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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.

Lesson 6F: page 1 of 15

Previous LESSON

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.

Review of the Second Carnot Principle

2nd Carnot Principle

Ch6, Lesson F, Page 1 - Review of the Second Carnot Principle