Three identical bodies of constant thermal capacity are at temperatures 300 K, 300 K, and 100 K. If no work or heat is supplied from outside, what is the highest temperature to which any one of these bodies can be raised by the operation of heat engines? If you set this problem up correctly you may have to solve a cubic equation. This looks hard to solve but in fact you can deduce one of the roots [Hint: what is the highest temperature of the bodies if you do nothing to connect them?].