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Homework Help: Isothermal process in a

  1. Dec 10, 2011 #1
    1. The problem statement, all variables and given/known data
    A thermally isolated chamber is pumped down to a very low pressure. At some point, the chamber is vented slowly so that it is filled with air up to atmospheric pressure, whereupon the valve is closed. The temperature of the air surrounding the chamber is T0=300 K. What is the temperature T of the gas in the chamber immediately after the valve is closed. γ=Cp/CV=7/5 for air. (ANS: 420K)

    2. Relevant equations
    Has the air done any work? Does low pressure means vacuum?

    3. The attempt at a solution
    T0/V0=T/V But what is V0?
  2. jcsd
  3. Dec 10, 2011 #2

    Andrew Mason

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    I am not clear on the facts. Is the air surrounding the chamber at atmospheric pressure (ie. open to the atmosphere)? If so, there is no change in temperature when it fills up the chamber. I don't see how the temperature of the gas entering the chamber will increase, in any event.

    Where did you get this problem?

  4. Dec 10, 2011 #3
    yeah it's a werid problem

    P1V1gamma = P2V2gamma

    if it is reversible and adiabatic, which it should be since you're given gamma?
  5. Dec 10, 2011 #4

    Andrew Mason

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    But it is not reversible. This is a rapid free expansion as the outside air fills the empty chamber. In any event, it is an expansion. So if any work is done by the gas filling the chamber, the internal energy will decrease. I don't see how temperature can possibly increase.

  6. Dec 10, 2011 #5
    whoops i missed that, so yeah you're right there is no way the temp could increase. It almost sounds like a similar process in which they liquify hellium
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