Energy of the Ideal Gas from State Functions

This means the energy can be any function of Therefore, the ideal gas 

Here we have added Ci as an additive constant. Since R = Cp — Cv and k = CpfCv we come to 

In the constant C2 we have built in 1 - k, but also other terms to ensure that the expression has the physical dimension of an energy. 

We generalize now the considerations and introduce the energy as a function of the entropy, volume, and mol number U(S, V, n). Now volume and entropy are no longer the quantities of 1 mol of gas but the volume and entropy as such, and n is the number of moles of gas we are dealing with. Equation (4.2) changes now into 

Combining Eqs. (4.6) and (4.7), using the same arguments as above, we arrive at 

---