Internal Energy of an Ideal Gas

Theorem: Internal Energy of an Ideal Gas

The Internal Energy $U$ of an ideal gas depends on the number $f$ of degrees of freedom of a single gas particle, the total number $N$ of particles and the Temperature $T$ of the gas and is given by the following equation, where $k_B$ is the Boltzmann Constant:

$$U=\frac{f}{2}{k}_{B}NT$$

NOTE

Alternatively, $U$ can be expressed in terms of the amount of substance $n$ and the Molar Gas Constant $R$.

$$U=\frac{f}{2}nRT$$

PROOF

TODO