Equipartition Principle

- relates temperature of a system to its average energies
- says that each independent squared term contributes 1/2 kT to the average internal energy per particle
- only works at temperatures where the excited vibrational states have significant occupancy (we need the spacing to be <

Equipartition Translation

contributes 3RT/2 to the internal energy

non-linear molecules

- 3 degrees of rotational freedom
- 3 degrees of translational freedom
- 3N-6

linear molecules

- 2 degrees of rotational freedom
- 3 degrees of translational freedom
- 3N-5

equipartition principle: vibration

each vibrational degree of freedom contributes TWO squared terms to the energy

occupancy of vibrational states

most molecules at room tempertaure, even the first excied state has almost no ocuplacy

Heat capacity

at constant volume, the heat capacity measures quantitavely the abilty of a system to take energy into its internal degrees of freedom

- heat capacity is directly related to the internal energy

the internal energy for a gas of non-interacting molecules

is the sum of the contributions from translation, rotation etc.

heat capacities - Rotational contribution at low temperature

describes temperature at which excited rotational levels are significantly occupied and is typically small. So rotation excitation happens at almost all temperatures

heat capacities - vibrational contribution

vibration is significantly affected by quantisation up to many hundred Kelvin. It describes temperature at which excited vibrational levels are significantly occupied and is typically large. Vibrational excitations typically only happen at high temperatures