# Ideal gas: Energy

The energy of the ideal gas is given by (Hill Eq. 4-16)

where is the molar gas constant.
This energy is all *kinetic energy*, per degree of freedom, by equipartition. This is because there are no intermolecular forces, thus no potential energy. This result is valid only for a monoatomic ideal gas. The general expression would be

where is the number of degrees of freedom. This number is 3 for atoms; if would be 6 in principle for diatomic molecules, but in normal conditions 5 is a very good approximation since vibrations are "frozen" (as explained in the entry about degrees of freedom.)

## References

- Terrell L. Hill "An Introduction to Statistical Thermodynamics" 2nd Ed. Dover (1962)