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Carnot cycle, fundamental equation of ideal gas

  1. Apr 24, 2012 #1

    fluidistic

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    1. The problem statement, all variables and given/known data
    Assuming that the auxiliary system in the Carnot cycle is a monoatomic ideal gas whose fundamental equation is [itex]S=\frac{NS_0}{N_0} +NR \ln \left [ \left ( \frac{U}{U_0} \right ) ^{3/2} \left ( \frac{V}{V_0} \right ) \left ( \frac{N}{N_0} \right ) ^{-5/2} \right ][/itex].
    1)Find the adiabats in a diagram T-V.
    2)Sketch a P-V diagram of the cycle.
    3)Describe the operation of a cycle as a refrigerator.
    4)Describe the functionning of a Carnot cycle as a heat pump.

    2. Relevant equations
    [itex]dS=0[/itex].


    3. The attempt at a solution
    For 1) my strategy is to first use [itex]dS=0= \frac{\partial S} {\partial N}dN+\frac{\partial S} {\partial U}dU+\frac{\partial S} {\partial V}dV [/itex] then isolate V in function of T. But after having done all the derivatives, the remaining equation is still quite complicated.
    Oh wait... there's no variable "T" inside it. Maybe I should get T as [itex]\frac{1}{\frac{\partial S }{\partial U}}[/itex]? Then I consider all variables but "V" as constants? And then graph that function?


    Edit: This cannot be, I get [itex]T=\frac{2U}{3NR}[/itex] that way. Absolutely no dependence between T and V...
     
  2. jcsd
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