Alternative Approach - The Clausis Inequality

Note: If you are not familar with derivatives you may wish to skip this section.

Introduction

The above development of the second law is based on intuition. It is a good approach to understanding the law, but it does not allow us to make any calculations.

So we will look at another approach. It puts the second law in the form of a mathematical postulate.

Second Law Postulate

The postulate has four parts:

1. There exists an extensive, additive property called ENTROPY.
2. The entropy can be divided into two parts:
   1. An external part due to heat transfer with the surroundings
   2. An internal part due to irreversibilities within the system
3. The internal part is zero for reversible changes and positive for irreversible changes
4. The external part (dS_e) is related to heat by

[math]dS_e=\frac{dQ}{T}[/math]

where T is always positive

Clausis Inequality

The entropy is therefore the sum of the internal and external parts: [math]dS=dS_e+dS_i[/math] where dS_e is given above and since dS_i is either zero or positive according to the number 3 in the postulate.

Therefore,

[math]dS\geq\frac{dQ}{T}[/math]

This is called the CLAUSIS INEQUALITY.

The Clausis inequality is the probably the most important equation in thermodynamics.

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