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Another Thermo Question

  1. Feb 26, 2007 #1
    1. The problem statement, all variables and given/known data

    See Attachment



    3. The attempt at a solution


    Well to start off I know the gas is monatomic

    I can find the work done by finding the area under each curve/line:

    [tex]W_{AB} = p_0(2v_0-v_0) = p_0v_0[/tex]
    [tex]W_{CD} = (p_0/32)(8v_0-16v_0) = \frac{-p_0v_0}{4}[/tex]

    I cant think of how to find the area under the other two curves, im guessing integration but I dont know how to set it up.

    After I find these other to, what do I do?

    Thanks
     

    Attached Files:

  2. jcsd
  3. Feb 26, 2007 #2

    FredGarvin

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    Science Advisor

    I can't see the attachment yet, but finding the area between two curves is easy. The easiest way to do it is to subtract the area under the lower curve from the area under the upper curve.

    If you did it in one integral, you could set up the limits of integration from one curve to the other.
     
  4. Feb 26, 2007 #3
    [​IMG]
     
    Last edited: Feb 26, 2007
  5. Feb 26, 2007 #4
    for isentropic expansion and compression in ICEs we use the same principle u used to find the first 2 works.
    we use : W= (PoVo-PoVo/4)/(1-k) k=Cp/Cv. for isentropic adiabatic compression or expansion.

    How did u know the gas was monoatomic?
     
  6. Feb 27, 2007 #5

    Andrew Mason

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    Homework Helper

    Where do you get this? It works for BC but not DA

    Generally, for reversible adiabatic paths:

    (1) [tex]W = K\frac{V_f^{1-\gamma} - V_i^{1-\gamma}}{1-\gamma}[/tex]

    where [itex]K = PV^\gamma[/itex]

    This is just the integral [itex]\int dW[/itex] where [itex]dW = dU = PdV = KV^{-\gamma}dV [/itex] (dQ=0)

    Since for DA [itex]P_f = 32P_i[/itex] and [itex]V_f = V_i/8[/itex] the numerator in (1) is simply:

    [tex]P_fV_f - P_iV_i = 32P_iV_i/8 - P_iV_i = 3P_iV_i[/tex]

    for BC, [itex]P_f = P_i/32[/itex] and [itex]V_f = 8V_i[/itex] the numerator in (1) is simply:

    [tex]P_fV_f - P_iV_i = 8P_iV_i/32 - P_iV_i = -3P_iV_i/4[/tex]

    Apply the adiabatic condition [itex]PV^\gamma = constant[/itex] to one of the adiabatic paths and solve for [itex]\gamma[/itex].

    AM
     
    Last edited: Feb 27, 2007
  7. Feb 27, 2007 #6
    Thanks Andrew
     
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