## Conceptual Physics (12th Edition)

As discussed on page 345, Carnot's equation states that the ideal efficiency of a heat engine is $\frac{T_{hot} – T_{cold}}{T_{hot}}$. Mathematically speaking, the only way to achieve perfect conversion of heat to work, i.e., an efficiency of 100%, is when the temperature of the cold reservoir $T_{cold}$ is at absolute zero, 0 K. This is easier to see when Carnot's equation is re-written as $efficiency_{ideal} = 1 - \frac{T_{cold}}{T_{hot}}$. The third law of thermodynamics prohibits the cold reservoir from having a temperature of absolute zero, so no heat engine can be 100% efficient.