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Gas contained in bottle

  1. May 19, 2006 #1
    Sir,
    An open mouthed bottle contains a gas at 60 degree Celsius. To what temperature should the bottle be heated so that ¼th of the mass of the gas may leave?
    I think that by increasing the temperature the gas molecules gain enough energy to overcome the intermolecular forces of attraction. But I don’t know how to relate them mathematically. Please help.
     
  2. jcsd
  3. May 19, 2006 #2

    Andrew Mason

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    PV=nRT

    AM
     
  4. May 19, 2006 #3
    The volume and the number of moles of the gas are not given. How to calculate the temperature?
     
  5. May 19, 2006 #4

    Andrew Mason

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    PV=nRT

    There are two ways to approach this. Consider it as equivalent to a volume expansion to 4/3 of the original volume, 1/4 of which is outside the bottle, or consider it as a loss of 1/4 of the number of molecules from a fixed volume.

    P is constant. R is constant. In the latter case, V is constant and nf is 3/4 of ni. So how must T change if PV = nRT still holds? In the former case, n is constant but Vf = 4Vi/3. Again, work out how T must change in order for the ideal gas law to hold?

    AM
     
  6. May 19, 2006 #5

    Gokul43201

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    I think AM meant to say 5/4, not 4/3.

    Edit: In light of subsequent posts, please disregard the above line.
     
    Last edited: May 20, 2006
  7. May 19, 2006 #6

    Andrew Mason

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    Actually, I meant 4/3. I originally thought 5/4 but changed it. The volume expanding to 4/3 original volume leaves 3/4 of the original gas in the bottle.

    AM
     
  8. May 20, 2006 #7

    Gokul43201

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    Yes, that's right...I take that back. The answer is clearly 4/3. As for an approach to solve the problem, I find making V -> 4V/3 less intuitive than making n -> 3n/4 (at fixed V, and ignoring the escaped gas). Nevertheless, by the first approach, my error was in forgetting about the thermal expansion of the escaped gas (by a factor of 4/3).
     
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