3:46 "S" is short for "S does not appear in the word entropy", just as "p" is short for "p does not appear in the word momentum". It's a very convenient naming scheme.

Every now and then you should throw in little maths problems like 10-4 or 2+7 so I can follow along and feel good about myself managing to keep up.

Ludwig Boltzmann, who spent much of his life studying statistical mechanics, died in 1906, by his own hand. Paul Ehrenfest, carrying on the work, died similarly in 1933. Now it is our turn to study statistical mechanics. ―David L. Goodstein, introduction to States of Matter 1975

As a chemical engineering student, nothing is more devastating than when the gas is not ideal and you can't use ideal gas equation

Just reminded me of the three laws of thermodynamics from undergrad days: 1) you can't win, 2) you can't break even, and 3) you can't get out of the game.

13:43 it may also be helpful to know that “eulers theorem” refers to at least a dozen different theorems in vastly different areas and that google seems to lack any regard for this

It's amazing how intuitive the idea that "adding energy to a gravitational bound system slows things down" becomes from playing enough Kerbal Space Program.

Physics student here. The only time I have ever encountered the term "vis visa" is in the book More Heat than Light by Philip Mirowski. Among other things, it talks about the history of the concept of energy in physics. Vis visa is an old fashioned term for kinetic energy (but defined as mv^2) which Leibniz came up with. He also uses the term vis mortua (literally dead force) for potential energy. Weirdly there were all kinds of inconsistent definitions of "force" in early mechanics and the term energy didn't get introduced until way later by Thomas Young.

The effortless switching from chemistry to physics to astronomy to comedy and back in all of these videos is like a form of performance art ... I'm hooked.

This is so far past my sixth grade education level and so far outside what I thought was my areas of interest, yet here I am, eager to learn and try my damndest to understand things I will never be able to use beyond when I'm geeking out to friends. Thank you for making this more accessible and genuinely enjoyable.

I appreciate your advice of people being familiar with the ideal gas law. The NFL had a whole "cheating" scandal because no one understood that pressure in footballs change with temperature. It even got a fun "gate" name: deflategate

Mathematicians typically use H to represent entropy, and there's actually an explanation. In the beginning of statistical mechanics, Boltzmann used E, but Gibbs and others used η. Eventually other people started referring to Boltzmann's "E-theorem" as the "H-theorem," where the "H" is probably supposed to be a capital eta. After a while, Boltzmann gave in and started calling it his "H-theorem" too. Then, 50 years later, Claude Shannon named his concept of information-theoretic entropy after Boltzmann's H-theorem, but he didn't know it was supposed to be the Eta-theorem, because of some combination of the distance in time, the fact that Shannon was a mathematician and not a physicist, and the general trend away from Greek and Latin and toward English. So he just thought it was an H and now we're stuck with that. However, I still have no idea what Clausius's excuse for S is. As far as I can tell, he literally just wrote "Let us denote this quantity by S," and I guess that was that. (OK, fine, he *literally* literally wrote "Bezeichnen wir diese Größe mit S".) Maybe "S" stands for Shannon. Clausius wrote his paper 50 years before Shannon was born, but I don't see why that should matter.

You said dark matter at 9:04 and Fritz Zwicki in the same sentence and my classically conditioned brain immediately went: "Dark matter do we need it do we need it do we need it how much what is it do we need it do we need it do we need it" help

Got a bit lost on the math (though it's cool to have it) but every single thing was worth the end and the mockumentary, particularly the guest appearance from Michio Kaku. Amazing. Love this channel.

Okay so after binge watching your entire channel, a few thoughts. 1) amazing comedic timing. I have laughed so much. Thank you. 2) I am infinitely more interested in science/data/academia than I ever thought I would be, specifically because of how you present it in an interesting/engaging way. 3) it's fine 4) you are like Jenny Nicholson levels of good at this, and while I know this is not your main thing, this channel deserves millions of subscribers. 5) that said, no pressure at all in like making a ton more content even if your channel does end up getting substantially larger.

It’s amazing how prolific you’ve been recently.

And YES to 'magnets do no work.' I've always had this intuition, but would love to hear a real explanation.

Your editing is quickly becoming my favorite part of my favorite KZfaq channel

"this paper is shockingly readable" "the mean via viva of a system is equal to its virial"

Clausius really just got sick of people asking why the sky was blue and wrote his PHD thesis on it and I can respect this.

“orphans in the orphan-crushing machine” 😂

*grabs popcorn and the cat* so excited! a new video by my favorite scientist just dropped! 😀

32:49 Michio Kaku: "... agony, agony..." This channel is developing some lore. Lore: The Kaku Agony

wow i love that you used to be able to put half a definition in latin and just expect people to get it. academia was wild in the 19th century when everyone went to the same 2 schools

The virial theorem is used regularly by people running molecular dynamics simulations, as it gives a way to estimate the stress when all the atoms are wiggling around.

For real, a video titled "Magnets: How they do no work" could kill it in the algorithm.

I'd enjoy a 'magnets do no work' video. Also - "The mean vis viva of a system is equal to its virial" sounds like a line from My Fair Lady.

And just like that, my meal prep time is instantly enhanced. Also, as a mathmetician, i just thought people were being cooky and saying "oiler" and continued to say "Yuler" until a friend pulled me aside years later.

it's really great to see your channel becoming so successful! as another woman in STEM, it's nice to see so many people listen to and appreciate your work on these videos. they have been the soundtrack to my work for the past few weeks!

you're damn right it's fine. your ability to be genuine is so refreshing for this platform.

Hey, I've invented a perpetual motion machine. It's so simple. It doesn't run off of fuel AT ALL. Just use your legs. I call it Pedalpetualmotion. I mean, sometimes you get tired, but I think that's just a practice thing.

I don't comment on KZfaq often, but felt compelled to just say that your videos are absolutely fantastic! Your passion for learning and science is extremely contagious and you present it all in a very well-spoken, informative and humorous way. Just top-notch stuff. Thank you for elevating the level of science communication on KZfaq, it is truly inspiring.

So fun fact. In information theory, entropy is not given the letter S, but instead the letter Η. So for years I was like "that also makes no sense". But I recently discovered that actually the Η is not a capital h, but a capital η (eta, for those who dont know). Which actually checks out. My mind was blown.

the only two things i took out of my thermodynamics class were: 1. enthalpy is not entropy. i don't know what it is, just that it's not entropy 2. steam is not an ideal gas, don't try to use the ideal gas law with steam

Just soon after Sabine and veritasium made videos about entropy... And I was thinking about entropy and how it makes the difference between life and non-life for weeks now and suddenly everyone makes videos about entropy which makes me think about it even more, and now I am overwhelmed

I do hope you this as a compliment, because I intend this as a compliment, but as a former high school teacher, I would like to say that you would make an _amazing_ high school physics teacher. You have this way of expressing complex ideas through relatable and interesting stories. At the school where I taught (I taught art, not science), the students who were not already math(s)-literate and nerdy about science, tended to _hate_ their physics classes. I think this is mostly because my physics teacher colleagues just taught formulas and concepts that their students needed to know in order to pass their final exams; but they didn't tell stories. They didn't nurture a love, or at the very least, an appreciation of the subject. Students just wanted to survive the class and prayed to the Lord God Above (or Vishnu or Ganesha or whomever) that they would pass the semester exam and then actively purge their brains of everything they had learned once the semester is over. Very few of them actually came away with any kind of appreciation of physics/chemistry/biology. Now, I'm sure you've taught (or perhaps are currently teaching) undergrads, and that's fine, and no doubt, you're very good-your channel is proof of this-but I bring up high school physics because high school is the time that can make or break a student's love of a subject, and for the most part, is where they determine their career path. Teachers play a critical role in this process by how they present the subject to their students. Do they share their love/passion for the subject by telling stories or do they just hand out worksheets and regurgitate the textbook? Your videos make it clear that you are passionate about astrophysics and science in general. While most of your videos are about an hour long, I don't _feel_ like I've sat through an hour-long physics lecture. There are no boring bits, but also, I don't feel overwhelmed by a flood of information. _THAT_ is why I think you'd make an excellent high school physics teacher.

It makes me so happy to see your channel growing. Can't wait to listen to this one at work!

That was the best Nova I’ve ever seen … but maybe you could add a few more novas to your Nova? All I can say is thank god I’ve been binge watching Walter Lewin teaching MIT 802 classes all day or I might not have understood the roughly 1.3% of what you said like, at all! I did recognize many of the formulas as they flew by (“ooo … pretty”) so that was good for me. Even saw the 4pi denominator I was introduced to about 3 hours ago. In short: I loved this video and will probably have to watch it only 9 or 10 (hundred) more times as I work through the homework. Such awesome.

I'm a stoned software engineer and you made physics far more intuitive than every prof I've ever had.

I just came across your channel... OMG you are such a dork! Please never stop making these!

Great video Angela! I've been interested in astrophysics for years and never had the viral theorem explained so clearly. Thank you!

NOVA is what made me love science as a kid, and it will always have a special place in my heart. You're absolutely right about the ridiculous and overly dramatic way it's presented though. You were spot-on and hilarious.

I've found yourt channel about half a week ago and now I watch your video as it goes online for the first time. So thought provoking

Your Michio Kaku impression at the end really cracked me up !!!!!! love your videos so much

This was super educational, thank you a ton! I love your videos, but this one is particularly great

This video did such a good job at spreading around it went virial.

Always overyjoyed to see one of your videos in my sub feed. Really love your content and your perspective.

I just discovered your channel and this is quickly becoming one of my favorites! You are so awesome, inspiring, and entertaining!

michio kaku killed me, how does it feel like being the funniest person alive

I’m a biochem major and you inspire me to be a biophysics major!! 😭😭

"excercise to the reader" were my most feared words when I was in uni taking any math or math-adjacent course

You actually make one of the most interesting science videos on the internet. I loved this one.

Leviathan Wakes! I'm in the fourth book of the series, awesome book. Nowadays, there are are theorems that could be called "viral" theorems....but seriously, there is no more solid branch of physics than statistical physics...it's so powerful that it stands on its own, even if the rest of physics, for some weird reason, is proven wrong. Also, if anything, the most important equation is S = k ln Omega, it encodes all the important statements in thermodynamics!

Nova was (is?) fantastic for children! It's simplicity and dramatic liberties made it brain candy for me as an 8-12 year old. I wouldn't love math and science the way I do now, even though I've personally outgrown Nova.

You have become my favorite KZfaqr in the shortest span of time. It's been awhile since I don't get excited about a new video from one of my subscriptions. Thanks for making KZfaq pleasent again :)

You are legit my fav youtuber. I havent even gone to school yet (almost 30 and finally attempting), but ive been binging your stuff bc its so entertaining

S could be a reference to Sadi Carnot. Claussius studied Carnots ideal heat engine and his corrections to Carnot's model made Claussius' name around 1850. By studying that ideal heat engine he also discovered a quantity (entropy) which is conserved in the ideal case, but not in real engines

I took my pet rock to the rock doctor and was told I had to exercise it more because it was too sedimentary... Another great video, thank you!

the joy you had describing thermo dynamics made up for me trying to keep up in astrophysics... it sounded more like you were describing change of state then temperature for your negative scale ...thank you for taking the time to film this

Hi, I'm nobody from nowhere and usually just a lurker, but I feel compelled to post that I just found your channel and I love it. I couldn't science my way out of a paper bag but I find your content easily digestible, entertaining and informative. I hope you have a wonderful day.

Love your content! Keep it up! ❤

"the mean vis viva of the system is equal to its virial" is the new "mitochondria is the powerhouse of the cell" in my brain now thank you for the new brain worm that I will never be able to dislodge

OMG that last part of the video was great! I love the particular flavor that you put into your videos, it makes your content so unique and fun. Also, as a non-physicist I didn't understand most of the video, but I had no idea about these concepts and the gravothermal catastrophe in particular is so interesting and counterintuitive. Keep up the good work!

wow, this was a great video! Great exposition! The classical virial part was crazy. Never heard of that before! Cheers

Yay! Angela made a virial video! 😛 PS - When I was in school, I used to get entropy and enthalpy confused. I always wondered who was the sadistic SOB who made those confusing terms.

acollierastro is hilarious, and incredibly informative.

OMG! You are hilarious. I've never had so much fun not comprehending half of the math in a 30 minute lecture. I should have read the section before the class. And yet, I got the point, and quite a big reveal it was.

You asked if anybody uses virial theorem in their work. I used it to develop HECSS which is an alternative to molecular dynamics as a configuration generator for interactions modelling in solid state. You can find it on scipost physics if you are interested.

You've officialy become the youtuber I'm most excited to get notifications from. Also as a fellow dark matter person, your last video has been so helpful in learning how to explain what I do to people!

Perfect content, as always

You have a delightfully veiled deadpan delivery. Best science comedy on KZfaq.

Very good and also entertaining, as always. Nitpick: PV = n R T is used more in chemistry or physics related to chemistry, while the form p = n k_B T is more frequently used in many branches of physics (here, k_B is Boltzmann's constant - named after the Austrian scientist who developed the theory of statistical dynamics / thermodynamics). Pressure rises if you put more particles "n" into your tires, or if you raise the temperature "T" in your pressure cooker.

I'm partial to PV = NkT myself, but that's probably stat mech rubbing off on me. Definitely didn't understand entropy until then, heck couldn't even keep it straight from enthalpy before that course. Oddly, I never heard of the gravothermal catastrophe - Hot bods get hotter!

I feel so sorry for all those people that never had latin and greek in school... My 8 years of it were hell... But it is so useful...like for everything...

No idea what's happening in the math parts, but your explanations of the concepts and ideas allows me to follow along well enough!

over the past week, this has become my favourite channel on KZfaq. Thank you for existing, human

Encountering Euler written before hearing him mentioned by someone else is super commendable and shows a ton of initiative and enthusiasm for education!

Yeahhhhh, was just looking for something to fold laundry to! Thank you physics mommy!!!!

i love the ideal gas law. when i was 15 i maintained the atmospherics simulation subsystem for an open source game set on a space station. i got to know PV=nRT very well over the years handling those simulations

Love that you started this video reading Leviathan Wakes. The Expanse was one of my most favorite TV sci-fi shows ever, starting from the 1960s forward.

I was a mathematics major in college, and at 51 years old, I just learned how to pronounce Euler this year.

Ok, I just have to ask cause you have thrown a pile o' books in a several episodes and started this one with one of my favorites of all time. Was wondering if you had a book list anywhere of your personal favs? I've read most of what you have had on screen so far I believe, but want to know if I am missing some gems :D

When I grew up in the 80s, Nova wasn't so cringe. I've tried to watch it in the last decade and it always disappoints. Your calm (and amusing asides) are more like how it used to be, thanks for this!

I always love the way you talk and present. It’s like funny and amusing without going “full comedy.”

PV = nRT is probably the only thing I remember from AP Chem. Also despite knowing how Euler is pronounced I always forget when im speaking 😭

'...Prussia, which doesn't exist anymore'. Entropy strikes again.

Looks like this is your latest, I've been binge watching your videos today, they are all great, thank you!

Your videos are the highlight of my week. Thank you for sharing your brightness and intelligence with the world

As a trans woman your videos have taught me so much about being a woman.

"Having made arrangements for the care of his other children, Ehrenfest fatally shot his younger son Wassik, who had Down syndrome, then killed himself" I'm okay with forgetting this guy. Good to know Hatsune Miku connected Stat mech and quantum mechanics in the early 1900s before her Minecraft success.

I was a physics major in college. Never needed the Work = Force x Distance equation in anything outside the assignment of the week. It did come up later (after graduation) in relation to dictatorial bosses (Grumman Aerospace comes to mind). They'd ask have you covered any ground? They didn't care about the effort expended, since 0 distance meant 0 work, and then they refused to pay you. P.S.: I love your multicolor esthetic with a dark theme on your calculations. So comfortable on the eyes. My physics professes tended to use blaring cellophane overhead projectors with 1 KiloWatt bulbs in darkened auditoriums, plain black markers, and rapid hands to crank the slide to the next position. Please note they also didn't care about the difference in their writing scribble speed vs. the student's cognitive processing delay added to their own copying speed. An illustration of entropy increasing. Bye!

I love you, you're so cool! 😎 Thank you for doing all of this, including and especially for all the work we don't see! I really appreciate these gifts of yours! 🌌

This is hilarious! I need more of you in my life - learnt more in 30 mins that I have in 6 weeks of lectures

i love listening to your videos as I drive to/from work. Not sure if I learn anything but i feel smarter afterwards

Oh my god having Angela explain the virial theorem as I go to sleep was not something I thought I would want in life. If having a parasocial attachment is wrong then I don't want to be right.

I just found your channel and I loveeee itttttt please keep up the good work!

gravothermal catastrophe is the coolest pair of words i've ever heard. you have my full attention for 33:51.

32:48 “it’s like a bowling ball: agony, agony” this is the content I come to this channel for

Great video, also your sound is great now. Good job.

Sometimes I hate the KZfaq algorithm, but not tonight. You just got another professional nerd as a subscriber.