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## Homework Statement

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)

## Homework Equations

Qin = Wout + Qout

mc(Th-Tf) = Wout + mc(Tf -Tc)

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

## 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 :)