Someone at MIT received a credit for letting go of a balloon, and I'm here for it.

@bird9

3 жыл бұрын

what have you done ?

@aidenpearce9066

2 жыл бұрын

@@bird9 here for someone at MIT received a credit for letting go of a ballon

The best video I've seen on entropy/thermodynamics. I really liked the graphical illustrations and the clear and simple explanations. Thanks a lot.

@omkarpatil9234

7 жыл бұрын

same here!

@jonahansen

Жыл бұрын

Absolutely!

Best video on Entropy I've seen so far.

There are several comments and questions showing that a few things need to be clarified here: 1/ From the thermodynamic viewpoint, entropy "S = Q/T" (in J/K) is measure of the ability of a working fluid at temperature T to convert an amount of thermal energy Q employed in this process into work. In thermodynamics Clausius theorem shows how the variation of S, which can be denoted Delta S can be calculated knowing the variation of Q and possibly T depending on the working conditions imposed. From kinetic theory, we can understand that the lower the entropy for a given working fluid is, the better the conversion system is, as it means that its number of microstates is "low" enough to avoid the much dispersion of thermal energy among the microstates and rather convert it into work. 2/ As regards the combinatorics, I copy and paste what I wrote as replies to comments made further below: First, it is assumed that there are 2 energy levels per atom. So, that makes 8 levels to possibly occupy as one distributes the 5 quanta, with at most 2 per atom. In combinatorics, there is this formula: n!(k!(n-k)!). So with n=8 total number of states and k=5 quanta to distribute, you end up with 8!/(5!3!) possible combinations, which are the 56 microstates for the hot system in its initial state. That said, for the cold system in its initial state, you can disregard the two energy levels per atom as you have only 1 quantum of fixed value to distribute, so whatever atom gets it, it also occupies the same level, and the other level becomes irrelevant in this initial state. In the final state, you conserve the total number of quanta: 5 + 1 = 6, and as the two subsystems thermalize each of these get 3 quanta to distribute among 4 atoms, with at most 2 quanta for an atom. The thing that you need to see is that given there are only 3 quanta to distribute among for atoms, there will always and surely be one among the four which will not be occupied; so given that each atom has 2 energy levels, then we get to distribute 3 quanta over 6 levels in total per each subsystem. Hence with the same combinatorics formula: n!(k!(n-k)!) with n = 6 levels and k = 3 quanta, you get 6!(3!3!) = 20 microstates per each subsystem in their final state after thermalization. The total number of microstates is the product rather than the sum for the whole system made of distinct subsystems: for each microstate in the cold system you have 56 in the hot one; or equivalently, for each of the microstate in the hot system you have 4 in the cold system. In total that makes 224 microstates in the initial state. After thermalization, you get 20 in each subsystem, so the total being their product, your reach 400 in the final state, which is larger than 256. And you recover Delta S_{universe} = k ln(400/256) in J/K. I hope this can help the viewer who has questions.

This is so helpful. In my class they basically introduced entropy like the room metaphor and were like, "moving on." This actually addresses the concept. Muchos Gracias.

Let me briefly describe the math problem. (56 microstates for 5 quanta of energy distributed in 4 atoms) First, you could think this example as a equation "a+b+c+d = 5" Second, you could regard this equation as "distribute 5 objects into 4 categories", and if you need separation of 4 categories, you'll need "3 dividers". Third, imagine you are distributing 5 objects and 3 dividers, just like distribute "+ + + + + | | |", you'll calculate by 8!/5!3! , then you'll come to an answer of "56". If this helps you, don't hesitate to give me a kudos XD.

@gerasimosmelissaratos6058

2 жыл бұрын

It was good up the "3 dividers". 4 categories, understandable, but what are the 3 dividers? Why do we need them and why do we add them to the 5 objects?

@abrahamkassahun5847

2 жыл бұрын

Thanks a lot!

@abrahamkassahun5847

2 жыл бұрын

@@gerasimosmelissaratos6058 As I understand it, the dividers are tools to convert the problem into an easier problem for counting. Any ordering of the quanta and dividers represents a microstate like "+|+|++|+". By counting the number of ways the dividers (or alternatively the quanta) can be positioned in the total space of 8, we can get the number of microstates. We don't simply do a permutation since the relative ordering of the quanta to each other or the dividers to each other doesn't matter.

@gerasimosmelissaratos6058

2 жыл бұрын

​@@abrahamkassahun5847 So that was it. Thank you very much, that "+|+|++|+" was what I was missing.

@abrahamkassahun5847

2 жыл бұрын

@@gerasimosmelissaratos6058 Yw :D

Thank youuu sir !!!!! I have been searching for the real meaning of entropy for a year ,once again thank you!!!

The best, the one and only true definition and demonstration of entropy. Sir, you are a gifted genius.

Wonderful. The entropy, being the most important yet difficult to explain, is marvellously explained in the video. Thank you.

Wow, best video ever on entropy. Thanks a lot to Prof Lienhard and MIT

Such an excellent explanation! Thank you!

Thanks a lot mr. Lienhard, very effective explanation, greetings by a mechanical engineering undergrad student from Italy!

Best explanatory video EVER!

Best explanation I've ever heard!

Absolutely well done and definitely keep it up!!! 👍👍👍👍👍

Sir you so formal looking but still so informal, awesome, just awesome

Much clearer that my old undergraduate thermodynamics courses (almost 20 years ago !). Entropy was a very puzzling concept to me until I started statistical physics courses.

@TCSCskater

Жыл бұрын

Yes

Thanks! This helped clearing things up. Keep posting these videos :)

So clear, so concise and dense, so usefull...Bravo bravo bravo...

Very good video seen so far on microstates/ entropy.

Well done. Thanks for the explanation.

Thankyou for your wonderful explanation with a humble voice sir....and best of luck to you too for here and after..

Brilliant! So education can be efficient after all.

And thank you for having me watch this video ie making it in the first place :D

This video was brilliant. Thank you

this video takes us to the root ,a BIG thanks

the bessstttt lecture

Best video on entropy

I couldn't get in MIT with a gun and mask and a million dollar donation. But this Prod did a very good job giving me a cocktail party coversation understanding of the subject 😊😊😊😊😊😊😊

this is very good explanation. Thanks

Thank you so much,

Fantastic Lecture

thanks to my teacher for uploading the link to this video, I understand much better now

Thanks for the information :)

Great Explanation

it was awesome, thanks

how do you make it clean the room though ? lets put it to work ...

Awesome stuff guys MITOCW rocks

It really helped me . Thanks for d effort 🙂🙏

Great video!

Great Video Thanks !

Damn, This helped so much!

great explanation

great lesson👍

Thank you.

Grate video. Thanks.

Great video

thank you.

Excellent Video - Kudos! Thank you for feeding my curious mind. True knowledge exists in knowing that you know nothing. And in knowing that you know nothing, that makes you the smartest of all. - Socrates

@omkarpatil9234

7 жыл бұрын

hmmm got it. actually nothing is everything!

great, thanks a lot

It was so easy to understand rather than consuming some abstract equation about entropy

That's great video

Can the formula on minute 10 be explained? Thanks

Very good.

The only video I got some clarification

Thanks!

Very well explained...I even emptied a bag of chips to this :D

what is entropy again?

@mikebellamy

5 жыл бұрын

@@veronicanoordzee6440 That is INCORRECT.. Entropy is NOT a measure of energy at all..

@mikebellamy

5 жыл бұрын

@@veronicanoordzee6440 Ludwig Boltzmann says that..

@mikebellamy

5 жыл бұрын

@@veronicanoordzee6440 You clearly don't understand the Boltzmann equation for the absolute entropy of a system of particles.. s = k. ln (W).. "W" or Omega has NO UNITS it is just a COUNT and as such is NOT restricted to the distribution of ENERGY in the system. It is a count of the number of MICROSATES in a chosen MACROSTATE.. and the microstates of any system are the total number of distributions of MOMENTUM (energy) and POSITION (geometry) of the system.. So a container of gas with of two elements with all the atoms of each in opposite halves of the container is a lower entropy state than if all the atoms are mixed. Note mixing in this case involves NO ENERGY EXCHANGE..

@isaac.zeitgeist

5 жыл бұрын

Entropy is a quantity proportional to the amount of energy of a system that can't do any work (sorta)

@mikebellamy

5 жыл бұрын

@@veronicanoordzee6440 That is not the meaning of W in s = k.log W A microstate is a specific distribution of momentum AND position of particles. Which is why a sandcastle is lower entropy than a pile of sand at the same temperature. It is purely an improbable geometry and nothing to do with energy distribution.

A good basic introduction to Chemical Thermodynamics in Physical Chemistry. Physical Chemistry by Peter Atkins takes several hundred pages of heavy duty Mathematics to teach this vital information - buy the book and study!

So if you increase the truth of the system, you also increase the bullshit of the surroundings.

@soulscanner66

7 жыл бұрын

You have accurately summarized the relationship between quality videos like this one and KZread comments. I'm not sure if this applies to the Second Law of Thermodynamics, though ;-)

Ever heard about water-proof sand? Second law of thermodynamics will show you how! This video is part of my group project in Thermodynamics, relating second law of thermodynamics and hydrophobic interaction, which allows the existence of life to occur without breaking the principle of increasing entropy in the universe. Please comment if you have any idea/suggestion for improvements. Thanks! Hopefully we all learn something new from this vid. Enjoy:D 2nd Law of Thermodynamics & Hydrophobic Sand

Microstate is very obviously for describe entropy, but not so chemicaly. Another examples that naerly chemist are: change color in procces transform no2 to n2o4, malting ice, vapour liquid and other. In these case entropy represent by "warm/temperature". It is that material increase or decreace its temperature till to need dissipates internal energy for realize these processes.

Sir thank you ... 🥰👍

Can you please share the link for this whole governing rules series.

thanks professor now i got it entropy is the measure of disorder :ٍ] :D and really you are the best

Mit is the best

About 56. you have : $ $ $ $ $ o o o o the Last o is fixed, then you have to combinate 8 elements, 5 $ With 3 o , then: 8!/(5!*3!). on the other hand, it is suposed all the sistem ( the two bars) are isoleted ( q = 0) from the Univers. Thanks for the video from Spain.

Thanks

This is the 1st time I learned about entropy

The key to understand entropy is that energy is quantized as well as the idea of micro and microstates

What I do not understand is why entropy is calculated separately for the second case where the bars touch. Why isn't it (6+8-1)C(8-1) = 1716 microstates instead of 20 microstates?

@HarryCallahan72

7 жыл бұрын

I was confused too but I think I've got it: this example represents a simplification of more complicated processes, ergo why are they named System and Surroundings when both are exactly the same physical objects? For instance if a hamsters runs on a wheel the wheel is the system and the hamster is the surrounding which transfers energy to the wheel. In this case they aren't actually combining as one heat conductor but the principles should still apply, and be mathematically modelled as per above. Something like that... ;-)

@vsotofrances

6 жыл бұрын

I agree with you, the final number of states should be 1716., the final total entropy ln(1716)=7,44775128 the original total entropy ln(56)+ln(4)= 5,4116460519 , so the increase in universe DSuniv=2,0361052282 . If you take 1716/exp(DSuniv)=224= 56*4 which are the number of original states. ln(56)+ln(4)=ln(224) The problem I think comes from the fact the he is "splitting" the final system into two, to compair the two bars,..this is an "extra gain" of information and therefore the final entropy decreases from ln(1716)=7,44775128 to ln(400)=5,9914645471 (am I right?)

@carloitalogabrieldenegrimi8205

5 жыл бұрын

What I understand is that you calculated all the posible microstates for all the macrostates. Check the dices explanation at min 5:48, the macrostate 7 has 6 microstates but all macrostates have 36 microstates (what you calculated as 1716 in the atoms part) so entropy would tell the chosen configuration would be the macrostate 7 who has more microstated then the others so it increases the entropy of theuniverse the most; any other configuration would increase the entropy too but at the end of the day, to increase the entropy of the universe, the other macrostates would transform eventually in the macrostate 7. In the atom example, i'll show all the posible macrostates where I mean GCN as (G+N-1)! / ((G-1)!*N!) Macrostate_i: MicroCold x MicroHot = MicroTotal M1: 1C4 * 5C4 = 4*56 = 224 (inicial macrostate) M2: 0C4 * 6C4 = 1*84= 84 M3: 2C4 * 4C4 = 10*35= 350 M4: 3C4 * 3C4 = 20*20 = 400 (chosen macrostate that increases the entropy the most) M5: 4C4 * 2C4 = 35*10= 350 M6: 5C4 * 1C4 = 56*4 = 224 M7: 6C4 * 0C4 = 84*1= 84 Total sum: 1716 So given this data I can say that when you are saying 1716, what you are really saying is just that all the quantums in this hyphotetical universe has 1716 ways to arrange between the two sistems but this 1716 ways are divided depending on how the quantums can be arranged in the two sistems that conforms the universe so to summarize, you should think in macrostatic ways ans see which has the highest entropy.

Great..... very well done.... (y) :D

It is fantastic, any normal person like me can understand about the defenition for ENTROPY. Thanyou very much.

Its the best explanation for entropy #mit 🤐 Make me a student of your peace

excellenté 👍

Hmm. I think John Lienhard (Lyin' hard) is one the best computer sims I've ever seen. Got some smart cats over there to MIT alright. Watch the eyes.

That is great. How we calculate the number of possible microstates (Gamma) of a system? is there is a rule for it?

MIT ❤️❤️

I need help with this: entropy seems to be the number of micro states, but it doesn't tell you how much the energy packets are ACTUALLY scattered . Or to be more precise: it doesn't tell the actual scatter-level of energy packets. How do I deal with this?

At 2:30, there is a liquid crystal solution in the pan. Does anyone know what exactly that liquid is?

To all wonderful teachers out there please consider The concepts of entropy or any other subject are not it's ramifications. If you want to impress it's importance to the laymen, a sprinkling of real world value & applications would go a long way. The absence of which is how my underfunded Utah educators lost me. Sincerity a former record holder in truancy.

Recommendable

Guess I'm not MIT material, but I get the concept on entropy now now.

13:25 Gas molecules are animated by Jennifer E. 'French' That's why at 7:31 , we see her country's flag!!!

@rahulmoitra4076

4 жыл бұрын

😆😂

In the given example we see the change of entropy conveniently with rise or fall in temperature. But applying that same logic, how can we describe the entropy change during phase change of materials as we know temperature is constant during the entirety of change of phase ? How does the number of accessible states change during phase change?

@amineaboutalib

Жыл бұрын

when a molecule becomes "freer" during a phase change, it has more accessible microstates even if its kinetic energy is the same

9:49 The number of ways of arranging 5 quanta of energy among the 4 atoms is the same as the number of arrangements of 0's and 1's in the string 01001010 i.e 8C3 = 56 The 0's are the quanta. For example the string 01100010 represents one quantum on one atom, no quanta on the next atom (no 0's between the two consecutive 1's), three quanta on the next and one quantum on the fourth. The string 10100001 represents no quanta on one atom (no 0's before first 1), one quantum on the next, 4 quanta on the next and none on the last.

@TwelfthRoot2

5 жыл бұрын

KeysToMaths this is moving towards Information Theory. There’s it’s called Shannon Entropy.

@sundaranarasimhan58

5 жыл бұрын

Thanks for your reasoning

got it!

So a system with a greater number of possible microstates has higher entropy than a system with a smaller number of possible microstates? This is what I am taking from the video, but it is never explicitly stated that way. Am I correct, or is it more complicated than that?

Why does stretching a rubber band decrease its entropy? I get that the molecules themselves are more aligned, but what effect does that have on energy spread i.e entropy?

great

I have to write a commentary of a book about the second law of thermodynamics, which advices would you give me ?

actual understanding of entropy meaning understand by this video than any other video. thanks to mit professor.

We can observe this process from OUTSIDE as we watch blackholes admit Hawking radiation it gives away the game of what blackholes truly are

The 2nd law of thermodynamics also explains why some processes are irreversible like unscrambling an egg or reconstituting ashes in the fireplace into a log.

@laughhello669

2 жыл бұрын

How... Can you please explain me? I'm an student. It will be very helpful.

the omega keeps confusing me, my mind keeps going to ohms law

@srushtinagargoje5604

3 жыл бұрын

😂

@MuhammadQasim-th3ed

3 жыл бұрын

😅😅😅 ...

How is the entropy of the earth's atmosphere changing if at all and why?

S = 0 , meams equilibrium ; so no energy is transmitted . *Is this means spontaneous process ?*

Beautiful, Thank You for covering all the important details

👍 lecture

At 7:31 the atoms basically become French, right?

@pintoguy

6 жыл бұрын

LOL. But you probably meant inverse french.