## Conceptual Physics (12th Edition)

Published by Addison-Wesley

# Chapter 18 - Think and Discuss: 80

#### Answer

Mechanical energy can be wholly converted into thermal energy. For example, a moving book skidding to rest on the floor converts its KE into thermal energy. However, the second law of thermodynamics prohibits a given amount of thermal energy from being wholly converted to mechanical energy.

#### Work Step by Step

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.

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