Entropy Is Not a Measure of Disorder

This post is part of a series, Nonsense and the Second Law of Thermodynamics.  The previous post is entitled:  What the Second Law Does Say.

Entropy is not a measure of disorder.  Entropy is not a measure of disorder.

To paraphrase Stanford  Professor H.C. Anderson, there are a lot of sentences in the English language that contain the words "entropy" and "disorder," and most of them are wrong.  There are many reputable text books and sources that say that entropy is disorder; nevertheless, entropy is not a measure of disorder.

Part of the problem is that "entropy" is a precisely defined term, whereas "disorder" is not.  It is possible to circumvent this problem by simply defining disorder to be nothing other than entropy.  Doing so, would make many of these sentences technically correct by making them tautologies, but it would also deprive the English language of a perfectly good word.

There are cases in thermodynamics, in which the entropy of a system is larger in a state that would be considered more orderly in common parlance.

Entropy is not disorder, not a measure of chaos, not a driving force. Energy's diffusion or dispersal to more microstates is the driving force in chemistry. Entropy is the measure or index of that dispersal. (Source.)

A common example of a case, in which, entropy defies the common notion of disorder is the freezing process of a hard sphere, fluid.  The solid, close-packed state is more ordered than the chaotic fluid state, yet it has higher entropy under some conditions!  In fact freezing in such fluids is entropy driven. 

To understand entropy, from a macroscopic point of view, it is necessary to understand something called a reversible process. The next few posts start the explanation of entropy from a macroscopic thermodynamic perspective. The next post is entitled: Reversible Processes.

Sources

• Atkins, P. W. Physical Chemistry, W. H. Freeman and Company, New York, 3rd edition, 1986
• McQuarrie, Donal d A., Statistical Thermodynamics,  University Science Books, Mill Valley, CA, 1973 
• Bromberg, J. Philip, Physical Chemistry, Allan and Bacon, Inc., Boston, 2nd Edition, 1984
• Anderson, H.C., Stanford University, Lectures on Statistical Thermodynamics, ca. 1990.
• Laird,  Brian B. , J. Chem. Educ., 1999, 76 (10), p 1388, Entropy, Disorder, and Freezing
• Lambert, Frank L., J. Chem. Educ., 2002, 79 (2), p 187,  Disorder - A Cracked Crutch for Supporting Entropy Discussions
• Thompson, Tim, the Definitions of Entropy 

Contents

1. Introduction
2. What the Second Law Does Not Say
3. What the Second Law Does Say
4. Entropy is Not a Measure of Disorder
5. Reversible Processes
6. The Carnot Cycle
7. The Definition of Entropy
8. Perpetual Motion
9. The Hydrogen Economy
10. Heat Can Be Transferred From a Cold Body to a Hot Body: The Air Conditioner
11. The Second Law and Swamp Coolers
12. Entropy and Statistical Thermodynamics
13. Fluctuations
14. Partition Functions
15. Entropy and Information Theory
16. The Second Law and Creationism
17. Entropy as Religious, Spiritual, or Self-Help Metaphor
18. Free Energy
19. Spontaneous Change and Equilibrium
20. The Second Law, Radiative Transfer, and Global Warming
21. The Second Law, Microscopic Reversibility, and Small Systems
22. The Arrow of Time
23. The Heat Death of the Universe
24. Gravity and Entropy
25. The Second Law and Nietzsche's Eternal Recurrence
26. Conclusion