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Tough thermo problem

  1. Sep 25, 2014 #1
    1. The problem statement, all variables and given/known data
    Gaseous helium is contained in a rigid container with a volume of V=0.5 m3, and is initially at a pressure of 500 kPa. Agitation by a stirrer transfers 250 kJ of work to the gas in an adiabatic process. Cv for the gas is constant and equal to 12.46 kJ/kmol*K. What is the final pressure of the gas?
    So
    At state 1: V=0.5 m3, P=500 kPa,
    Process 1->2: W=-250kJ
    At state 2: V=0.5 m3, P=?

    cv=12.46kJ/kmol*K


    2. Relevant equations
    Energy balance for the process:
    Q-W=deltaU+deltaKE+deltaPE
    Q=deltaPE=deltaKE=0 so
    -W=deltaU, W=-250kJ so
    250kJ=deltaU.


    3. The attempt at a solution
    This is what I have:
    250kJ=deltaU=n*deltau where u=U/n and n is the number of moles of helium.
    cv=du/dT so
    deltau=cv*deltaT and
    250 kJ=n*cv*deltaT

    I don't really know where to go with this problem to find anything to do with the pressure, the equation seems underdetermined. Help?
     
  2. jcsd
  3. Sep 25, 2014 #2
    Has mass been given? Or is the given volume specific as in m3/kg?
     
  4. Sep 25, 2014 #3
    No, no mass is given and the the volume given is not specific, it is just the volume of the tank.
     
  5. Sep 25, 2014 #4
    What about the number of moles? It's impossible to predict the temperatures without the mass or moles therefore you won't be able to predict the final pressure.
     
  6. Sep 25, 2014 #5
    no, the data given is the only available data. this is why I thought it was underdetermined. Can it even be done???
     
  7. Sep 25, 2014 #6

    gneill

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    Staff: Mentor

    You may want to throw the ideal gas law, PV = nRT, into your set of Relevant Equations. Note that ##C_v## is specified in terms of moles, and n in the ideal gas law is moles. Set up a ratio and ponder on what you know about the various variables:

    $$\frac{P V}{P_o V_o} = \frac{n R T }{n R T_o}$$
     
  8. Sep 26, 2014 #7

    rude man

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    This problem is unsolvable unless either the mass, no. of moles or initial temperature are given.

    You could proceed assuming initial temperature = room temperature ~ 293K.
     
  9. Sep 26, 2014 #8

    gneill

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    I think it may be doable. Just assume that the number of moles is n and see where things go using the ideal gas law and Cv to find the change in temperature given the change in heat. I think that the n will cancel out along the way.
     
  10. Sep 26, 2014 #9

    rude man

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    Send me a PM on how?
    rude man
     
  11. Sep 26, 2014 #10

    rude man

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    gneill is right. It is solvable.
     
    Last edited: Sep 26, 2014
  12. Sep 26, 2014 #11

    gneill

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    Done. Check your mail (inbox).
     
  13. Sep 28, 2014 #12

    gneill

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    @ashy : Did you resolve your difficulty?
     
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