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Kinetic Theory equation help

  1. Dec 11, 2011 #1
    Can someone explain me this theory ? and how to use the equation please

    I have this in my notes but I dont understand :(

    Average (translational) Kinetic Energy per molecule is

    E= 3/2kT

    The same, per mole, is U = 3/2 * R* T
  2. jcsd
  3. Dec 11, 2011 #2


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    The basics of deriving this involve quite a long string of steps and comes under the heading of 'bookwork'. I think you should just sit down with the book and follow it through. Else you can just accept it.
    If you don't have 'a book' then Wiki would be a way forward. Start with Boltzman Distribution
  4. Dec 11, 2011 #3
    Do you recognise the experimental equation for the gas laws in the form
    PV = nRT ? where n = number of moles
    So for 1 mole the experimental law is PV = RT

    The kinetic theory leads to an expression PV = (N/3) x mc^2 where N is the number of molecules.
    If this equation is written as 2(N/3) x 0.5mc^2 it makes no difference but it does highlight a combination 0.5mc^2 which is average KE of molecules.
    Putting the experimental equation and the theoretical equations together leads to

    RT = 2(N/3) x 0.5mc^2 or 0.5mc^2 = (3/2)TR/N

    so average KE = (3/2)TR/N
    R is the gas constant and N is the number of molecules in 1 mole (Avagadros number)
    The combination R/N of these constants is known as Boltzmanns constant, symbol k

    Therefore average KE = (3/2)kT

    Hope this helps
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