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Pressure and Temperature question: Ideal Gas Laws

  1. Dec 28, 2011 #1
    1. The problem statement, all variables and given/known data

    Find the pressure and temperature when given the following data on helium gas:

    Volume (V) = 0.10 m^3 ** Helium mass (m) = 4.0 amu ** Number of atoms (N) = 3.0 x 10^24

    Assuming PV = 1 then P=1/V then Pressure = 1.0 / 0.10m^3 = 10Pa

    2. Relevant equations
    PV = NkT arranged for T = PV/Nk OR PV = nRT arranged for T = PV/nR

    3. The attempt at a solution
    Mm = Mr x 10-3 = 4.0 x 10-3 so the mass is 4.0 x 10^-3 / 6.02 x 1023 = 6.6 x 10^-27

    The temperature T is then:
    T = PV/Nk
    T = P x 0.10m^3 / 3.0 × 10^24 mol−1 x 1.381 × 10^−23 J K−1

    But I have no idea how to get Pressure - Ive tried using Boyles law PV = constant but get lost

    Any pointers would be deeply appreciated
     
  2. jcsd
  3. Dec 29, 2011 #2

    NascentOxygen

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    Staff: Mentor

    One mole of an ideal gas will occupy a volume of 22.4 liters at STP (Standard Temperature and Pressure, 0°C and one atmosphere pressure).

    Though I think you still are lacking some information.
     
  4. Dec 29, 2011 #3
    Thanks for the reply, that's all I've been given - been told Charles Law and Botles Law may come in handy but don't know how!?
     
  5. Dec 29, 2011 #4

    NascentOxygen

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    Charles' and Boyle's Laws are just special cases of the general gas law.

    You are looking at: [itex]PV \div T [/itex] = constant
    but I think you can only find the quotient [itex]P \div T[/itex]
     
  6. Dec 29, 2011 #5
    You are given the number of atoms = 3 x 10^24 which = 5moles (n)
    If you substitute this into PV = nRT you can get T but the answer is not sensible ?????
    I can't see why you have been given the mass of He atom = 4 amu !!!
     
  7. Dec 29, 2011 #6

    gneill

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    It's possible that one might have to resort to the isentropic relationships for an ideal gas.
     
  8. Dec 29, 2011 #7
    I think I have just realised that shyguy is assuming that PV=1.... it is not a given in the question....I don't know any more to add!!!!!!
     
  9. Dec 29, 2011 #8
    Yes, but working out the math the pressure would be 10 Pascals and the Temperature would 0.0012 Kelvin - and that make hardly any sense!
     
  10. Jan 4, 2012 #9

    NascentOxygen

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    Does your textbook provide the answer to this?
     
  11. Jan 4, 2012 #10
    No, it's an assignment question but reading through the full wording it appears that the peak velocity is 1100m/s
     
  12. Jan 4, 2012 #11

    NascentOxygen

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    Is it really late at night where you are? :uhh:

    Velocity does not enter into the question. Well, only tangentially. :smile:
     
  13. Jan 5, 2012 #12
  14. Jan 5, 2012 #13
    Thank you!! Just what I was looking for!
     
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