# Relation between kinetic energy and temperature

by johnathon
Tags: energy, kinetic, relation, temperature
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 P: 40 Where does the 3/2 come from? $$\frac{1}{2} mv^2 = \frac{3}{2} kT$$
 Sci Advisor Thanks PF Gold P: 12,268 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.
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 Quote by johnathon 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.

 PF Gold P: 2,031 Relation between kinetic energy and temperature 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)

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