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Homework Help: Thermodynamics maximum and minimum temperatures

  1. Sep 27, 2005 #1

    asdf1

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    In the following question,

    "two moles of an ideal gas, in an initial state P=10 atm, V=5 liters, are taken reversibly in a clockwise direction around a circular path given by (V-10)^2 + (P-10)^2 =25. Calculate the amount of work done by the gas as a result of the process, and calculate the maximum and minimum temperatures attained by the gas during the cycle."

    how do you find the max/min temperatures? at first, i thought of trying to take the first derivative of the path, but the results are weird...
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    asdf1, Sep 27, 2005
  2. jcsd
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  3. Sep 27, 2005 #2

    HallsofIvy

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    The graph of (V-10)2+ (P-10)2= 25 is a circle, in the PV-plane, with center at (10,10) and radius 5. Since PV= NRT, T= PV/NR. Maximum temperature occurs on that circle where PV is a maximum, Minimum Temperature where PV is a minimum. It should be clear where that occurs from the graph. If not, maximize (and minimize) PV with the constraint (V-10)2+ (P-10)2= 25 (Lagrange Multiplier method probably is best).
     
    HallsofIvy, Sep 27, 2005
  4. Sep 27, 2005 #3

    asdf1

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    during a discussion with a classmate, he suggested to draw a 45 degree angle line through the origin... but why?
     
    asdf1, Sep 27, 2005
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