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Homework Help: Rms speed of ideal gas

  1. Dec 4, 2006 #1
    1. The problem statement, all variables and given/known data
    An ideal gas is kept in a container of constant volume. The pressure of the gas is also kept constant. If the initial rms speed is 1800 m/s, what is the final rms speed?


    2. Relevant equations
    v(rms)=square root of [v(avg)]^2=square root of (3kT)/m


    3. The attempt at a solution
    This was the only equation that I could find that dealt with rms speed, but the only problem is that I'm not sure how I can use just the initial rms speed to solve for the final rms speed with this equation.
     
  2. jcsd
  3. Dec 4, 2006 #2

    Doc Al

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    Could it be a trick question? :wink:
     
  4. Dec 4, 2006 #3
    how would it be a trick question?
     
  5. Dec 4, 2006 #4

    rsk

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    Is anything changing? Is temperature changing? Have you given us the full question? If everything else is unchanged, then so is rms speed.
     
  6. Dec 4, 2006 #5

    Doc Al

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    And that's why I'd call it a trick question. Be sure you state the problem completely, just in case.
     
  7. Dec 4, 2006 #6
    I understand what you're saying now. The problem says that temperature and pressure are kept constant and to find the final rms speed. I tried entering in the same speed as the answer, but the program said that that was the wrong answer.
     
  8. Dec 4, 2006 #7
    My mistake...it says that volume and pressure are constant but it says nothing about temperature.
     
  9. Dec 4, 2006 #8

    marcusl

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    I'd say 1800 * sqrt(Tfinal / Tinitial)
     
  10. Dec 4, 2006 #9
    the only problem is that the temperature is not given
     
  11. Dec 4, 2006 #10
    I sent my teacher an e-mail and he said, "First form the ratio of V_rms(ini)/V_rms(final), then you will see that
    to find the ratio of the rms speeds what you need is the ratio of the
    temperatures, which you can find using PV = NkT = constant" but I'm not sure how to figure out T w/o any values.
     
  12. Dec 4, 2006 #11

    Gokul43201

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    If PV = NkT and all of P, V, N and k are constant, then what can you say about T?
     
  13. Dec 4, 2006 #12
    ...it would have to be a constant too, right?
     
  14. Dec 4, 2006 #13

    Gokul43201

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    Yes, it would.

    In general, as long as the gas is in a closed container (no molecules can enter or escape, so N is fixed), you can rewrite the above equation as:

    (P1V1)/(P2V2) = T1/T2

    In this case, if P1=P2 and V1=V2, that leaves you with T1/T2=1
     
  15. Dec 4, 2006 #14
    so if I set it up as a ratio, like my teacher said, then it would be v(rms,i)/v(rms,f)=T1/T2=1
    so v(rms,i)/v(rms,f)=1
    so v(rms,i)=v(rms,f) right?
    But that would mean that they would equal each other and I already plugged in that number and the program said that it wasn't correct.
     
  16. Dec 4, 2006 #15

    Gokul43201

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    Either the program has it wrong, or you didn't write down the question correctly, or there's a typo in the question. Can't really say which it is.

    Maybe the best you can do is take the above (corrected - see PS below) argument to your teacher, and find out where the problem is.

    PS: There's a square root you're missing. v2/v1 = sqrt(T2/T1) - look at the equation you wrote down in the opening post.
     
    Last edited: Dec 4, 2006
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