Conceptual Physics (12th Edition)

Published by Addison-Wesley
ISBN 10: 0321909100
ISBN 13: 978-0-32190-910-7

Chapter 18 - Think and Explain: 59

Answer

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 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.
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