# What is the definition of entropy?

May 13, 2016

Entropy by definition is the degree of randomness or disorder (chaos) in a system.

#### Explanation:

Entropy by definition is the degree of randomness or disorder (chaos) in a system.

Here is a complete lessons about entropy, I hope you find it helpful.
Thermodynamics | Spontaneous Process & Entropy.

May 13, 2016

Entropy ($S$) is a measure of the number of ways the microstates in a system can arrange themselves to form a single observable macrostate.

That is, it is a quantity that describes the number of microscopic arrangement possibilities for a given system.

STATISTICAL MECHANICS DEFINITION

$\setminus m a t h b f \left(S = {k}_{B} \ln \Omega\right)$

where:

• $\Omega$ is the number of microstates that collectively generate the same macrostate (observable).
• ${k}_{B} = 1.3806 \times {10}^{- 23} \text{J/K}$ is the Boltzmann constant.

Take an ensemble (loosely-speaking, a group) of molecules that can be arranged in multiple ways. The more ways you can arrange them, the more "disordered" they are. This corresponds with a greater $\Omega$ giving a greater entropy $S$.

THERMODYNAMICS DEFINITION

A consistent thermodynamic definition of entropy is also:

$\setminus m a t h b f \left(\Delta S \ge \frac{q}{T}\right)$

(where ${q}_{\text{rev}}$ is reversible, i.e. efficient, heat flow, ${q}_{\text{irr}}$ is irreversible, inefficient heat flow, and ${q}_{\text{irr" < q_"rev}}$. Both ${q}_{\text{irr}}$ and ${q}_{\text{rev}}$ are contained in $q$.)

So another way you can think about it is that for a given temperature:

The more the heat that you put into the system affects the microscopic arrangement of molecules, the more "disordered" the system is.

GENERAL CHEMISTRY DEFINITION

This "disorder" is a definition of entropy you were introduced to in general chemistry, and is generalized to be greater for gases than for liquids, for instance.

Gases are more freely-moving than liquids, so gases can assume more microstates than the liquid phase of the same substance can. Thus, gases are more "disordered", and they have a higher entropy. 