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Equipartition Theorem Question!

  1. Oct 9, 2011 #1
    1. The problem statement, all variables and given/known data
    Assuming that pressure remains constant, at what temperature is the root-mean square speed of a helium atom equal to the root-mean-square speed of an air molecule at STP? Express your answer to 3 significant figures in Kelvin.


    3. The attempt at a solution

    the root mean square speed is given by vrms = Sqrt[3 kT/m]

    where T is the temperature and m is the mass of one molecule (k is the boltzmann constant)

    so if we take ratios, we get

    vrms(He)/vrms(O2) = Sqrt[T(he)/T(O2)] Sqrt[m(O2)/m(He)]

    I am using oxygen since air is a mixture and there is no such thing as a molecule of air. If you need to compare an ensemble of He atoms to an ensemble of air molecules, use molecular weight = 28.97

    so we have

    vrms(He)/vrms(O2) = Sqrt[T(He)/273][Sqrt[32/4]

    for vrms(He) = vrms()2), then

    1 = (T/273)(8) => T=273/8 solve for T

    So you get 34.125 C? Then going to Kevlin it would be 307.125 and rounding to 3 significant figures is 307?

    Is this right??
     
  2. jcsd
  3. Oct 9, 2011 #2

    ehild

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    T is the absolute temperature in K.

    ehild
     
  4. Oct 9, 2011 #3
    So it is 34.1 rounding to 3 significant figures?
     
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