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## Homework Statement

Two identical tanks of water are at absolute temperatures ##T_A## and ##T_B## respectively, where ##T_{A} > T_{B}##. The tanks each have a heat capacity ##C##, and they are thermally isolated from their environment. Suppose that a heat engine is installed in contact with the two tanks, in order to extract useful work from their temperature difference.

(a) Suppose that the engine is completely inefficient and generates no work. What will be the final temperature ##T_{f}## of the tanks at equilibrium?

(b) Suppose instead that the engine is the most efficient engine possible. What will be the final temperature ##T_{f}## of the tanks at equilibrium?

(c) How much work will have been generated by the efficient engine of part (b)?

## Homework Equations

## The Attempt at a Solution

(a) If the engine is completely inefficient and generates no work, then heat energy is being transferred from the hot tank with temperature ##T_A## to the cold tank with temperature ##T_B##. The tanks are identical, so each of them have the same mass ##m##. Therefore,

##mC(T_{A}-T_{f})=mC(T_{f}-T_{B})##

##\implies T_{f}=\frac{T_{A}+T_{B}}{2}##

Am I correct so far?