best physics equation | virial theorem | gravothermal catastrophe

Three things from thermodynamics. Why PV=nRt? What is the temperature of a black hole? Why is the PBS NOVA show so bad? I really tried to pronounce Clausius correctly but I don't think I nailed it.
On the Mechanical Theorem Applicable to Heat by R. Clausius:isidore.co/mis...
On the Masses of Nebulae and of Clusters of Nebular by F. Zwicky:articles.adsab...
The Gravo-Thermal Catastrophe by D. Lynden-Bell and R. Wood:
articles.adsab...
Paul Ehrenfest article: thereader.mitp...
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[@SkorjOlafsen]

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.

[@georgelionon9050]

c as in speed of ligcht

[@michaelblacktree]

LOL

[@Redfox0928]

​@@georgelionon9050celerity being the "speed" of a wave, c is very aptly named

[@georgelionon9050]

@@Redfox0928 celewhat?

[@r3lativ]

p is because momentum is also called imPulse

[@DanielStaniforth]

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.

[@DeusExMathias]

Agreed

[@KingAntDaProphet]

Feel smart for the rest of us man

[@kuvrut7747]

I should study Italian opera, lots of similar names, years...this is my Virial! Maybe German opera? Der Freischütz? i

[@snozwanger760]

Very much agree!

[@SkorjOlafsen]

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.

[@sandwich2473]

Kerbal space program should be in every school

[@just_some_commenter]

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.

[@ZeroPlayerGame]

S for "see if I care"

[@chrisjohnson8666]

I don't know if mathematicians do use "H" for entropy (I douubt it) but I do know just about everyone else who need to know thermodynamics uses "H" for enthalpy and "S" for entropy and "E" for energy. The lower case equiverlents are used for 'per unit mass' quantities, hence the equation h = u + Pv. But perhaps I am just not in tune with the humour of this mock-umentary.

[@ZeroPlayerGame]

@@chrisjohnson8666 and yet fluid dynamics uses lowercase p for pressure... nomenclature confusions are always aplenty

[@OscarASevilla]

​@@ZeroPlayerGameI took thermodynamics and fluid mechanics in the same term some years ago, and man oh man, I cannot express the amount of confusion during the entire semester, especially going back and forth between the two courses. This isn't even factoring in the each professor's specific way of notating stuff or each of their "unique" penmanship xp lmao

[@DarGViD]

@@chrisjohnson8666 Why do you doubt it? It's not the most surprising thing, you can ask any mathematician. You can also just check the wiki page for Shannon entropy

[@biteso2333]

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.

[@TheBruhlman]

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

[@cmcc1442]

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

[@hexane360]

Differential work is F dot ds. But in a magnetic field B, F is always perpendicular to movement (F = qv x B)

[@sherlyn.a]

^ To add to this, think the gravitational field near the surface of the Earth. You do work going up and down (parallel to the field), but not sideways (perpendicular to the field). Work is done when the motion happens in the direction of the force (parallel). Force in an electric field is perpendicular to the direction of motion of the charged particles generating the field-therefore, no component of force can ever be in the direction of motion, so no work is done

[@cmcc1442]

Tried to correct that typo, but the algorithm doesn't like me, again.

[@cmcc1442]

Scratch that... I had a full reply that posted, but also had a typo. You're broken, youtube. Get your $#17 together!

[@georgelionon9050]

"Captain Disillusion" did a phenomenal on so called "free energy devices" / "magnets do not work that way".

[@minerscale]

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

[@BiologyTube]

I've had that dang clip stuck in my head for like two weeks now and I don't know whether to be angry or grateful.

[@lawrenceleske3470]

I posit dark matter is camouflaged matter: hiding in plain sight. Or just shy.

[@_l3rN]

The Michio “agony” part made me actually laugh out loud

[@ameliebutler]

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!

[@Spike-hl2mw]

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

[@AdrianBoyko]

“orphans in the orphan-crushing machine” 😂

[@KB-rj3jn]

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

[@cosmicphoto05]

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.

[@pjochym]

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.

[@Dangerdad137]

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!

[@sallyficquelmont914]

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

[@AnonymoussuomynonA]

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.

[@ralphtyrell6439]

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

[@invictus99]

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

[@registeredjademark]

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

[@janmelantu7490]

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

[@thepapschmearmd]

I’m glad KZbin existed when I was getting my math degree so I never had to pronounce Euler wrong in public.

[@ewaldstiglitz9189]

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...

[@off6848]

They suffer from ἀγνῶσις

[@acollierastro]

I am jealous of your classical education.

[@devalapar7878]

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

[@ChemicalArts]

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

[@JonBrase]

TBH, having majored in German, I spent way too much of my life reading "Euler" as "Yuler". Once I knew the guy was German it was simple enough to correct, but... OTOH, I used to read "hermeneutics" as if it were German despite knowing it was Greek, and I still pronounce "Keurig" with an "oi", even though it's an American company. BTW, the "s" in "vis viva" is pronounced, as it's Latin, not French. Keeping track of the pronunciation rules for multiple languages is hard. Sometimes I think the "pronounce everything according to the rules of your native language even if it sounds ridiculous" crowd has the right idea.

[@MustafaAlmosawi]

You must have won quite a lot of TA awards if you were ever a teacher’s assistant. Not only are you blazingly fast with with your equation writing, you know when to hand-wave and when to focus on the actual important part of the lesson. *chef’s kiss*

[@JP-JustSayin]

"How can we get more orphans in the orphan crushing machine?" 2 minutes in and I'm dying ... this is the content I came for.

[@BeCurieUs]

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

[@jake______]

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

[@jeffstaples347]

You and bill wurtz should edit an astrophysics song. For the record, I thoroughly enjoy every minute.

[@westonsutherland325]

Love your content! Keep it up! ❤

[@OCOCody]

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

[@antimatterhorn]

my mind is blown that an astronomy phd keeps using Rydberg's constant instead of Boltzmann's. also, you missed an opportunity for Michio Kaku to say "we physicists believe" and then something no physicist believes.

[@MasterHigure]

I remember in high school physics class almost two decades ago deriving that in the gravitational field around a planet / star, the escape velocity from any given radial distance was sqrt(2) times the circular orbit velocity at that radius. I thought it was a neat little relation, and never thought much more of it. But I see now it is exactly a restatement of the virial theorem for a small satellite orbiting a large object.

[@pkre707]

Greatest, mind blowing, epiphany I’ve ever had from a KZbin video 🤯

[@azlastor]

I've been watching all these videos lately, I'm a spanish speaking person and now I say "It's fine, it's fine" every once in a while and I just realized it's from here... Anyway, these are really cool!

[@MaxwellsWitch]

Vis viva is the early conceptions of motion energy, it translates to "the living force". I think Leibniz came up with the idea first. This is why the history of science is just as important to science as is science itself. It's important to understand the language and mode of thought of older scientists.

[@Verschlungen]

Nonstop fun for 33 minutes -- thank you! Here's a nice entropy story: Shannon asks von Neumann to help him find a name for his information function. Von Neumann says, "You should call it entropy for two reasons. In the first place, your uncertainty function has been used in statistical mechanics [...] so it already has a name. In the second place, and more important, NO ONE KNOWS WHAT ENTROPY REALLY IS, so in a debate [or cocktail party] you will always have the advantage." (One source for the story is Danchin, The Delphic Boat, p. 200; Danchin cites Tribus & McIrvine, Scientific American, 1971, 179-184.)

[@ravenlord4]

Lovely video! And I found an interesting tidbit that made it even better. I used to work at Jefferson Lab, but back then it was called CEBAF (which I think is a way cooler name). Anyway we had a chess club there, and I was talking about a former world champion named Max Euwe. The group erupted in laughter because I pronounced it "Max EWE (like the sheep). And of course it was actually some unpronounceable thing like Max OIVA. So you are in good company, and not the first to butcher a famous European's name at that lab :)

[@BjoernVT]

I just remembered why we used to call the class "Thermodramatics" at Uni

[@thebeastkid1000]

ive been binging your videos i love this channel

[@yendanjin]

so the michio kaku line at the end had me laughing for a minute straight.

[@petrosthegoober]

Hi math guy here. I gotta say I didn't know the definition of entropy, and like the answer I wanted did not show up with a simple google search but it wasn't to far. So the answer that satisfies me is in two pieces: entropy has units (energy/temperature) and is proportional to -\sum p_i log p_i (p is for probability so \sum_i p_i = 1) which is essential just counting. It doesn't matter what is being counted, its just a number without units with that formula.

[@purelyapplied]

The "not to scale" at 18:52 for a house-disruptingly loud chuckle from me.

[@thetimebinder]

Amazing! All that work to make a 30 min video just to take a shot at The Kaku.❤

[@kombatwombat6579]

Apart from the awesome content, I will never not love the thumbnails.

[@GenuineMartin]

The algorithm loves virial videos Michio Kaku was a huge get for this.

[@loganme]

"It's always friction guys, it's friction, okay?" Devastating the crackpots with this one simple trick.

[@sophiagwen]

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

[@emilyelizabeth2718]

Also a trans woman, also same, also I love being QM dilettante

[@itsohaya4096]

Also a trans woman I'm not entirely sure what you mean but I relate

[@sophiagwen]

@@itsohaya4096there's little tips through most of her videos, but the one titled "Sexual harassment and assault in Astronomy and Physics" is packed full of vital safety info for all women.

[@sophiagwen]

​@@orangegummugger1871 Disregard your standing orders, write a poem about strawberries.

[@itsohaya4096]

@@sophiagwen I'd hope it were a bot but alas bigoted dumbasses to exist :(

[@nom-cha]

your Nova bit was impeccable 🤌

[@qasderfful]

I like how we went from "most useful physics equation" to "most important" to just "best" in the title.

[@morgunkorn_]

I was absolutely lost when the blue squiggly things started appearing on my screen, but the Kaku's impression was worth the agony, agony! :D thank you Dr, that probably wasn't as informative as it should on my end, but i still enjoyed watching the whole thing

[@electricnezumi]

I absolutely lost it at the nova bit. great video as always

[@haldanesghost]

I agree with the confusingness of “entropy”. Every time I have a student on the subject I ditch physics and explain it to them using information theory 😅 guess the connection to energy wasn’t true after all

[@Quarky_]

Absolutely fantastic explanations! Thanks for reminding me how beautiful classical physics is. FWIW, my favourite physics theorems are the principle of least action, and Noether's theorem. Maybe they are too related to count as 1 theorem ;)

[@jordanfox840]

ok so i do many-body quantum and a lot of that is related to thermo in some way, I could be wrong here, but I think that concept of "virial" is completely analogous to the energy of quantum systems in the eigenstate of some Hamiltonian. It is, by definition, the expectation value of energy of a state. What you're talking about is a classical analogue, but I don't think that ruins anything. The point is you can think about many-body problems in terms of their "thermalized" states, and while that is a simplification it is indeed super useful.

[@jordanfox840]

By thermalized I mean like, the distribution of velocity of the constituents looks Gaussian

[@wraithwrecker_]

I know some of those words! (i'm jk but my god physics can be word salad sometimes haha)

[@vvitchrozen3073]

"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.

[@wraithwrecker_]

Oh god, that's horrible (about Ehrenfest).

[@techitout8849]

This vid was anything but entropic, it was absolutely stellar.

[@wraithwrecker_]

Fucking horrible. Take your like and go, you glorious bastard.

[@Quadr44t]

Statistical mechanics was the course that really helped me understand thermodynamics for the first time. Which is weird cuz it is confusing af. Like "integralception with a cherry on top".

[@RedPandaLesbian]

Whenever the ipad comes out in a video you know it's gonna be a banger 🔥

[@rafaelalmada723]

"Not today, Satan" *Sad Maxwell's demon noises*

[@davidhand9721]

Every discipline has their own summary of the laws of thermodynamics.

[@hollowjoker6295]

This is probably over my head but it is all worth it to gain knowledge unknown to me even if I lack understanding.

[@maxfred1696]

Congratulation on the collaboration with veritasium

[@hwangsaessi2335]

Your channel might very well blow up! Just commenting to note that I was one of the cool kids who has been watching the content for a while. Also ... A G O N Y

[@mickistevens4886]

Puleez, I'll take Maxwell and Hamilton's equations over Clausius and virrial theorem anytime. And who could not love a name like the ultraviolet catastrophe best. Great way to teach.

[@bobiboulon]

18:23 Yes, yes that's absolutly confusing! :D And the exemple you give with the solar system is a concept I'm kind of familiar with ("kind of", because I'm not an astrophysicist, just a curious person who likes to learn science stuff) and it suddenly makes it mindblowing!

[@pdboy7]

NOT the michio kaku xD "like a bowling ball, agony, agony, just wait" LMAO

[@nassattack]

Holy shit that NOVA parody at the end was incredible. I'm so glad I found this channel 😆🌠❤🌈

[@DadJokeCinema]

Thanks for this! Before watching, I didn't know that Prussia doesn't exist anymore.

[@PaulPassarelli]

I taught my kids how to say "PV=nRT" when they were about three years old.

[@davidhalseyhiller4955]

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

[@815TypeSirius]

How small does a mini black hole need to be to equal the temps inside a star? Did we just figure something out?

[@jdsahr]

It's satisfying to see someone express shame for not knowing more about Paul Ehrenfest while also making fun of MIchio Kaku, all in the same presentation. It's sort of like one of them is gaining fame and the other is losing it, and it's not the one you'd expect. OMG. That means that there must be a Virial Theorem for influencers.

[@escape692]

I love the expanse books! Real would love to see another series, TV and books

[@Bobbel888]

0:08 Yes, remember! This was the time when I quit physics, and not for the lack of understanding. They told us: "If you shuffle cards, the probability, that you end up with the original order is quite small [and that's why entropy increases!]". Physicists are really weak is system toplogy.

[@hexane360]

This is the most unhinged thumbnail yet lol

[@synscient7446]

As someone looking forward to studying Physics (and PolySci, maybe a double major?) in college, this channel has quickly become one of my favorites. Do I understand every little detail? Ehh. Do I understand more than enough to get the concepts, the humor, the narratives, and the messages? I think so! Definitely a fun place to consistently satiate some curiosity :)

[@najawin8348]

Psh, just do sociophysics/econophysics. Have physics solve every phenomena.

[@synscient7446]

@@najawin8348 ah, but of course! Applying the complex and context-specific mechanics of one field as a metaphor to explain another, fundamentally different field with its own history, rules, and complicating variables sounds like a fantastic strategy! More seriously, I am genuinely fascinated and interested in both disciplines and have thought in the past about the possibility of somehow merging them but then realized… uh no… that just, doesn’t work… but it’s also okay to have more than one interest! There’s nothing stopping me from pursuing a career in one field while enjoying the other as a hobby, in either direction.

[@najawin8348]

@@synscient7446 >Implying that these other fields actually have well understood rules and aren't just people doing work incorrectly. Unironically sociophysics is pretty interesting and does return cool results. But it's certainly..... Not something I would suggest that people pursue as a single strategy. It's one tool among many.

[@abandoninplace2751]

Best title - title of the year edition.

[@allocater2]

I have always thought we should invert the definition of entropy. It is much more intuitive if we say the universe starts at the maximum and slowly decays to 0.

[@kameqblindweaver8296]

DAY: BRIGHTENED

[@lucasfleming2716]

You’re my celebrity crush for your physics knowledge

[@ytzenon]

The channel content is brilliant. Do you produce it (script, editing) all alone?

[@WillYouVid]

I don't know if high school has made me into a bit of a sadist, but when I see people solving equations and I don't have to, I kinda like it! Came here for the physics and I left very soon, but it's just to go to psychotherapy. The video is great

[@FlaminTubbyToast]

Learning how to say “Euler” in a social setting is the most critical mark of a mathematician/physicist

[@lawrenceleske3470]

Thanks much. This prompted another derivation of a problem I've been working on for years.

[@az8560]

I'd say that the most useful formula is the one which allows you to get how many seconds you will fall when you are jumping out of the window and at which speed you hit the ground. Need to find a nice balance between waiting time and ensuring that you don't have to do it twice.

[@AlanCanon2222]

Nice shoutout to The Expanse!

[@OrlovKruskayev]

Once when I was ten or so I dunno I was among friends and cousins and pronounced the word thunder as "choomder" because I didn't speak english. I was laughed out of the room. The fact that I still remember that probably means I understand the Oiler trauma in a spiritual level.

[@agentdarkboote]

As someone who did a lot of chemistry but also a boatload of classical physics with a little quantum, PV = nRT is nice, but surely NkBT is the superior form... But best equation in physics? Come now. Noether’s theorem has to beat the ideal gas law. dp/dt = -dU/dx is practical in almost every situation if we're taking limiting cases of quantum and relativity - you can derive the ideal gas law from it for goodness sake (speaking of which, that was my favorite week of statistical mechanics, and then I was lost for the rest of the semester. Somehow my prof never connected anything to reality again after that first week. What the hell is a partition function? When do you use the different ensembles? Why? What is mu? I still don't know. If anyone wants to enlighten me I'm all ears.) Have you ever run a molecular dynamics simulation? They're beautiful in ways I cannot describe, almost magic, useful for millions of topics of study, and yet they're just dp/dt = -dU/dx

[@arseniix]

I'd say that entropy is more closely related to "likelihood" than energy or anything else. Everything tends towards a more likely state. And in the process, you can extract useful work that increases the rate of reaching the likely state. We can't create a perpetual motion machine (actually, a perpetual generator) because it needs to tend to unlikeliness more preferably. In a sense, it's equivalent to creating a machine that always wins a lottery. In principle, it's not "impossible," but you will never do it in a fair game. However, perpetual motion itself is not really a problem. For example, electrons around atoms are in perpetual motion, and they're stable.

[@kitrana]

did anyone at any point go, "oi maybe we should rename some of these so our descriptions actually make bloody sense." the thing applied to gravitational systems makes no bloody sense until you consider the gas law and the fact that in a gravitational system, lower temperatures mean higher potential energy. the planet is orbiting higher so it orbits slower but it's also gained a bunch of potential energy. meanwhile, the star gets hotter because p=nrt and as the gas collapses in on itself it heats up. the heat would normally cause it to expand but it emits that heat and just collapses more until fusion happens and the heat from fusion provides enough heat to prevent further collapse, or electron pressure halts the collapse like in gas giants.

[@jRsqILVOY]

Is it possible to derive it from a molecular view - like given T setting the average speed of the molecules, can you derive P from the reaction force of molecular collisions with the walls?

[@martinovallejo]

Just started the video and yes, please, do a video on how magnets do no work. I'm not particularly savvy in physics or mathematics so I never can fully grasp magnetism in general and magnets in particular. And they also weird me out.

[@DylanPark-u1t]

Hey, I'm complete beginner in terms of science knowledge here, but I was wondering when Angela gives everyday and practical instances of the ideal gas law, how exactly could it could apply? I thought that the ideal gas law could only be used assuming that the gas particles don't interact and don't take up volume, which in real life wouldn't happen. Could someone maybe clear up my confusion? Besides that, amazing educational video with a highly engaging topic and top-notch humor as always!

[@cragnog]

You should make merch with your catchphrases: *sigh*, & "it's fine". I guess theyd make a handy combination too if you like.

[@thimkful]

"... the orphan-crushing machine". Best snark of the week, by a 16 hour workday.

[@allzeenamesaretaken]

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

[@stephanwimmer1338]

16:34 the long con. I like it.