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Unformatted text preview: Lecture 29 — Limits to e ffi ciency. Now one might expect that there should be some limitations on the e ffi ciency of a Carnot engine, beyond the constraints of conservation of energy. For example, you might or might not be persuaded that the following is true: It is impossible to convert heat to work with perfect e ffi ciency, that is, with Q l = 0. This statement is called the Kelvin formulation of the second law of thermodynamics. If you are not persuaded that this postulate is an always-true statement about the world, you probably will be persuaded by the following statement: It is impossible for heat to flow from a cold object to a hot object spontaneously, i.e., without any work being done. This statement is called the Clausius formulation of the second law. The reason for the qualification “spontaneously”, is the existence of heat pumps; if we do work, we can pump heat from a cold place to a hot place. Remarkably, these statements are equivalent — one implies the other. We now prove this by using the Carnot cycle. First, assume that Kelvin was wrong; that is, suppose we could have a heat engine with no heat exhaust, Q l = 0, and hence W =- Q h . Then (see Fig. 4) we could couple this....
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This note was uploaded on 04/01/2008 for the course CHE 220 taught by Professor Prof.marannas during the Spring '08 term at Penn State.
- Spring '08