Module 5 :
Lecture 19 : Carnot's Principles (Theorems)

Two consequences of the second law of thermodynamics are will known as Carnot's principles.

Principle I:

No heat engine operating between the two given thermal reservoirs, each of which is maintained at a constant temperature, can be more efficient than a reversible engine operating between the same two thermal reservoirs. Refer to Figure 19.1

Figure 19.1

Let two heat engines and operate between the given source at temperature and the given sink at temperature as shown.

Let be any heat engine and any reversible heat engine. We are to prove that the efficiency of is more than that of . Let us assume that it is not true . Let the rates of working of the engines be such that

 (19.1)

Since,

 (19.2)

Now let the direction of be reversed.

Figure 19.2

Refer to Figure 19.2. Since is a reversible heat engine, the magnitudes of heat and work quantities will remain the same, but their directions will be reversed as shown.

Since some part of (equal to ) may be fed to drive the reversed heat engine . Since, , the heat discharged by the reversed may be supplied to .

The source may, therefore, be eliminated. The net result is that and together constitute a heat engine which, operating in a cycle, produces net work , while exchanging heat with a single reservoir at .

This violates the Kelvin-Planck statement of the second law . Hence the assumption is wrong.

Therefore,

 (19.3)