dU = V dT + T dV

substituting the value Cp and Cv into the above

dU = CV dT + T dV

but T =0

dU = CV dT

relations between specific heat capacity at constant pressure Cp and at constant volume Cv

proving Cp-Cv =R

dH =dU+dW

→ dH =dU+d(PV)

dividing through by dT

 =+(PV)

 =+(PV)

note replace b in the above with δ and redrive the equation