Gibbs’ Paradox

J. Willard Gibbs

How wonderful that we have met with a paradox. Now we have some hope of making progress.

Niels Bohr


The Gibbs Paradox is one of the topics I discussed in my Finland Lectures as an example of problems that never went away. The paradox was, around 1875, discovered by Gibbs himself, who also proposed a solution. The latest paper I know of claiming a resolution was published in 2014[1] Read more

Another Carnot Mystery

On two occasions I have been asked, “Pray, Mr. Babbage, if you put into the machine wrong figures, will the right answers come out?” I am not able rightly to apprehend the kind of confusion of ideas that could provoke such a question.

Charles Babbage.

I learned about the Carnot cycle and its consequences teaching thermodynamics. Conscientiously following the textbooks, mainly because as teachers we are no longer allowed to deviate from them in order not to confuse the students. After a number of years I thought I had finally figured out the use and beauty of this cycle to introduce concepts like efficiency and entropy. Almost all textbooks follow the same ritual: introduce the cycle, “prove” how all reversible cycles must have the same efficiency regardless of working substance, and calculate the efficiency using the ideal classical gas isotherms and adiabats. Then finish the exercise by showing that if you integrate heat divided by temperature over the path of the cycle you get zero, and conclude that there is a state quantity, to be called entropy. Then make some remarks about irreversibility and Clausius, and continue on to the next topic. And I like to think that after a few years I could follow that ritual fairly well. Not that I was impressed by the level of student understanding come exam time, but hell, it is thermodynamics, nobody understands that. Fortunately the powers that be, and a lack of others wanting to teach something as arcane and useless as thermodynamics, left me in a position to yearly try to increase my knowledge and understanding of the field.

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Carnot’s Reversible Engine

In bodies employed to realize the motive power of heat there should not occur any change of temperature that may not be due to a change of volume.

Sadi Carnot

Steam engines were very complicated machines by the time Carnot started thinking about their efficiency. More than a century of technological advance had already gone by. He was able to abstract the essentials, and with outdated knowledge, even in his time, derived an expression for the maximum efficiency that we still teach and use today. In the mean time he also laid the ground work for the concept of entropy and the second law of thermodynamics. It is somewhat of a mystery to me how that was possible with all the mistakes he made, and misconceptions he had.

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Debunking Jennings

S happens

Bumper sticker

In 2002 Jennings and coworkers wrote a paper [1] in which they claimed that photosynthesis is more efficient than a Carnot heat engine running between the same temperatures. In fact, their final sentence reads: “Thus, \(1-T/T_r\) represents a kind of efficiency horizon beyond which negative entropy is produced and the second law is not obeyed. As this is impossible for a heat machine, it serves to underline the difference between photosynthetic photochemistry and a heat machine.”

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Intelligent Design

De bewust verkeerde weergave van de betekenis van de tweede hoofdwet door creationisten en andere voorstanders van het zogenaamde intelligent design.
The Flying Spagetti Monster

Je hoeft als wetenschapper maar kort in het gezelschap van christelijke gelovigen te verkeren om te horen te krijgen dat evolutie niet kan omdat dat volgens de tweede hoofdwet onmogelijk is. Wat naast de triomfantelijke toon waarmee dat te berde wordt gebracht -Ja, jullie wetenschappers kunnen wel van alles bedenken maar wij gelovigen doorzien zo waar het ene het andere tegenspreekt- nog het meeste irriteert is dat niemand van diegenen die dit beweren kennelijk de moeite heeft genomen om deze wet te bestuderen.  Nu heerst er natuurlijk in die kringen een groot geloof in autoriteit, en men meent misschien dat hun religieuze leiders die moeite wel hebben genomen. Maar daarvan heb ik eerlijk gezegd nooit enig spoor gezien. Die leiders lijken meer bezig met het verdoezelen van de tegenstrijdigheden in hun eigen heilige teksten, en het verketteren van diegenen die het ware woord verkeerd interpreteren, dan met de studie van de wetten van de natuurkunde die door het denkend deel der mensheid zijn ontdekt. Niet door het bestuderen van duizenden jaren oude overgeleverde teksten, maar door het zorgvuldig en kritisch beschrijven en analyseren van verschijnselen die iedereen vandaag om zich heen kan zien. Read more