nrdt =nc_vdt+f(v)

so c_p-c_v=R+f(v)/ndt From this i am not getting c_p-c_v=R for real gas.Please tell where i am wrong or is it that c_p-c_v is not equal to R for real gases

H= U+PV.............
dh=du+d(PV)........
(Here we are putting PV=nRT which is ideal gas equation and not true for real gases in general)
dh=du+d(RT)..........
dh=du+RdT.;........
frac{ dh }{ dT }=frac{ du }{ dT }+R
C p=C v+R..........
C p-Cv=R
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