Boltzmann's Entropy Equation: A History from Clausius to Planck

Boltzmann's entropy formula was created by Max Planck in 1900! So, why did Planck create this equation and how did it end up on Boltzmann's grave? I used primary sources to explain the history of this famous and confusing equation.
My Patreon Page (thanks!):
www.patreon.com/user?u=15291200
The music is from the awesome Kim Nalley of course www.KimNalley.com

[@thomassynths]

Correction: `log` is a transcendental function, not a trigonometric function. (Side note: all the trig funcs are transcendental.) Transcendental means that the function cannot be described by a polynomial.

[@Kathy_Loves_Physics]

Thank you for clarifying. I had never heard of the term transcendental functions (The problem of learning my math solely to help me with my physics). I wish I could fix my videos after publishing.

[@profjoshtan]

While this is true, one can, of course, derive the logarithm using only trigonometric functions via infinite series! :)

[@thomassynths]

@@profjoshtan Sure, but the same can be said about using infinite polynomials. So to be more pedantic, the addendum is "finite polynomial". (Can also talk about coefficients needing to be a "rational" field, such as real rationals, complex rationals, etc... but simplifying here for the non-mathies.)

[@thomassynths]

@Arthur Fair enough. I've yet to read Wildbergers Rational trig, though I'm a fan of his channel.

[@nasseemmuttur778]

@Arthur , interesting to follow your debate. Am no mathematician nor physicist but just have an inerest in physics among many other subjects. I never stop learning. Greetings from Mauritius.

[@family-accountemail9111]

We had to write an essay on the first and second laws, we had thought we were finished until we watched this now we can rewrite making it a lot clearer how the ideas evolved and correctly attributing them , you're very good at getting the information across and I thank you very much for your work. I will be watching more!

[@Kathy_Loves_Physics]

How do you like the video, sorry I made you do more work. I also videos on the origin of the first and second long as you might want to check them out as long as you’re changing things are ready and please tell me if I can help.

[@jackd.ripper7613]

Bassi. You are just friggin' awesome. The most underrated channel on KZbin.

[@Kathy_Loves_Physics]

Thanks - blushing now

[@Kathy_Loves_Physics]

Jack, I decided to start with the life of Planck as that got the most votes AND I am going to Bologna in June to study more about Laura Bassi's life so I will probably make the video about her in July. I wrote more about it (and her) on Patreon: www.patreon.com/posts/my-next-video-is-33502544

[@pieteruys2032]

As a student one of the subjects in my final undergraduate year was Statistical Mechanics. I was hugely impressed by the sheer brilliance of the reasoning involved. it is an intellectual tour de force. Thank you for presenting this history

[@sonarbangla8711]

Extremely beautifully and masterfully explained by Kathy. Why Plank's equation was engraved on Boltzmann's tomb stone is one of paying respect out of indebtedness on the part of Plank, perhaps saddened by the death of a great man and teacher. Kathy you video sounded like music to my ears. Thank you.

[@anonymous.youtuber]

Thanks for these very interesting stories. So often the historical context is missing from the teachings, which is a pity because it makes the study of science so much more colorful. It really struck me that the quantization concept emanated from kinetic gas theory, up until now I was made to believe it was only considered to explain the discrete character of spectral lines in relation to atomic theory. Your videos are so enlightening. Respect !

[@jamesboulger8705]

I worked very hard to understand the historical context because it helps tremendously if you write on these subjects.

[@MrHARRYGOODNIGHT]

The historical point of view also aids in the overall technical understanding of the subject. Kudos.

[@petematthews9346]

I had to laugh when I heard "…but we already have a Planck's constant." Reminds me of Euler-how many things are named for or attributed to him? My favorite comment about Euler was that all of the things attributed to Euler should be named for the second person to have discovered them. Anyway, thanks for the wonderful survey of the history of the Thermodynamic Laws.

[@ogbanugot6078]

This was so good. Please do Bohr's model and then Planck. But I'll probably watch all four if you do them.

[@Tom-sp3gy]

Please make a video on Edwin Hubble and George Lamaitre and how Mr Hubble didn’t believe in the Doppler effect explanation of redshift

[@profjoshtan]

From watching this, I have come to appreciate for the first time why we focus on Boltzmann's H-theorem in spite of it not quite doing what many physics teachers who teach it claim it does. In classes where the H-theorem is taught, it is often argued that it proves the second law of thermodynamics. A bit of judicious searching the internet will find all sorts of debunking of that claim and, indeed, it does not *quite* do such a thing. But it is weird that it is a topic, then, in so many statistical mechanics courses. Why this weird theorem that doesn't really have much practical application beyond its cute result? Well, one possible answer struck me when watching this video. This is the work that Planck identified as being the first invocation of the logarithm in relation to statistical mechanical properties. So it is an homage to primacy rather than anything truly fundamental. This is why I like this channel. In my physics education, I was taught superficial anecdotes about a lot of this history which gave almost hagiographic accounts of discovery and scientific advancement. Kathy approaches the subject from a much more contextual approach that uncovers some of the weirdness and arbitrariness that still infects our choice for approaching physics to this day. Thank you for this channel!

[@exwhyz33]

Your videos (all of them) are nothing short of fascinating, not least for the amount of work you put into finding the facts and their lineage - Thank you very much.

[@demeloalex]

Thank you! So clarifying! Your explanations shine like a sun in my mind! 🙏🙏🙏

[@lawrencedoliveiro9104]

4:42 Maxwell’s equations were derived very much from the experimental work of Michael Faraday. Faraday was a gifted experimenter, but he lacked the mathematical background (indeed, any kind of formal education) to make theoretical sense of his own empirical numbers.

[@jaybingham3711]

Adding even more issues of dubious attribution to the mix as today's referenced Maxwell equations are actually Heaviside-Hertz derived equations.

[@j.raimundosilva2101]

Your channel is great and unique!!! I just got here and i'm marveled with the context you put to scientific discovery and how people made the theories. Thanks and keep up this great work, it's not easy to find these informations. It would be good if you put your sources on the vídeo description for those willing to research on their own as well.

[@anjinsantaipan4393]

Love your videos explaining the history and especially all the interplays between the main characters. Well done and please keep it up!

[@wim0104]

Your work should be on the freshmen curriculum for every STEM course! I was lucky to have a physics and an optical physics instructor much like this, starting from the basics and open our eyes.

[@picksalot1]

Only recently discovered your videos. Been enjoying them. It's important to get the history right. Thanks

[@jakelabete7412]

Your 'lectures' are absolutely delightful.

[@dougieh9676]

Love Boltzmann ❤️❤️❤️ I’ve been obsessed with Thermodynamics for sometime now. It’s both fascinating and disturbing. Can’t get enough!!! RIP Ludwig!!! The world wasn’t ready for you in your time but your ideas are common knowledge now. More Thermodynamics pretty please. ❤️

[@9613ENKI]

thank you. this kind of historical context makes clearer even the math of thermodynamics. great video.

[@mariocanedo196]

A video on Bohr's model would be awesome!

[@Stafford674]

I have only just discovered your channel. It is awesome.

[@BrightBlueJim]

I find myself becoming deeply absorbed in your articles, with an ever-increasing enthusiasm. Keep it up - you are a gem.

[@jgboyer]

My sentiments exactly, Kathy is enlightening!

[@aletheia4581]

Wow! I've just discovered this channel. Amazing piece of history. Amazing piece of work by Kathy. I think it is important to understand the historical context of physics, which is often disregarded, as we pursue of the fundamental laws of nature.

[@Kathy_Loves_Physics]

Glad you liked it

[@stauffap]

I can't believe i've never seen your channel! I have loved videos about the history of scientific discoveries for years! This video especially was very interesting :)

[@bobbymcdingdong]

Ooooh Kathy, you are spoiling us! Another fantastic entropy video - many thanks!

[@Kathy_Loves_Physics]

Anything for you Robert

[@minioasislibrary5222]

Kathy, thanks for your interesting video ! this is awesome ! you explained the history that always skip in the class...

[@225rip]

You put so much energy into your videos.

[@SudaNIm103]

This was my favorite video of yours so far!

[@Richardj410]

I just found your channel. Thank Thank You. Oh my this is wonderful. Alas how could anyone give these a thumbs down.

[@bobvar72]

This was pretty awesome! Great history here. I always thought Boltzmann came up with it. My respect for Planck grows even further.

[@Mumbo_Jumbo69]

my respect grown h times

[@valipearuna6372]

I can clearly see the passion you have for physics... Keep up the good work Do some episodes on classical mechanics

[@chinaskarina698]

This is a great video!!! Thank you for sharing your knowledge! :D

[@vibratingstring]

This is so cool to hear. Like someone else said below, we learn all the science out of its original context. Really really interesting to learn the dynamic personal interplay that resulted in the seeming magic of modern physics.

[@codemant5224]

I love your videos soooo much! Great information and charming enthusiasm!!

[@Kathy_Loves_Physics]

Codeman T thanks.

[@swangleewatanakarn7701]

Love your video. Thank you for post it here.

[@skshum]

Kathy makes physics history fun to listen and learn. Thank you

[@enricolucarelli816]

Wow! From Spain, all my respect and gratitude. I always thought that the historical development of knowledge is an essential ingredient towards its comprehension. Your videos are amazing 👏👏👏👏

[@jesussanchezherrero5659]

Yo también

[@jhee0419]

Thanks a lot for posting this wonderful clip

[@klingeron5929]

These videos are incredibly interesting and unique, thank you

[@h2energynow]

Awesome loved all the illustrations.

[@JagdishCVyas]

Enlightning story on Boltzmann's constant. Thanks.

[@artdonovandesign]

That was an incredible and mesmerizing video! Thank you, Prof. and... What is that beautiful painting on the wall?

[@ericreiter1]

I love you Kathy. Curious of your references, sources.

[@martingrillo6956]

As I don't like Entropy that much, I cannot consider this episode the best of all the more than good ones you created. It's a bit too much content for a single video to me. Keep up adding your excellent work. Cheers

[@afowler13]

your channel is brilliant!

[@sherafgankhan9327]

Madam you are awesome. Ive been out of university since 1999, working as an electrical engineer now. Your videos make me go back in time and question what i have learned. In a good way! Thank you for your videos...

[@hansvetter8653]

Great story telling! Thank you!

[@Sandcat87]

Been on KZbin since 2007 and never bothered to subscribe to anyone but holy smokes, that was awesome! Do them all, I'll watch them all. Fantastic explanation of a side I'd never known before (read Louisa Gilder's Age of Entanglement, which picks up more or less where you leave off here). Fantastic! Thanks

[@Kathy_Loves_Physics]

Wow what a lovely compliment (and I guess I need to check out the Age of Enlightenment book)

[@a1m1i1r1g1a1l]

love your videos, show them to my students. thank you

[@Kathy_Loves_Physics]

a1m1i1r1g1a1l I’m so glad. What kind of classes may I ask?

[@afifakimih8823]

So all of those years we were wrong!! From today I will introduce students Boltzmann entropy equation is actually Planck Entropy equation. And Thanks to this channel, I learn many truth about Science!!

[@nassehk]

I really enjoy your videos. As a metallurgist these names and formula were my bread and butter at school but I never knew the history behind them. Thank you and please keep up the good word.

[@vibratingstring]

Exactly! Gibbs-Duhem equation, Boltzmann's constant, Carnot-Clausius theorem, Curie temperature, Debye tempurature, Maxwell-Boltzmann equation...Nernst heat theorem, Neumann-Kopp rule, Taylor's theorem, Schottky defect, Wulff plot...Poisson's ratio, Young's modulus---alll of them have stories--and many more!

[@speckofdust272]

Really great delivery that I greatly enjoyed ... more please 👍🙏👏🏻👏🏻👏🏻👏🏻👏🏻👏🏻

[@Kathy_Loves_Physics]

You got it!

[@ABCD_V]

Awesome ! Please keep making stuff like this ♥️

[@davidkleinthefamousp]

Ty for a great series

[@arleygutarra9776]

Absolutely delightful. Thank you very much for your thorough and comprehensive research. I'm currently self studying Statistical mechanics and the relationship between quantum mechanics and statistical mechanics often confused me (mainly because of the intercalation of them, I was unsure if what ideas and/or experimental results inspired the respective equations). Although this is not a university Lecture and you didn't explain the maths, trust me that you really helped me a lot in my studies.

[@Andres-is3lj]

best physics channel on youtube. Rare passion for thermodynamics right here

[@TheMrgoodmanners]

this channel is just awesome!

[@Kathy_Loves_Physics]

Thanks

[@Pedritox0953]

Wonderful video Kathy!

[@alphaomega1089]

1. Theorist. 2. Experimenter. 3. Mathematician. Try to be all three when calling yourself a scientist. Never imagined history could be used to learn anything. An underrated discipline.

[@shawnmulberry774]

I thought entropy was a word from long ago being repurposed but I looked and sure enough its first use was in 1867. Clausius wins an award for a cool name. We get to say this word all the time now.

[@Kathy_Loves_Physics]

Clausius wins for a lot of things. Grossly underrated scientist IMHO. (not really a humble opinion to be honest)

[@varahamihiragopu6667]

​@@Kathy_Loves_Physics We call them Newton's three laws of motion, even though the first law was known long before Newton. The laws of thermodynamics should properly be name Clausius' Laws. But perhaps his luck is similar to that of Antoine Lavoisier, after whom the Law of conservation of mass was originally named, but later removed

[@neuronerd5211]

Love, love, love! And your enthusiasm is also the best. I've always thought that physicists have the best sense of humor.:))

[@Kathy_Loves_Physics]

I often think we have the worst sense of humor but I may know too many physicists 🤣

[@michaelzumpano7318]

I’m so glad you don’t shy away from a little math.

[@jbflores01]

Fascinating!... as always! Finally found the source of why Quantum Mechanics was created!

[@manuelhe46]

I’m reading Schrödinger’s What is Life and this really helps the background

[@SustainableDreams]

Back after a PBS vid. Go get ‘’em Gal! Your narrative surpasses the pros! Thanks for being awesome!

[@Trp44]

The real joy you bring is not dependent on anything you say… you are electricity… I enjoy so much your grasp of truth

[@pedzsan]

A KZbin video titled "What is the Ultraviolet Catastrophe?" also talks about Plank and the problem first encountered with black body radiation and the concept that energy must be quantized.

[@PabloMayrgundter]

Bohr. Tho, I'd love to see Gibbs to have this taken to the modern era. He also influences the development of radio which might help with your upcoming vid on TV. Cheers! Great work :)

[@user-ym6gp2oz5p]

Wow very well explained!

[@Zamicol]

Another excellent video.

[@climbeverest]

Madam you are incredible!! I am loving all your videos, please before history of physics melts away, continue what you do please

[@Kathy_Loves_Physics]

Thank you so much I’m not worried about the history melting away as much as me melting but thanks for the nice comment

[@climbeverest]

@@Kathy_Loves_Physics please I am loving Dirac and the start of positron, if you find more, please, also debroglie, planck, anyone who lived on the cusp 19-20th century, after 50s I think physics became so complicated, thanks!

[@edwinrg5768]

Wooooow. I loved it! Amazing video!

[@Kathy_Loves_Physics]

Thank you so much!!

[@TenzinLundrup]

Thanks for this video. I shall now call k, Planck's first constant (usually attributed to Boltzmann). Planck not only introduced it but determined its value.

[@jonathanjackson7047]

Great videos. As a grad student, we would take courses in Statistical Mechanics and Thermodynamics without any of the historical background. It's very interesting to see the evolution of these ideas and how people were thinking about things. As an idea for a future video, I'd love to know how Newtonian mechanics progressed into Lagrangian and Hamiltonian mechanics. We use the later extensively, but I'm not at all sure of how they were formulated. They seem to pop up out of nowhere in Mechanics courses like magic.

[@rasmusfriberg5520]

Fantastic work on scientific history. You should actually write a book on all your insights of the scientific history. You just made me realize that Planck is an even greater scientist than i thought. It is also easier to understand why he came to the conclusion: "Science advances one funeral at the time"

[@billclinton6040]

I had to take statistical thermodynamics as an undergrad. It was one of the last courses I took long after I had studied thermodynamics from a non-statistical or classical point of view. The professor was really good and made what could've been a horribly confusing topic somewhat comprehensible. I always marveled at that class because despite its name, the class devoted a big chunk discussing quantum mechanics (we basically derived Schrodinger's Equation from statistical thermodynamics). So, in a bizarre twist, even though I was not a physics major, I have had at least an intro to quantum mechanics. And for what it is worth, that class was much easier than my class on electromagnetism. Anyway, perhaps it was explained (I don't recall though), but now I understand the link between statistical thermodynamics and quantum mechanics and Planck's role. Max Planck's name was mentioned all throughout that course, and I grew to marvel just how brilliant that man must have been. I still have my notes and textbook from that class (even though it has been decades) because many of the derivations we did were quite literally works of art. I too have struggled to understand entropy. I know this comment is way late, but I think a follow up to this video that includes Claude Shannon's thoughts on entropy is definitely in order.

[@timjohnson979]

Great video as always, Kathy. Please do all the videos you mentioned. The order is not important, just their stories.

[@Kathy_Loves_Physics]

Will do Tim. Don't know how long it will take me but I will definitely make all 4 videos.

[@ardecki7961]

You're doing amazing work. I really appreciate how much effort you're putting in these videos. As for the next topic I would prefer Bohr's theory, but other's ideas seem fine too.

[@Kathy_Loves_Physics]

Glad you liked it.

[@SineCatenis]

I only wish that your tutorials were around when I first learned thermodynamics three decades ago-your videos are so clear and the historical background is invaluable!🫡

[@diemilio]

OMG! My new favorite KZbin channel!

[@orialtman6176]

I want to hear you tell all of these stories! But if I have to choose, let's hear Bohr's Model. Your explanations of the history really gives my chemistry class the context it's missing to understand it.

[@Kathy_Loves_Physics]

I will get to all of them eventually - promise.

[@rienzitrento8397]

Do all of them . Really interesting thanks

[@macroman52]

Now try explaining Boltzmann's H-theorem, which (under certain assumptions of randomness) shows that a function H (related to entropy, as Planck agreed) always increases for a collection of molecules undergoing collisions. I understand it was controversial since it appeared at first to be based only on Newton's laws for collisions, which are time reversible, yet it gave an irreversible law. One of Lorentz's students, c1900, wrote a paper on this, trying to explain, for hard sphere collision dynamics, where the irreversibility comes from. As I remember it, that paper looked at how tiny changes in the initial conditions led to large changes in the outcome of collisions.

[@footshot13]

Oh, the contributions of the female species. Through your efforts to highlight those fundamentals the bulbs would not be as bright and ( I too have no dog in the race.)But thanx the subject is enjoyable, and you make it so. William Dupree

[@rogerpitcher2636]

How interesting you make Physics, almost makes me wany to pick up where i left off 60 years ago!

[@brucejackson4219]

Well presented amiga.

[@petercalkins3011]

Kathy; Thank - You, Thank - You, Thanks - You. Your videos are on par with Bronowski's "Ascent of Man" and CalTech's "The Mechanical Universe". Please relate your basis of thermodynamic articles to Einstein's work on Brownian Motion. On another related topic, please bring to life the zeitgeist of the debate between the proponents and opponents surrounding the existence of molecules. The debate that is not appreciated today.

[@wellesmorgado4797]

Thanks for communicating this point the public! These 2 articles by Swendsen (doi: 10.1119/1.2174962 & 10.3390/entropy-e10010015), I believe at least the second one is open, might be of interest by showing how Boltzmann true entropy definition helps to get rid of Gibbs' paradox.

[@KevinOrePflucker]

Very nice explanation, thank you for the video. I'd like to add that the reason the scientific establishment in Vienna (not Germany) didn't like the idea of molecules was that they were influenced by the instrumentalist philosophy of Ernst Mach. For them, the unobservable entities proposed in scientific theories (e.g. molecules) were just "useful instruments" to explain sensorial phenomena and said nothing about reality itself. Thus, they opposed the treatment of molecules as real entities and didn't accept any further formulations on them, such as Boltzmann's. All of this also had a political aspect, as the newborn Austrian bourgeoisie knew it had to incentivize science to be able to compete with the rest of Europe but at the same time feared the atheist and atomist materialism of socialdemocrats, which threatened their power. Instrumentalism was for them a perfect solution.

[@KevinOrePflucker]

For instance, the alderman who you mention honored Boltzmann's grave, Julius Tandler, was a social democrat.

[@Kathy_Loves_Physics]

Thank you for that amazing analysis. I know nothing about philosophy but it is fascinating how philosophy and politics can alter science.

[@vibratingstring]

@@Kathy_Loves_Physics If you haven't already done it, there is all that craziness of the French Revolution--and greats on both sides. The great Laviosier died by the Guillotine!

[@rayoflight62]

Yes. If you note, all the current of neo-positivists headed by Wittgenstein declared that the entire realm of reality was exclusively based on what could be perceived, and made one big cauldron of tought - only theories. As a philosopher, I consider the neo - positivism a form of obscurantism, which placed a toll -albeit limited - on the progress of science and philosophy.

[@rayoflight62]

Guess why. As a scientist and representative of the Government, he determined that tobacco, to give the best smoking experience, had to be added 4% water. He was formally executed for selling adultered goods to the populace.

[@ELECTRICMOTOCROSSMACHINE]

I am a history addict, and this is like crack. Best stuff I've ever heard!.

[@itsevilbert]

I always thought that Television was invented by the Scottish engineer John Logie Baird, but Farnsworth did make it practical by being all electric instead of being a mostly mechanical device. Anyhow I vote for Laura Bassi, just because I've never heard their name before. Great video as always, thank you.

[@Kathy_Loves_Physics]

Count Dracula you are right. Technically Baird invented the first television and Farnsworth invented the fist all electric television and I should have said it that way (but the “television” invented by Baird is a far cry from what we think of as televisions whereas Farnsworth’s vision was pretty far reaching and advanced).

[@tomasb7645]

WOW, EXTREMELY well done. Abstract info enmeshed in practical context makes learning easy and fun; you obviously do this well Kathy!!! THANK YOU for sharing your talent and this great stuff.

[@ulotrichous]

This was a terrific video! Thank you Kathy! I vote for Bassi too.

[@Kathy_Loves_Physics]

Glad you liked it. Now I don't know what I would prefer to win as I want to make all 4 videos next. Hrmm.

[@Kathy_Loves_Physics]

I decided to start with the life of Planck as that got the most votes AND I am going to Bologna in June to study more about Laura Bassi's life so I will probably make the video about her in July. I wrote more about it (and her) on Patreon: www.patreon.com/posts/my-next-video-is-33502544 (you don't have to be a Patron to read the page)

[@pstark4]

Thanks! Love the history. I remember his name but I love those ideas, I didn’t know they were his.

[@pstark4]

I wrote a joke opinion, thinking that youtube counts comments, ei opinions and polemics make you money. Shame all that wind is wasted in reddit when It could support content creators.

[@LadyAnuB]

My reply to Boltzmann's beer glass counting would be, "Shouldn't that be empty beer glasses?" 😀

[@neilmckay8649]

Is there a single book that tells the story of these great people? What a fascinating read that would be

[@Kathy_Loves_Physics]

Why do you want the answer served to you on a silver platter? I always enjoy finding out the answer for myself, and then sharing it with the world.

[@josesaldivar655]

What you must do is to learn the paper by Bokrzmanb so you know who did the equations at least on words. Similar things among Euler and Bernoulli in fluids.

[@meibing4912]

Super interesting. Had no idea: Boltzmann constant = Planck's constant = Bohr's constant. (turns out first naming these things is very important, have a friend who is very close to solving the the Collatz conjecture or 3x + 1 problem - already told him to make sure that the solution (if/when cracked) will be called xxx's equation).

[@ihbarddx]

Wonderful presentation. You asked for suggestions for future topics. I would like to suggest Newton's Second Law. In another video, you mentioned (in passing) that it wasn't originally F=m*a. Physics teachers become combative whenever I mention this. No one else on KZbin (that I can find) has addressed the issue. Perhaps you would be good enough? In any event, thank you for your good work!

[@camilorivera4685]

Thanks Kathy. Greetings from Colombia.

[@Kathy_Loves_Physics]

Camilo Rivera you are welcome. Cheers from San Francisco