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Homework Help: Kinetic theory of gasses Integration problem

  1. Apr 27, 2008 #1
    1. The problem statement, all variables and given/known data
    In the temperature range 310 K and 330 K, the pressure p of a certain nonideal gas is related to volume V and temperature T by
    p = (24.9 J/K) T/V - (0.00662 J/K2)T^2/V
    How much work is done by the gas if its temperature is raised from 314 K to 324 K while the pressure is held constant?


    2. Relevant equations
    Pv=NRT
    W=integral(p dv)


    3. The attempt at a solution

    W=integral((24.9 J/K) T/V - (0.00662 J/K2)T^2/V dv)
    I am not sure what to use for the limits of integration. the problem gives me a range of temperatures, is there any way that I can use those? I am very sure the limits of integration should be in units of m^3.
     
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  3. Apr 27, 2008 #2

    Hootenanny

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    HINT: Can you use the given equation to calculate the change in volume from the change in temperature?
     
  4. Apr 27, 2008 #3
    Then I get V1=7165.9J/P and V2=7414.6J/P. can I use those as the limits of Integration?
     
  5. Apr 27, 2008 #4

    Hootenanny

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    I would say so :smile:
     
  6. Apr 27, 2008 #5
    what do I do with the T and T^2 parts of the pressure equation?
     
  7. Apr 27, 2008 #6

    Hootenanny

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    Notice that when you substitute the limits in, the expressions for pressure cancel.
     
  8. Apr 27, 2008 #7
    I think i am doing somthing wrong. I integrate the equation p = (24.9 J/K) T/V - (0.00662 J/K2)T^2/V right? so what do I do with the T and T^2? Would I treat them as a constant during integration?
     
  9. Apr 27, 2008 #8

    HallsofIvy

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    No, T is not constant. You know that
    p = (24.9 J/K) T/V - (0.00662 J/K2)T^2/V
    with P constant. That is the same as
    V = (24.9 J/K) T/P - (0.00662 J/K2)T^2/P

    dV= [(24.9 J/K)/V - (0.00662 J/K2)(2T)/V]dT

    and you can do the entire integral in terms of T.
     
  10. Apr 27, 2008 #9
    how did you get p to cancel out?
     
  11. Apr 27, 2008 #10

    Hootenanny

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    'Cancel out' was a poor phrase to use. I should have said 'change of variable', it's been a long day :zzz:
     
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