# Relation between kinetic energy and temperature

Where does the 3/2 come from?
$$\frac{1}{2} mv^2 = \frac{3}{2} kT$$

sophiecentaur
Gold Member
2020 Award
A particle can move in any of three directions (that's where the 3 comes from), with kt/2 being the kinetic energy carried by motion on each the x,y or z dimensions.
This link gives a short and sweet bit of book work. That Hyperphysics site is good for many things, actually.

Doc Al
Mentor
Where does the 3/2 come from?
$$\frac{1}{2} mv^2 = \frac{3}{2} kT$$
There are three translational degrees of freedom, each contributing 1/2kt to the total energy. This from the equipartition theorem.

Taking it back a step the 3kT/2 can be found by equating the two ideal gas equations,one being obtained experimentally(PV=RT) the other being obtained theoretically using kinetic theory(PV=Nmc bar squared/3)