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Heat engine and efficiency

  1. Feb 27, 2017 #1
    1. The problem statement, all variables and given/known data
    Two identical bodies of constant heat capacity ##C_p## at temperatures ##T_1## and ##T_2## respectively are used as reservoirs for a heat engine. If the bodies remain at constant pressure, show that the amount of work obtainable is ##W = C_p (T_1 + T_2 − 2T_f)##, where ##T_f## is the final temperature attained by both bodies. Show that if the most efficient engine is used, then ##T_f^2 = T_1T_2##

    2. Relevant equations
    My professor's hint: "If the most efficient engine is used, then $$\frac{dQ_1}{T_1}+\frac{dQ_2}{T_2}=0."$$

    3. The attempt at a solution
    I was able to do the first part of the problem by using ##dW=dQ_h-dQ_l## and ##dQ=C_pdT.## I don't know where to start for the second part, and I don't understand how my professor's hint is supposed to be used. Any help would be appreciated, thanks!
     
  2. jcsd
  3. Feb 27, 2017 #2

    kuruman

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    Integrate your professor's hint and solve for Tf (upper limit).
     
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