As a young man I tried to read thermodynamics, but I always came up against entropy as a brick wall that stopped any further progress.  – James Swinburne (1904) [1]

The second law of thermodynamics, which is known also as the law of the dissipation or degradation of energy, or the law of the increase of entropy, was developed almost simultaneously with the first law through the fundamental work of Carnot, Clausius and Kelvin.  But it met with a different fate, for it seemed in no recognizable way to accord with existing thought and prejudice.  The various laws of conservation had been foreshadowed long before their acceptance into the body of scientific thought.  The second law came as a new thing, alien to traditional thought, with far-reaching implications in general cosmology.  Because the second law seemed alien to the intuition, and even abhorrent to the philosophy of the times, many attempts were made to find exceptions to this law, and thus to disprove its universal validity.  But such attempts have served rather to convince the incredulous, and to establish the second law of thermodynamics as one of the foundations of modern science.

– Lewis and Randall (1923) [2]

In previous posts (here, here, and here) I suggested that Gibbs’ work moved fast through the scientific community. That wasn’t entirely accurate.  His work met with resistance for several reasons, starting with the high-density of his writing, his high-intensity mathematics, which most chemists weren’t prepared to handle, and finally the fact that the 2^nd Law of Thermodynamics was still confusing to many.  Wrote Kragh [3], the 2^nd Law appeared “in as many forms as there are writers” as manifested by the different versions proposed by Carnot, Joule, Thomson, Rankine, and Clausius.  While many of these forms were “primitive”[4] to the ultimate form involving entropy, this wasn’t known then.  And even if it had been known, it wouldn’t necessarily have helped.  Which brings us to the last reason for the resistance.  The addition of entropy to the 2^nd Law only made the confusing more confusing.  Most if not all didn’t even know what entropy was and to place such a “ghostly quantity”[5] at the center of a body of work did not help in gaining the work’s acceptance, especially in the chemist community.  In a way, this unwelcomed and ungrasped outsider was forced upon them. 

The rise of physical chemistry

Even though Gibbs embraced entropy as a means to understand chemistry, and indeed was arguably the first to give entropy prominent status in this field, he himself was not a chemist.  He along with Helmholtz, a self-proclaimed “physicist among chemists,”[6] were both outsiders.  Initially, his and later Helmholtz’s theories became situated between physics and chemistry in the new field of physical chemistry, which wasn’t a bad place to be as it afforded the physical chemists a certain comfort and freedom in a whole new field.  But such a situation could only last so long.  Soon the chemists realized the opportunities offered by physics and eventually adopted physical chemistry into their own now-larger world.

The rise of entropy

Entropy, as a newly discovered property of matter, would eventually overcome the barriers that rose against it.  It offered too much to be ignored.  It served as one of the critical building blocks of Gibbs’s work on equilibria and also facilitated the quantified analysis of irreversible change in chemistry. 

As the works of Gibbs and Helmholtz spread, many began to recognize that entropy, while not solely central, was still the final property of matter that enabled the first fundamental equation to be written (dU = TdS – PdV) and from which all chemical thermodynamics would follow.  Entropy completed the puzzle.  It was a property of matter that was directly linked to issues of mechanical, thermal, and chemical equilibrium, and while it was also a property that would eventually characterize chemical equilibrium using probabilistic arguments, what it meant in the late 1800s was irrelevant.  The only thing that was relevant was that it enabled completion of the path, based on primitive properties that chemists could work with, that led from an initial state to a final state.

Lewis & Randall (1923) – a classic thermodynamics textbook that embraced entropy

There was no specific date when entropy was fully accepted by the chemists.  It happened over time, in fits and starts, with its inclusion in the textbooks being the best measures of true acceptance.  But if one were forced to pick a date, the 1923 publication date of Gilbert Lewis and Merle Randall’s Thermodynamics would be as valid as any.  While Lewis and Randall focused on their own developments involving fugacity and activity, concepts which also took time to be accepted, they additionally spent considerable time and care to explain entropy and all of its implications, such as its role in the calculation of “free energy.” Such growing acceptance of entropy simply reflected its fundamental role in nature, not as a rule-of-thumb or an empirical correlation or a mathematical curiosity, but as a fundamental property of matter, just like temperature and pressure but for the unfortunate fact that it didn’t lend itself to either direct measurement or ready understanding.

The end of classical thermodynamics

This now brings us to the end of classical thermodynamics but not to the end our journey with entropy.  Classical thermodynamics worked perfectly, the equations all locked together in a mathematically precise way, all effectively deduced from the first (differentiated) fundamental equation of nature, Clausius’s dU = TdS – PdV.  One simply can not help but be awed by how much could be generated from such a singular starting point.

The start of statistical mechanics

While this new science rapidly grew and enabled great breakthroughs in science and industry, the curious couldn’t simply sit by and not ask, why?  The equations worked, yes, but why did they work?  What was happening at the molecular scale that explained why the equations worked and what they meant?  While the atomic theory had not yet achieved breakthrough, this didn’t stop the curious from thinking, well, I don’t know if atoms exist or not, but let’s assume they do exist.  Let’s create a mathematical model for such a system and see what it predicts.  If the predictions agree with nature, well then maybe our starting assumption was indeed correct.  And this is indeed what the curious did.  The mathematical density of the resulting work was very high.  But the results were amazing and in the end strongly supported the existence of atoms. 

What’s next?

The largest obstacle to entropy’s acceptance into the scientific community was undoubtedly the fact that no one knew what it meant when Clausius first introduced it, not even Clausius himself.  A few may have perceived what it meant.  But no one really knew.  As the road to understanding entropy necessarily leads through the world of probability and statistics, we now turn towards the final steps that got us there: Clausius and his development of the kinetic theory of gases, Maxwell and his inclusion of statistics in physics, and finally Boltzmann and his inclusion of probability theory in physics.  All of these efforts led to the rise of statistical mechanics, statistical thermodynamics, and the fundamental definition of entropy based on probability.

Learn more about the intersection of Gibbs and chemistry!

Learn more about the dissemination of Gibbs’s work into the world of chemistry in my book, Block by Block – The Historical and Theoretical Foundations of Thermodynamics.

References

[1] Swinburne cited in: Kragh, Helge, and Stephen J. Weininger. 1996. “Sooner Silence than Confusion: The Tortuous Entry of Entropy into Chemistry.” Historical Studies in the Physical and Biological Sciences 27 (1): 91–130. p. 121.

[2] Lewis, Gilbert Newton, and Merle Randall. 1923. Thermodynamics and the Free Energy of Chemical Species. New York: McGraw-Hill Book Company, Inc. p. 110.

[3] Kragh, 1996, p. 111.

[4] Hinshelwood quote in: Kragh, 1996, p. 129.

[5] Berry, Charles William. 1913. The Temperature-Entropy Diagram (3rd Edition). New York: John Wiley & Sons. p. ix.

[6] Kragh, Helge, 1993. “Between Physics and Chemistry: Helmholtz’s Route to a Theory of Chemical Thermodynamics.” In Hermann von Helmholtz and the Foundations of Nineteenth-Century Science, edited by David Cahan, 403–31. California Studies in the History of Science 12. Berkeley: University of California Press. p. 194.

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