Question

In the , we showed that if the Clausius statement is false, the Kelvin statement must also be false. Now show the reverse, such that if the Kelvin statement is false, it follows that the Clausius statement is false.

a) True
b) False

Answer 1

The Kelvin and Clausius statements are equivalent in expressing the second law of thermodynamics. If the Kelvin statement is false, it implies that a perfect heat engine exists, which leads to the conclusion that the Clausius statement must also be false due to their interrelated nature.

Step-by-step explanation:

To demonstrate the equivalence of the Kelvin and Clausius statements of the second law of thermodynamics, let's consider the Kelvin statement is false. This implies that a heat engine can convert all heat extracted from a heat source into work with no other effect, such as heat transfer to a cooler reservoir.

If we combine this hypothetical perfect heat engine with a real refrigerator, which requires work to transfer heat from a cool to a hot reservoir, the refrigerator's work requirement is offset by the engine's work output, meaning the overall system doesn't need any external energy input to transfer heat from cold to hot. This contravenes the Clausius statement, which asserts that heat cannot spontaneously flow from a colder to a hotter body without external work. Therefore, negating the Kelvin statement inherently means the Clausius statement is also negated, showing their interdependence.