The internal energy is the sum of all the
energy associated with molecular motion:
translation, rotation, and vibration.
Equipartition of Energy:
Each degree of freedom contributes kT/2 to the internal energy.
What is a degree of freedom?
Each independent energy storage mode is a degree of freedom:
For a monatomic ideal gas, there is only translation and the internal energy is:
|nRT monatomic ideal gas|
Diatomic molecule: 3 translational and 2 rotational degrees of freedom. Thus:
|NkT diatomic ideal gas (intermediate temperatures)|
Careful! This result applies at intermediate temperatures. At low temperatures only translation contributes, and at high temperatures two additional degrees of freedom arise associated with vibration (kinetic & potential energy). Thus:
|NkT diatomic ideal gas (high temperatures)|