Reconciling thermodynamic and state definitions of entropy | Physics | Khan Academy

[@alexrosellverges8345]

Probably the best videos about entropy out there, i just got tired of hearing "disorder" and analogies to rooms, thank you very much!!

[@jakariarahman7953]

So did i

[@samehum]

@poemZX: This is my understanding: if you substitute numbers into the equation you will get a huge number, but if you take the logarithm of that number you will get a smaller number which is easier to deal with. For example say S=4000000000000 (4 Trillions) BUT Log(S)=Log(4000000000000)=12.60. 12.60 is much easier number to deal with especially if you are graphing the numbers. Hope that helped!

[@CyberneticOrganism01]

What this shows is that 2 definitions of entropy (1 thermal, 1 statistical) are equivalent. So S = integral dQ/T = k ln Omega. Now recall that temperature is a redundant concept. 1/2 kT = average kinetic energy. Substitute this into above integral. We get integral dQ / E = 2 ln Omega; Boltzmann's k is eliminated. Now both sides are dimensionless. RHS is a measure of subjective information. LHS is also a subjective measure of information b/c heat *is* subjective!

[@ozzyfromspace]

Congratulations, you successfully blew my mind. I hope you're happy.

[@sidneydean.]

thank you sal i appreciate all your videos but i really appreciate this one. Entropy has been a tough thing for me to grasp until now.

[@glowish1993]

Mindblowing video linking the two sides of entropy, thank you so much this helped a lot!!! I was listening to Interstellar's OST with this video xD, definitely added to the dramatic effect

[@CyberneticOrganism01]

Corrections: 1. When I said LHS & RHS are both dimensionless, their unit can also be information bits. 2. I should have said "heat cannot do useful work without a difference in temperature".

[@biprodevsarker5047]

This video has awfully low views and likes than any other in this playlist, although I think it deserves the highest in this playlist, because we are not taught this in undergrads. I mean I knew both of them, but never thought they can be related like this!

[@virupannamedikinal]

It would be such a waste of me if I don't finish watching all of your videos in this playlist,thank you so much Sal Sir.

[@gooddeedsleadto7499]

Example of entropy 3 switches in your room, x 2 positions or states for each switch, on, off How many ways? For two positions in case of two switches, we see four possibilities , (on,off);(on, on); (off,on);(off,off) For two positions in case of three switches , we see 8 possibilities.o In case of (on,off) (on,off) (on,on) =2 In case of (on,on) (on,off) (on,on) =2 In case of (of,on) (on,off) (on,on) =2 In case of (of,of) on,off) (on,on) =2 Add them up 2 states and 3 switches 8 ways X to the power n is the number of possibilities Entropy is directly proportional to number of ways Proportional to Equal signs brings constant k Higher the number of ways higher the entropy Higher the disorder in lights you want to leave on or off in the hall.

[@colorsfun394]

I congratulate you for even daring to deal with area of thermodynamics like this.its a brilliant try to communicate the intrinsic nuances of the area of thermodynamics which people, even if they know, don't know how to get through to other people. Thanks a lot

[@CyberneticOrganism01]

What is perplexing is that, heat can be measured with a thermometer, which is a real physical object. So we think heat must be "real". The 2nd law (which says that entropy strictly increases) implies that heat cannot do useful work. But, we can easily imagine a configuration where there is an energy that looks like heat (to the naked eye), that can be measured with a thermometer, but yet CAN do useful work. With the naked eye we would not know which is which.

[@dimlighty]

Replying to your comment to remind you of your this very old comment.

[@CyberneticOrganism01]

@@dimlighty I don't remember saying that or know what I was talking about 🤣

[@CyberneticOrganism01]

@@dimlighty OK, I rewatched the video and sort of understand what I was talking about...

[@CyberneticOrganism01]

@@dimlighty The commonly accepted explanation is that those "exceptional" states that I referred to are statistically extremely improbable so that they can be ignored. I've always had trouble accepting that...

[@MisterTutor2010]

I have a question. How do you define the number of states (X) can be in? Should the number of possible location and momentums of each particle be infinite? This video does make sense when I consider X in the abstract (not bother with specific numbers).

[@Kram1032]

I wonder, why are a lot of videos, as far as I can tell this one included, not in their apropriate playlist yet? Shouldn't that either go into the physics playlist or in an own thermo-dynamics one? Because frankly, this one is much better than what you have about the topic in the physics playlist. I have yet to check the suggested videos on the right but I'm almost certain, that's the case with most of your newer ones.

[@suryavikramrizal3462]

Sal it was really mind blowing... you are doing a gr8 job.

[@diagonir]

Thank you very much for spending time to help us unenlightened ones ! two thumbs up!

[@s0m0c]

At 21:24 Sal may have meaned: "we`ll call it Boltzmann constant, so it's really just R divided by that."

[@tsingtak642]

I've been searching this kind of video for years and now I have found it.

[@medwatt]

I admit, my mind was blown and my entropy exploded.

[@ull893]

Amazing..Finally it all makes sense !!!

[@TheRoadsidePicnic]

All power to the SAL ! I dont know what it is but this way these videos are explained always seems be nuch better than books or uni,

[@dimlighty]

Replying to your comment to remind you of your this very old comment.

[@subhasissarkar1357]

Thank you so much sir. I was searching for this relation for a long while

[@Oh4Chrissake]

Beautiful. Thank you, Sal.

[@sannathmathapathi]

this was mindblowing

[@idster7]

i definitely do not understand why: 1) the number of possible states the molecules can take in either system is not infinite, and 2) loss of pressure against the piston constituted work done, but loss of pressure filling the empty space did not constitute work done. it is still an exertion of pressure.

[@mr.gakhar397]

Mindblowing explanation sal

[@hahs4]

just to say, i did the exam and your video realllly helped me

[@dimlighty]

Replying to your comment to remind you of your this very old comment.

[@300483rahul]

Sal you are great, thank you so much.

[@dineshbagwe8555]

hii in this video , u use the word state , what that actually mean, its physical state or its position or its state of motion

[@GaudioWind]

Nice video. But can we have a more rigorous definition for the term “state” of each particle? I suppose we can also define entropy for a non ideal gas, right? Would “state” be defined the same way for the atoms and ions in a solid material?

[@KiriharaIzaki]

These videos are still legit in 2013. Thanks Khan.

[@amandadube156]

I love that there's somebody out there who thinks the concept of entropy dramatically changes every few years+

[@dimlighty]

Still legit in 2022.

[@Robotomy101]

can confirm entropy is still the same as of May 2022 this vid is still working

[@chrisrothwell2440]

Thank you. That was great!

[@deepkushagra]

in the statistical model, we started with S as a unitless quantity. it was the number of states. deltaS is also Q/T, which is not unitless. Or is it that by "state" of the system do you mean an aggregate of momentum and position for all the atoms? if yes, then do the units match?

[@koolgokishere]

man.!!!! you are the best.......

[@gooddeedsleadto7499]

Could u explain the reason for replacing x to the power n with log of x to the base e?

[@JimiToBabel]

I did have an AHA moment. That's pretty cool.

[@dimlighty]

Replying to your comment to remind you of your this very old comment.

[@amishah939]

What exactly does Sal mean when he says *X different states of an atom* . Shouldn't each atom have infinite different states?? And what exactly does *state of an atom* mean? I mean what properties are we including??

[@deepkushagra]

how is k from statistical model equal to k from isothermal model... please share the reason for not treating them differently

[@faizagha2362]

How did the configuration of two particles with three potential states go 9?

[@Jtngetabettername]

Does Symmetry lead to entropy, or entropy leads to symmetry? Or are both possible?

[@goedeck1]

If it was a plus sign then would it be (2x)to the n power times x to the n power (product instead of fraction)?

[@fahmidaafreen9855]

BEAUTIFUL

[@blueshadow1996]

Hey..cool..I will check your vids from the start..Great vid man..usefull

[@dimlighty]

Replying to your comment to remind you of your this very old comment.

[@joshux3210]

Where is the previous video where entropy was defined (macroscopically) ?

[@goedeck1]

11:11 does the minus sign factor in when you convert the form of the log terms?

[@JohnnyAmbidextrous]

So the entropy of the the universe is increasing because the universe is expanding. Entropy is driven by the expansion of space-time.

[@norwayte]

That's just great. Thank you, Natural Born Teacher.

[@dimlighty]

Replying to your comment to remind you of your this very old comment.

[@junhanliao1444]

This may be a dumb question... At the very end of the video, do you mean N·ln2 is the number of potential microstates of the system?

[@poemZX]

Maybe im missing something, but why the heck did we just randomly put a logarithm up front on the S= function ?

[@ichimarugin8302]

Beautiful

[@Kram1032]

OH, I see... this is in the Chemistry playlist... I guess I gotta check that playlist for thermodynamics videos too, then...

[@tyrosinekinase]

@CyberneticOrganism01 a thermometer measures temperature (roughly: average energy, an intensive system property), not heat (roughly: total energy, an extensive system property). If you pour two cups of coffee from the same pot, you don't have twice as much temperature, but you do have twice as much heat. The 2nd law does not imply that you can't use heat to do work, only that you cannot do so with 100% efficiency. Some of the heat energy will fail to get converted into work.

[@heramb575]

Aren't there infinite possible states for each particle?

[@DirtBlockGames]

could someone kindly explain to me why it is that temperature doesn't increase when the wall is 'blown open'? The volume increases, so the pressure should decrease... so shouldn't the temperature also decrease? Conversely, if you suddenly compressed the box, wouldn't the temperature increase along with the pressure? Am I right in thinking that the distinction here is that compressing the box takes work and therefore transfers energy to the particles? I'm really not sure. Thanks in advance

[@Jan_D-vm5rk]

@DirtBlockGames Why should the temperature decrease? I think he explains it rather well at 6:37 where he says: "temperature is a measure of average kinetic energy", and because there is nothing which changes the velocity of the atoms, the temperature remains the same. A logic question now would be: in the case of a slowly expanding volume the temperature decreases, so apparently the speed of the molecules must decrease. What is the reason for that in this case? The reason is that in the case of a wall which is at rest, the molecules collide with the wall and are reflected back with the same velocity. So the temperature remains constant. But when they collide with a moving wall they reflect with a lower speed and so the temperature decreases. This can be explained as follows. Let us say that the atoms have a speed v1, and the wall has a low speed v2, both to the right.. Then, as seen from the wall the atoms arrive at a lower speed: v1-v2. As seen from the wall they also reflect with this speed, so v1-v2, but in the other direction. So their speed relative to the wall is now v2-v1. Because the wall moves itself with a speed v2, the actual speed of the atoms is higher, namely (v2-v1)+v2 = 2*v2 - v1. Because v2 is low this has a negative sign, and we are interested in the absolute value of the speed which therefore is v1 - 2*v2.. So we see the speed has decreased. So the temperature decreases. With this kind of molecular calculations we can calculate the loss of energy of the gas in the case of a certain pressure, and it turns out that the result is exactly the same as obtained from the macroscopic rule W=p*∆V , where W is the change of energy, p is the pressure, and ∆V is the change of volume. And yes, you are absolutely right with thinking that the distinction here is that compressing the box takes work and therefore transfers energy to the particles.

[@Cesariono]

But can two particles assume the same state? I feel like this isn't being accounted for.

[@rezaadili1161]

does any body know whats the title of the previous video? i mean the first video introducing entropy thanks

[@elangz9201]

Nice vid khan, but can smbody tell me the definition of the entropy unit J/kg.K means?

[@gary311098]

hey! guys where i can find vdos on exergy and thermodynamic relations( maxwells equations)

[@AndrewCedricThe2nd]

@poemZX did u figure it out?

[@JoshKaufmanstuff]

What drawing program is being used?

[@hahs4]

sal i love you but entropy managed to do the one thing i thought was impossible i dont get it but maybe this is because i have some gaps?

[@dimlighty]

Replying to your comment to remind you of your this very old comment.

[@riturajborah382]

is this how Boltzmann derived that ?

[@saamanthameegoda]

experiencing an ahahaaaaaa!!!! moment nw :D

[@MusicalRaichu]

You haven't given me a convincing explanation of entropy. Firstly, a particle's position is continuous so you can't accurately enumerate the states at all. Secondly, just because you've added heat does not change the number of potential states. There are still the same number of particles in the same volume.

[@MusicalRaichu]

Also in the first example where you just blew away the wall, you said the system was adiabatic, so no heat was added or removed. That means the earlier definition of change in entropy would give you 0, while the state-based definition definitely increases.

[@shaun1098]

@@MusicalRaichu yeah, i am really confused by that. If Q =0 then delta S =0 too? But it isnt as it logically makes sense for it not to be? I am confused big time

[@ahmadd4408]

One assumption made about entropy is that each molecule holds a position in a unit cell lattice, so its position isn't actually continuous.

[@theshaful]

'we know that from common sense'

[@CyberneticOrganism01]

Mind-blowing indeed. But this still doesn't prove the 2nd law via a statistical interpretation. I believe that such a proof is impossible. The ultimate reason is that one cannot derive time-asymmetry from time-symmetric laws of physics. What we regard as heat energy is *subjective*, and thus the second law is also about our subjective knowledge. Is the 2nd law "real"? That is the most intriguing question. I suspect that the law is an illusion that can be broken.

[@HotPepperLala]

A-HA!

[@whittakertheo4593]

He lost me at “if”

[@erikdejong4509]

I haven't had calculus, this is terrible, I understand that concept of what happens on the molecular level but these calculations pff, and I can't find the definition of isostatic and quasistatic.

[@dimlighty]

Replying to your comment to remind you of your this very old comment.

[@joeschmo6925]

Mrs. Dietrich is a terrible teacher...

[@dimlighty]

Replying to your comment to remind you of your this very old comment.