Heat engine and efficiency

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1. Feb 27, 2017

danyull

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. Feb 27, 2017

kuruman

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