This is only true for an ideal gas. Since it's true for an ideal gas, then we can go ahead and replace this with Cv, and then we have Cp=Cv+R Cp with Cv plus R, which is what we were after.

常犯的一个错误，这只对理想气体成立,因为对理想气体成立,所以我们可以继续，用Cv代替,这项，最后得到。

麻省理工公开课 - 热力学与动力学课程节选