# Does a Carnot-efficient heat engine recover all work that was initially done?

There are two adiabatic containers filled with an ideal gas. In container A work is done which eventually turns completely into heat, leading to a temperature difference between container A and container B. Does a Carnot-efficient heat engine between the containers recover all the work that was initially done in container A?

• It doesn't turn into heat. It turns into internal energy. The heat exchanged with the surroundings is zero in an adiabatic change. – Chet Miller Oct 7 '17 at 12:27

Since it is a cycle, the Carnot cycle requires both heating and cooling. Since cooling is the loss of internal energy, and not through work, some of the energy added by heating container A is not converted to work. The portion of the heating energy which is converted to work is called the efficiency of the cycle. For a Carnot cycle, it is given by $\eta = 1 - T_L / T_H$ (wikipedia). Unless $T_L = 0$, your engine will have to cool down and lose some of its energy thermally.