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Homework Help: Carnot heat engine

  1. Mar 20, 2010 #1
    1. The problem statement, all variables and given/known data
    A heat pump takes heat from a hot resevoir and disipates heat to a cold one. Both resevoirs are equal mass and specific heat capacity. Show that as the heat engine does maximal work the final temp of the resevoirs = Tf = SQRT(TcTh)

    2. Relevant equations
    Qin = Wout + Qout
    mc(Th-Tf) = Wout + mc(Tf -Tc)

    Efficiency = Wout/Win = 1- (Qin/Qout)

    3. The attempt at a solution
    Well I know i somehow need to get TcTh^2 in order to get the solution so I used efficiecy as 1 for maximal work out but I also assumed no work in which means I'm dividing by 0! Or if I say 1= 1-Qin/Qout then Qout = 1-Qin and now im just confused. Help please :)
  2. jcsd
  3. Mar 20, 2010 #2


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    Homework Helper

    Remember from calculus how to find the maximum (or minimim) of a function?
  4. Mar 20, 2010 #3
    Are you meaning differentiate and set to 0 and then solve? Differentiate again and is D^2f(x)/Dx^2 < 0 then it's a maximum?
  5. Mar 20, 2010 #4


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    Yep, but you should only have to differentiate once. It should be pretty clear whether you have a max or min.
  6. Mar 20, 2010 #5
    Thank you, Which equation do I differentiate?
  7. Mar 20, 2010 #6
    Ooo right ok so I have dw/dQ_h = (T1-T2)/T1 = 0

    therefore T1-T2 = 0 so T1=T2=T and so

    dw/dQ_h = (T-T)/T which is 0 which doesnt help me :S
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