# Why is potential energy zero in this calculation of partition function?

In section 7.2 of Rief's "Fundamentals of Statistical and Thermal physics". While calculating the partition function for ideal gas he writes:

$$\begin{array}{l} \displaystyle{Z' = \int{ \exp{\left\{- \beta \left[\frac{1}{2m} \left({\mathbf{p}_1}^2 + \cdots + {\mathbf{p}_N}^2 \right) + U\left(\mathbf{r}_1, \dots , \mathbf{r}_N\right) \right]\right\}}} } \\ \hspace{15em} \displaystyle{\frac{d^3\mathbf{r}_1 \cdots d^3\mathbf{r}_N d^3\mathbf{p}_1 \dots d^3\mathbf{p}_N}{{h_0}^{3N}}} \end{array}$$

Then he says

Why is $$U$$ taken to be zero?

• For an ideal gas we take by definition $U=0$. – Dani Oct 4 '18 at 7:03
• $U$ is the potential energy as stated in your equation and the text, not internal energy. – K_inverse Oct 4 '18 at 7:27

Thus for an ideal gas, $$U=0$$ (where $$U$$ is the potential energy).