# Review of the Second Carnot Principle

## 2nd Carnot Principle

:
All reversible power cycles operating between the same two thermal reservoirs have the same efficiency.

The thermal efficency of a reversible thermodynamic cycle:

• does not depend on the working fluid or its properties
• but only on the temperatures of the two thermal resevoirs.
We learned how to calculate η in Chapter 5:
Now, based on the 2nd Carnot Principle, we expect to find an equation that relates the thermal efficiency of a HE to the temperatures of the two reservoirs:
η = fxn( TH , TC )
We begin this lesson by determining the function that relates η to TC and TH.
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### Ch 6, Lesson F, Page 1 - Review of the Second Carnot Principle

• In the previous lesson, we learned that the efficiency of a reversible cycle, such as the Carnot Cycle, depends ONLY on TH and TC.
• But, wait a minute.  In chapter 5, we learned that the efficiency of ANY heat engine is 1 – QC / QH.
• That means that efficiency depends ONLY on QH and QC.
• Which is correct ?
• Well, BOTH statements are correct !
• And THAT presents us with an opportunity to dig a little deeper into the relationship between the Q’s and T’s associated with the reservoirs.
• This investigation will yield an important insight into the nature of absolute temperature scales.
• It will also yield a simple, elegant relationship between Carnot Efficiency and the reservoir temperatures.
• So, let’s start investigating.