1. Ideal gas: Statistical mechanics
Temperature is related to averaged kinetic energy
For each of projections
(degrees of freedom):

2. Theorem of Equipartition of Energy:
Statistical mechanics
Theorem of Equipartition of Energy:
Each degree of freedom contributes ½kT to the energy of a system, where possible degrees of freedom are those associated with translation, rotation and vibration of molecules

3. Boltzmann Distribution:
Statistical mechanics
Boltzmann Distribution:
Distribution function (number density) nV(E):
It is defined so that nV(E) dE is the number of molecules per unit volume with energy between E and E + dE
Probability P(E):
It is defined so that P(E) dE is the probability to find a particular molecule between E and E + dE

4. Statistical mechanics
Free particle:
Harmonic oscillator:

5. Averaged values: Averaged energy: Averaged velocity: Usually:
Statistical mechanics
Averaged values:
Averaged energy:
Averaged velocity:
Usually: