entropy

In second-semester college chemistry, just this year, I learned about the concept of entropy. Entropy, I was told, measures the tendency of a system to fall into disorder. And that’s probably what my instructor – a caring, competent, and well-educated person — thought correct, no doubt because that was what he himself learned as a college student. Entropy, we learned, is a measure of chaos.

This is a familiar concept, since culturally we speak of messiness (messy desks, messy rooms) as demonstrations of an increase in entropy.

I was completely fascinated by the concept of entropy, and had to learn more. I looked it up on the internet, and was most surprised by what I found. My teacher, along with generations of other scientists and educators, had been misled.

What we had all been taught (we students and my teacher as well) was wrong.  Thermodynamic entropy is not a measure of chaos. It is not a measure of the tendency of systems to fall into disorder and decay. The most current view of entropy states that entropy “measures the dispersal of energy: how much energy is spread out in a particular process, or how widely spread out it becomes.”

So how was the misconception of entropy as disorder born?

In the nineteenth century, the Austrian physicist Ludwig Boltzmann first described entropy as “disorder” in an attempt to aid the visualization of his theory of what molecules do spontaneously. Boltzmann’s innocent description is the foundation of a century of misunderstanding.

Why is a messy desk with towering to-do piles a poor example of an increase in entropy? Because towering to-do piles do not assemble themselves spontaneously, and entropy measures the spontaneous behavior of atoms and molecules. A change in entropy can be “disorderly” — a speeding car smashing into a brick wall — but entropy is not itself a measure of the increase in disorder. It’s a measure of energy spreading out, no matter how orderly or disorderly the fashion in which this happens.

Not all changes in entropy require an increase in “disorder.” When a heated chunk of metal radiates its heat into the surrounding environment, is that disorder? When you pour cream into coffee and the liquids spontaneously mix, is that disorder?

Boltzmann’s brilliant career shouldn’t be judged on this misstep, but nonetheless this piece of misinformation found its way into chemistry textbooks and classrooms everywhere.

Because textbook authors focused on Boltzmann’s good theory but still used his bad description, nearly every student in chemistry or physics in the last century has learned that entropy is disorder, or at least the tendency towards disorder. Boltzmann’s description stuck, and the misconception became part of chemistry classrooms for over a century.

But since 2002, when a retired chemistry professor questioned the error in a series of articles and saw his questioning take root in the educational community, the majority of new editions of General Chemistry texts have removed disorder in connection with entropy. Nowadays they use some variation on the idea that entropy measures the dispersal of energy.

Below are some changes in entropy represented as the dispersal of energy rather than the tendency to disorder (the following are adapted from the website Entropy Is Simple…):

hot pans cool off

water spontaneously flows down Niagara Falls

the air in a tire will blow out into the atmosphere if the tire’s walls are punctured

when gasoline is mixed with air in a car’s cylinders, it reacts with oxygen if a spark is introduced

So what’s a good simple definition of entropy? Think of entropy as a measure of the flow of energy to dispersal. More specifically, entropy is a measure, at a specific temperature, of all types of energy flows from the state of being localized to the state of being dispersed.

Here are some closing thoughts, again from Entropy Is Simple…:

Although order/disorder is still present in some elementary chemistry texts as a gimmick for guessing about entropy changes (and useful to experts in some areas of thermodynamics), it is both misleading and an anachronism for beginners in chemistry. It has been deleted from most first-year university chemistry textbooks in the U.S.In the humanities and popular literature, the repeated use of entropy in connection with “disorder” (in the multitude of its different common meanings) has caused enormous intellectual harm. Entropy has been thereby dissociated from the quintessential connection with its atomic/molecular energetic foundation.

The result is that a nineteenth century error about entropy’s meaning has been generally and mistakenly applied to disorderly parties, dysfunctional personal lives, and even disruptions in international events. This may make pages of metaphor but it is totally unrelated to thermodynamic entropy in physico-chemical science that actually does impact our lives. It is as ridiculous as talking about how Einstein’s relativity theory can be applied to a person’s undesirable relatives in Chicago.

For an overview of thermodynamic entropy and the fascinating Second Law of Thermodynamics, check out Entropy Is Simple….

Articles for students and educators on the subject of entropy can be found at entropysite.com.

Thanks to the Polish website ENTROPIA for the image that appears in this post.

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