Boltzmann's Entropy Equation: A History from Clausius to Planck
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- เผยแพร่เมื่อ 22 พ.ค. 2024
- 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
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.
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.
While this is true, one can, of course, derive the logarithm using only trigonometric functions via infinite series! :)
@@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.)
@Arthur Fair enough. I've yet to read Wildbergers Rational trig, though I'm a fan of his channel.
@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.
Bassi.
You are just friggin' awesome. The most underrated channel on TH-cam.
Thanks - blushing now
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
Explaining the history just makes learning about science so interesting. Awesome!
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!
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.
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.
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
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!
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.
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.
Adding even more issues of dubious attribution to the mix as today's referenced Maxwell equations are actually Heaviside-Hertz derived equations.
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. ❤️
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 !
I worked very hard to understand the historical context because it helps tremendously if you write on these subjects.
The historical point of view also aids in the overall technical understanding of the subject. Kudos.
I find myself becoming deeply absorbed in your articles, with an ever-increasing enthusiasm.
Keep it up - you are a gem.
My sentiments exactly, Kathy is enlightening!
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.
Your 'lectures' are absolutely delightful.
Thank you! So clarifying! Your explanations shine like a sun in my mind!
🙏🙏🙏
This was so good. Please do Bohr's model and then Planck. But I'll probably watch all four if you do them.
Love your videos explaining the history and especially all the interplays between the main characters. Well done and please keep it up!
I’m so glad you don’t shy away from a little math.
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.
Back after a PBS vid. Go get ‘’em Gal! Your narrative surpasses the pros! Thanks for being awesome!
Ooooh Kathy, you are spoiling us! Another fantastic entropy video - many thanks!
Anything for you Robert
Please make a video on Edwin Hubble and George Lamaitre and how Mr Hubble didn’t believe in the Doppler effect explanation of redshift
Only recently discovered your videos. Been enjoying them. It's important to get the history right. Thanks
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.
This was my favorite video of yours so far!
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
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...
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!!
50 years ago I was taught college physics by the sequence kinematics, dynamics, electromagnetics, and finally a little quantum theory pulled more or less out of thin air. Thermodynamics was taught as a minor theory of gasses and heat engines. Today I believe thermodynamics is far more fundamental and I wish I had studied it in more depth. Modern hot topics like black holes and theories of the universe rely heavily on thermodynamic principles. Incidentally the main reason Planck calculations were so accurate is that precise optical measurement devices were developed at the time for the new electrical lighting industry.
Love, love, love! And your enthusiasm is also the best. I've always thought that physicists have the best sense of humor.:))
I often think we have the worst sense of humor but I may know too many physicists 🤣
I love you Kathy. Curious of your references, sources.
I have only just discovered your channel. It is awesome.
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.
Glad you liked it
I’m reading Schrödinger’s What is Life and this really helps the background
This was pretty awesome! Great history here. I always thought Boltzmann came up with it. My respect for Planck grows even further.
my respect grown h times
thank you. this kind of historical context makes clearer even the math of thermodynamics. great video.
The real joy you bring is not dependent on anything you say… you are electricity…
I enjoy so much your grasp of truth
Awesome loved all the illustrations.
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.
These videos are incredibly interesting and unique, thank you
Kathy makes physics history fun to listen and learn. Thank you
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 👏👏👏👏
Yo también
You put so much energy into your videos.
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.
Love your video. Thank you for post it here.
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 :)
A video on Bohr's model would be awesome!
love your videos, show them to my students. thank you
a1m1i1r1g1a1l I’m so glad. What kind of classes may I ask?
Great story telling! Thank you!
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!🫡
I just found your channel. Thank Thank You. Oh my this is wonderful. Alas how could anyone give these a thumbs down.
Wonderful video Kathy!
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.
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!
best physics channel on youtube. Rare passion for thermodynamics right here
Kathy, thanks for your interesting video ! this is awesome ! you explained the history that always skip in the class...
Enlightning story on Boltzmann's constant. Thanks.
I love your videos soooo much! Great information and charming enthusiasm!!
Codeman T thanks.
your channel is brilliant!
Really great delivery that I greatly enjoyed ... more please 👍🙏👏🏻👏🏻👏🏻👏🏻👏🏻👏🏻
You got it!
Thanks a lot for posting this wonderful clip
this channel is just awesome!
Thanks
That was an incredible and mesmerizing video! Thank you, Prof. and... What is that beautiful painting on the wall?
Ty for a great series
I can clearly see the passion you have for physics...
Keep up the good work
Do some episodes on classical mechanics
This is a great video!!! Thank you for sharing your knowledge! :D
Fascinating!... as always! Finally found the source of why Quantum Mechanics was created!
Awesome ! Please keep making stuff like this ♥️
I am a history addict, and this is like crack. Best stuff I've ever heard!.
Been on TH-cam 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
Wow what a lovely compliment (and I guess I need to check out the Age of Enlightenment book)
Wow very well explained!
A TH-cam 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.
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.
OMG! My new favorite TH-cam channel!
Another excellent video.
Do all of them . Really interesting thanks
Well presented amiga.
Thanks Kathy. Greetings from Colombia.
Camilo Rivera you are welcome. Cheers from San Francisco
This was a terrific video! Thank you Kathy! I vote for Bassi too.
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.
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)
Madam you are incredible!! I am loving all your videos, please before history of physics melts away, continue what you do please
Thank you so much I’m not worried about the history melting away as much as me melting but thanks for the nice comment
@@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!
How interesting! Thanks.
I don't mind your arms moving all over. At first it bothered me I must confess. Now I couldn't care less. The content and its delivery (pace, style, graphhics, etc) are absolutely captivating. Seriously, I don't mind. It's a part of the package that's totally fine with me.
Wooooow. I loved it!
Amazing video!
Thank you so much!!
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"
Wow. wow, wow, a great video again !
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 :)
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.
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.
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.
Clausius wins for a lot of things. Grossly underrated scientist IMHO. (not really a humble opinion to be honest)
@@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
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.
How interesting you make Physics, almost makes me wany to pick up where i left off 60 years ago!
Happy Kathy paints scientific pictures with words. Thank you.
I have a feeling Bob Ross is smiling.
you video are so good
P.S.: I LOVE the outtakes !!!
a wow presentation
Is there a single book that tells the story of these great people? What a fascinating read that would be
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.
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.
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
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.
Great video as always, Kathy. Please do all the videos you mentioned. The order is not important, just their stories.
Will do Tim. Don't know how long it will take me but I will definitely make all 4 videos.
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.
I will get to all of them eventually - promise.
Thanks! Love the history. I remember his name but I love those ideas, I didn’t know they were his.
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.