Temperature and kinetic energyFrom the ideal gas law
and from the above result we have
then the temperature takes the form
The temperature becomes
Eq.(1) and Eq.(4) are called the "classical results", which could also be derived from statistical mechanics; for more details, see .
Since there are degrees of freedom in a monoatomic-gas system with particles, the kinetic energy per degree of freedom is
As noted in the article on heat capacity, diatomic gases should have 7 degrees of freedom, but the lighter gases act as if they have only 5.
Thus the kinetic energy per kelvin (monatomic ideal gas) is:
- per mole: 12.47 J
- per molecule: 20.7 yJ = 129 μeV.
- per mole: 3406 J
- per molecule: 5.65 zJ = 35.2 meV.