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Homework Help: Derivation of the average translational kinetic energy of a molecule

  1. Sep 10, 2011 #1
    1. The problem statement, all variables and given/known data

    Hello, this is not actually a homework problem. I just can't seem to understand the derivation of the average translational kinetic energy of a molecule. I am startled by the way the velocities are added.

    2. Relevant equations

    My undergraduate level textbook says that (vx^2)av = (vy^2)av = (vz^2)av, but then it says (v^2)av = (vx^2)av + (vy^2)av + (vz^2)av = 3(vx^2)av

    How can velocities being vectors be added this way? I am surely missing something here.

    3. The attempt at a solution
  2. jcsd
  3. Sep 10, 2011 #2


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    I thinking you are missing the importance of subscripts. It is certainly true that the square of the magnitude of the 3-d velocity vector is always


    what does this become when you replace the components with their averages which are all equal to each other?
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