Entropy: Origin of the Second Law of Thermodynamics

How did Clausius create entropy and why? I read his original papers to follow how possibly the most confusing concept in Classical Physics was created.

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Some references:

“to cast the theory of Carnot overboard…” Clausius, R “First Memoir” (1850) The Mechanical Theory of Heat (1867) p. 17
In August, 1850 Rankine wrote to William Thomson thanking him for “calling my attention to the paper by Clausius … I approve of your suggestion to send a copy of my paper either to Clausius or Poggendorff” Found in Smith, Crosbie Energy and Empire: A Biographical Study of Lord Kelvin (1989) p. 320
“There is no doubt that Clausius…” Truesdell, C The Tragicomical History of Thermodynamics (2013) p. 204
“…[Clausius’s] hypothesis is so mixed…” Found in Smith, Crosbie Energy and Empire: A Biographical Study of Lord Kelvin (1989) p. 343
“rare modesty “ Robert Clausius “Obituary Notices of Fellows Deceased” Proc. Royal Society of London Vol. 48 (Dec 31, 1891) p. 292-3
“this form…. is incomplete…” Clausius, R “Fourth Memoir” (1854) The Mechanical Theory of Heat (1867) p. 111
“simply the absolute temperature…” Clausius, R “Fourth Memoir” (1854) The Mechanical Theory of Heat (1867) p. 135
“the algebraic sum of all…” Clausius, R “Fourth Memoir” (1854) The Mechanical Theory of Heat (1867) p. 133
“Heat cannot by itself…” Clausius, R “Fourth Memoir” (1854) The Mechanical Theory of Heat (1867) p. 117
“the disgregration is not accompanied …” Clausius, R “Sixth Memoir” (1862) The Mechanical Theory of Heat (1867) p. 222
“a general property of… transformations …” Clausius, R “Sixth Memoir” (1862) The Mechanical Theory of Heat (1867) p. 244
“the algebraic sum of all the transformations…” Clausius, R “Sixth Memoir” (1862) The Mechanical Theory of Heat (1867) p. 247
“it may be proved to be impossible practically to arrive at the absolute zero…” Clausius, R “Sixth Memoir” (1862) The Mechanical Theory of Heat (1867) p. 250
“bring the second fundamental theorem…” Clausius, R “Ninth Memoir” (1865) The Mechanical Theory of Heat (1867) p. 327
“intentionally formed the word entropy…” Clausius, R “Ninth Memoir” (1865) The Mechanical Theory of Heat (1867) p. 357
“1. The energy of the universe is constant. 2. The entropy …” Clausius, R “Ninth Memoir” (1865) The Mechanical Theory of Heat (1867) p. 365
“waste of mechanical energy available to man …” Thomson, W “On a Universal Tendency in Nature to the Dissipation of Mechanical Energy” The Philosophical Magazine Vol. 4 No. iv (1852) p. 304
“the second great law of thermodynamics…” Thomson, W “On the Age of the Sun’s Heat” Macmillan’s Magazine vo. 5 (March 5, 1862). P. 388
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[itsevilbert]

I'm just leaving a comment to bump your rank, because far more people need to see your videos.

[DickHoskins]

I have a PhD in chemical physics, decades ago, retrained as an epidemiologist, now retired. And I am cycling back to physics and having so much fun with your videos. I think more teaching of science from a historical perspective would enhance understanding and definitely enhance retention. All of us scientists stand on the shoulders of giants and those of lesser contributors, but both need to be recognized and studied as to how they came up with all this stuff. Thank you for making these wonderful videos.

[artdonovandesign]

There are tens of thousands of science and physics channels on this platform.

However, none so concise, so informative and so enjoyably understandable as Professor Kathy's. This level of intellectual clarity in all things 'physics' is a rare treasure.

[vickash]

I’ve studied physics for so many years on my own, this is probably the best channel i’ve come across. I cherish your work Kathy.

[vishank]

Physics, when taught along how it came to be the way it is, becomes one of the most beautiful things in the world! Love this video, ma'am. Amazing work!💎💎

[robertharvey]

When i was teaching thermodynamics I explained entropy as a measure of the quality of heat and gave an example of pouring a cup of hot water into a tub of cold water. The heat had not gone anywhere, but its value or quality had been reduced as its entropy increased.

[antonyjohnson]

Entropy is without doubt one of the most amazing facets of Physics, and your explanation of the history of its discovery is fascinating and very well researched.

[sjpbrooklyn]

Every physical chemistry student learns the three laws of thermodynamics in the first week: of class 1: You can't win. 2: You can't break even. 3. You can't get out of the game. Thank you for a truly delightful tour of some of the most interesting and important aspects of the discovery and articulation of some of our most basic physical laws. Many years ago I was taught the Carnot cycle and phenomenological differential equations of entropy as an undergraduate. It wasn't until graduate school that I was introduced to statistical mechanics, canonical ensembles, and partition functions. It was all a very satisfying theoretical unification of macroscopic and microscopic behavior of molecules, but the macroscopic equations were much more useful in the laboratory, especially delta S = integral of heat capacity/T x dT. We used a scanning calorimeter to measure heat capacity as a function of temperature during a solid-solid phase transition in certain polymer crystals, and were able to determine the entropy change between the two solid states, which we could also predict from molecular energy models.

[mskEduTech]

I m a professor in mechanical & I see your videos for better explanation to my students. Good work done by u.

[jlmassir]

I just want to say that the clarity of your exposition and the correct stress on the important conceptual parts reveal how deep is your understanding of physics. Everybody has something to learn from your videos, from high school students to professors.

[David_Lee]

Thanks for this! Even with a master’s in mechanical engineering, this is one of the best explanations I’ve ever heard.

[FranFerioli]

Excellent. As an engineer, through college, I was taught thermodynamics in the language of Kelvin and Clausius (it was long time ago, but not nearly in the 19th Century). I never fully grasped it until in grad school I picked up a book someone left in the lab. It was titled Something-Something Statistical Mechanics and it was a revelation!

[alphasaith]

A miracle. Something on the internet that CLEARLY explains the second law of thermodynamics (and gives a history lesson). Find a way to stick some Jake Chudnow music in the background and you got something I could watch for eternity.

[edwinrg]

Brilliant video! I'm a PhD student in Chemical engineering and I think you are the very first person on YouTube or any University I've even being (already 3), or even any book I've ever read who finally does a video with the correct interpretation of Clausius ideas.


I absolutely agree with you, this ideas cannot be fully understood without the historical background of the different scientist who participated on this revolution.


I wish with all my heart you could make a video explaining the second and first law combined. Where they finally concluded entropy is the conjugated variable of the temperature. I think every book has the mathematical derivation starting with dS= dQrev/T, dU = dQ + dW and dW=PdV to finally arrive with dU = T dS + PdV. However I think there is a lack of the fundamental understanding. I think somehow Clausius was thinking in the idea of disgregation and how by knowing the disgregation we could then know the temperature and vice versa.


As you mentioned this idea of disgregation is connected with the position of the particles (the possible positions) which is also connected with the Boltzmann equation.


I think this is all beautifully connected and I hope you can make a video talking about it =D


Thanks for your video. Great Job!!! Looking forward to see more of your content!

[johnward]

Another really good post. I think a historical perspective is valuable because to understand the answer you first have to understand the question. Indeed a correctly framed question is the necessary prelude to getting an answer to it. History gives us some, at least, of this element; plus of course the human interest. Other physics channels use this to some extent (Yong Zhong, Alexander Unzicker, Pierre Robitaile, all well worth checking out) but you Kathy are a master of this technique.

[tonyduncan]

Having been magnificently click-baited previously, now I'm greatly fascinated, and looking forward to more of your work. How much easier it would have been to learn this stuff, which I did, as a schoolboy/student in the late 50s/early 60s if the teachers/lecturers had also related the wonderful stories behind these discoveries. It makes a whole lot of difference. Thanks. PS Clausius never got a mention when I was 'taught' Thermodynamics. Or maybe I forgot.

[robertsalazar]

I love your term 'messyness' for entropy. Never in a million years would I have made that connection.
However, I did teach my daughters that most games we played were high entropy to low entropy games. My PHd microbiology daughter knows now what that means.
I've listen to many of your talks. Outstanding!

[mnhklgn]

Without question the finest history of thermo lesson I have ever witnessed. Add to that the *absolute clearest* explanation of the derivation and description of the 2nd Law. I will be looking for and using your videos in my Physics classes for sure!

[DarkStar-ospv]

Just discovered your channel a couple of days ago. I find your presentations both enlightening and engaging! I'm a frustrated former physics students from the mid 70's who had that pursuit close when it was discovered I have dyscalculia. So much for my dreams of being a working astronomer! However, throughout my life I've tried to keep as current as possible with both fields. I've always enjoyed rich science programs that respect the intelligence of the audience. Keep up the excellent work!

[jaewokG]

"how Boltzman got credit for an equation and a constant … _next time!"_ is the nerdiest cliffhanger ever. thankfully, I'm watching this 2 years in the future and won't have to wait.