# Alternative Approach - The Clausis Inequality

Thermodynamics | |
---|---|

Introduction | What is this thing called Thermodynamics??? | Definitions | Thermal Equilibrium and Zeroth Law | Limitations |

First Law | Work, Heat, Energy, and the First Law | Work, Heat, Energy, and the First Law (simplied) | Derivatives | Derivatives Exercise | Reversibility, Enthalpy, and Heat Capacity |

Second Law | Things to Think About | Observations and Second Law of Thermodynamics | Alternative Approach - the Clausis Inequality | Consequences of the Second Law | Consequences of the Second Law (simplified) | Carnot Principle - motivation and examples | Equivalence of Second Law Statements* |

Third Law | Third Law of Thermodynamics | Consequences of Third Law* |

Development of Thermodynamics | The Thermodynamic Network | Network Exercise | Equations of State | Thermochemistry |

* Optional Section |

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.^{[1]}^{[nb 1]}

## Second Law Postulate

The postulate has four parts:

- There exists an extensive, additive property called
**ENTROPY**. - The entropy can be divided into two parts:
- An external part due to heat transfer with the surroundings
- An internal part due to irreversibilities within the system

- The internal part is zero for reversible changes and positive for irreversible changes
- The external part (dS
_{e}) is related to heat by

- There exists an extensive, additive property called

[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.

## Note

- ↑ A postulate is a statement which is regarded as true

## Reference

- ↑ Adapted from Reid, Charles E. (1990) "Chemical Thermodynamics" Singapore:McGraw-Hill