1. Limited time only! Sign up for a free 30min personal tutor trial with Chegg Tutors
    Dismiss Notice
Dismiss Notice
Join Physics Forums Today!
The friendliest, high quality science and math community on the planet! Everyone who loves science is here!

Another Thermodynamics Question

  1. Oct 31, 2004 #1
    Why does U = (3/2)nRT?
  2. jcsd
  3. Oct 31, 2004 #2
    Thats not true in all cases. Its onlytrue for , if I remember correctly, monatomic ideal gases. The reason why its true has to do with the "degrees of freedom" of the gas. Monoatomic gaese have only 3 degrees of freedom(they can only move in the x, y and z directions and cannot rotate) For diatomic gases, it would be U = 5/2 nRT since we added two more degrees of freedom(two planes of rotation)
  4. Oct 31, 2004 #3
    Yes i understand. I should have asked why

    where f = degrees of freedom
  5. Nov 2, 2004 #4


    User Avatar
    Homework Helper
    Gold Member

    This is done by the equi partition theorem.
    It states that we add 1/2KT per degree of freedom and 1KT per degree of Vibrational freedom.
    An interesting case is when we consider a diatomic gas like Hyrdogen gas.
    We expect U to be
    [tex] N_a[ \frac{3}{2}KT + \frac{2}{2}KT + 1KT] [/tex]

    from velocities in x,y,z directions, the rotation about x,y and vibrational (1/2mv^2 and 1/2kx^2) respectivley
    [tex] = \frac{7}{2}RT [/tex]

    But experimentally we find that
    [tex] U= \frac{5}{2}RT [/tex]

    This is because at room temperature vibration does not seem to contribute

    Therefore [tex] \gamma = \frac{7}{5} [/tex] at room temperature
Share this great discussion with others via Reddit, Google+, Twitter, or Facebook