Thermodynamics - maximalization of temperature

[lakmus]

Homework Statement

We have three metal cubes, the same material, same size. Two cubes
have temerature 300K, third 100K.

On what maximal temperature can
we heat the on of the cubes?

The Attempt at a Solution

If we want to get higher temperature than 300K we need to
use the gradient of temperatures two cubes to get some work,
which we can after use to heating the third cube. I tried to place
ideal heat machine, which work on base of carnot cycle between
the two cubes (one 300K other 100K) - but I just have two temperatures
and on wiki is written, that to work from carnot cycle I need entrpy too.
So I don't know how to continue.

Thanks for any help.

 

[CWatters]

Can you post the exact wording of the question? Does the question allow you to use a heat pump or are they just expecting you to apply conservation of energy?

 

[lakmus]

I can use heat pump. If I understand well the energy conservation law, then
the maximal temperature is 300K, any other manipulation will just make
average (so maximal temperature in the system will be lower) of temperatures . . .