Abusing Thermodynamics: Granville Sewell

This guy is a mathematician, indeed a Professor of Mathematics at the University of Texas, El Paso. Let us look at the abuse of thermodynamics by Granville Sewell:
http://www.math.utep.edu/Faculty/sewell/AML_3497.pdf

Here is an opening comment that seems to summarise his position:

Of course the whole idea of compensation, whether by distant or nearby events, makes no sense logically: an extremely improbable event is not rendered less improbable simply by the occurrence of ‘‘compensating’’ events elsewhere. According to this reasoning, the second law does not prevent scrap metal from reorganizing itself into a computer in one room, as long as two computers in the next room are rusting into scrap metal—and the door is open.1 (Or the thermal entropy in the next room is increasing, though I am not sure how fast it has to increase to compensate computer construction!)

There is all sorts of nonsense in there that you would think a university professor would know about.

Let us start with the first sentence, and think about a cup of coffee cooling. It starts high in entropy at 100°C, it ends up low in entropy at 20°C. The Second Law is maintained because the drop in entropy in the cup is "compensated" by the rise in entropy in the cups surroundings, as the heat is dissipated. Sewell declares that this common experience "makes no sense logically"! So right from the start we can see this guy is spouting nonsense.

He goes on to talk about probability. Probability lies at the heart of the second law. For the coffee cup, it is more probable that a chunk of heat energy will end up in the surroundings than in the cup, and when you are talking about unimaginably huge numbers of chunks of heat, that "probable" becomes a certainty - the cup will always cool down.

Sewell's understanding of this is woeful. He appears to think that the cup cooling is an improbable event, but that event is compensated by the heat going into the surrounds event. What he is missing is that it is all one process (it is like saying that running the tap is one event, and filling the bath is another; the reality is that this is one process).

Then Sewell considers computers, again showing a woeful misunderstanding of what the Second Law can do. All the Second Law says is that entropy must go up. It does not say that if entropy goes up then the process will happen - that would be nonsense. Think about the entropy in a cup and a telephone. The entropy must be higher in one of the other, and yet we do not see cups spontaneously change into telephones or vice versa. The Second Law can tell us what is impossible, it will not tell us what will happen. How can a university professor not know that?

He has to know that what he says is not true. The guy is lying.

Later he goes on to invent his own entropies:

However, there is really nothing special about ‘‘thermal’’ entropy. Heat conduction is just diffusion of heat, and we can define an ‘‘X-entropy’’ (and an X-order=-X-entropy), to measure the randomness in the distribution of any other substance X that diffuses; for example, we can let U(x, y, z, t) represent the concentration of carbon diffusing in a solid, and use Eq. (3) again to define this entropy (c? = 1 now, so Qt = Ut ), and repeat the analysis leading to Eq. (5), which now says that the ‘‘carbon order’’ cannot increase in a closed system.2

Let us say that X is water, and then look inside a freezer. There is water vapour in there, as the freezer is not turned on yet, spread out evenly throughout the compartment. Turn the freezer on (with the door closed, so this is a closed system as far as the water in concerned) and that water will turn to ice on the sides. It has gone from being spread out, to being concentrated on the sides. The water-entropy has decreased, disobeying Sewell's bastardisation of the Second Law!

Of course, the reality is that you cannot just make up new entropies and pretend they must be governed by the Second Law. Surely a university professor would know that? Surely a professor of mathematics has the brains to realise that sometimes things become concentrated?

Of course he does!