Relation between kinetic energy and temperature

  1. Where does the 3/2 come from?
    [tex]\frac{1}{2} mv^2 = \frac{3}{2} kT [/tex]
  2. jcsd
  3. sophiecentaur

    sophiecentaur 14,705
    Science Advisor
    Gold Member

    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.
  4. Doc Al

    Staff: Mentor

    There are three translational degrees of freedom, each contributing 1/2kt to the total energy. This from the equipartition theorem.
  5. 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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