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V_RMS problem . Need help with it!

  1. Dec 7, 2012 #1
    V_RMS problem..... Need help with it!

    1. The problem statement, all variables and given/known data

    Find T, the temperature at which O2 gas molecules have an rms speed of v = 699 m/s.

    2. Relevant equations

    It's the rms form I have used.

    [itex]v_{rms} = √(3RT/M)[/itex]

    3. The attempt at a solution

    Let

    M = 32 g/mol ≈ 32 * 10^(-3) kg/mol
    v_rms = 699 m/s
    R = 8.314 J/(mol * K)

    Attempted to solve for T. Here is what I have:

    [itex]v_{rms}^{2} = 3RT/M[/itex]
    [itex]T = v_{rms}^{2}M/(3R) [/itex]

    Plug and chug in the values, and I got 627 K, which is not correct.
     
  2. jcsd
  3. Dec 7, 2012 #2

    TSny

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    Re: V_RMS problem..... Need help with it!

    Your work looks good to me. Are you sure the answer is incorrect?
     
  4. Dec 7, 2012 #3

    gneill

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    Re: V_RMS problem..... Need help with it!

    I seem to recall that the available energy modes for a diatomic gas are different than for a monatomic gas. 5/2 vs 3/2 as I recall. Some googling may be in order. Try "kinetic energy diatomic" or something along those lines.
     
  5. Dec 7, 2012 #4

    TSny

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  6. Dec 7, 2012 #5

    gneill

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    Re: V_RMS problem..... Need help with it!

    Well, so much for my memory then. Carry on, nothing to see here... :smile:
     
  7. Dec 8, 2012 #6
    Re: V_RMS problem..... Need help with it!

    Check your calculation. What do you get? I have the answer 627 K, but the system marks it incorrect.
     
  8. Dec 8, 2012 #7

    TSny

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    Re: V_RMS problem..... Need help with it!

    I also get 627 K. I assume the answer in to be in Kelvins.
     
  9. Dec 8, 2012 #8
    Re: V_RMS problem..... Need help with it!

    Increasingly strange.

    My professor told me to use this form which is right. v_rms = √(5RT/M).

    I entered in the value of T for the HW assignment, and I got the right answer. How strange... :\
     
  10. Dec 8, 2012 #9

    TSny

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    Re: V_RMS problem..... Need help with it!

    Yes, strange. Don't think he/she is correct. The 5 should be a 3. Just web-search "rms speed gas" for many examples.
     
  11. Dec 8, 2012 #10
    Re: V_RMS problem..... Need help with it!

    Actually, he said that because the velocity is diatomic, but as you said; no matter if the particles are atomic or not, v_rms = √(3RT/M). I believe he is thinking of the kinetic energy of the diatomic particles.
     
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