Entropy

[@benjamincordes207]

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]

same here!

[@jonahansen]

Absolutely!

[@Vladislav-x8g]

Arguably the most clear explanation of entropy among these youtube vids

[@DawsJosh]

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

[@bird9]

what have you done ?

[@aidenpearce9066]

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

[@DavidGreybeard]

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.

[@hooh5479]

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.

[@omarfaruqi4743]

Best video on Entropy I've seen so far.

[@musaddikhossain5862]

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

[@jamesmouce]

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]

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]

Thanks a lot!

[@abrahamkassahun5847]

@@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]

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

[@abrahamkassahun5847]

@@gerasimosmelissaratos6058 Yw :D

[@vickybhandari3525]

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

[@adrient3957]

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]

Yes

[@hassanazizi8412]

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

[@vittoriopiaser9233]

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

[@robertsullivan4773]

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 😊😊😊😊😊😊😊

[@akiraming6083]

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

[@LadiesLoveLuis9]

what is entropy again?

[@mikebellamy]

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

[@mikebellamy]

@@veronicanoordzee6440 Ludwig Boltzmann says that..

[@mikebellamy]

@@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]

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

[@mikebellamy]

@@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.

[@christa6181]

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

[@undefined.infinity3106]

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

[@amelienaderprieto5899]

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

[@lucgootjes3552]

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

[@anindoadhikary4323]

This is the 1st time I learned about entropy

[@alexb-private]

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

[@soulscanner66]

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

[@brainstormingsharing1309]

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

[@Anirban456Mandal]

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

[@randallreid2852]

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]

hmmm got it. actually nothing is everything!

[@himanshupadnani]

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

[@rahulmoitra4076]

😆😂

[@corykinservik5470]

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.

[@jacobvandijk6525]

Brilliant! So education can be efficient after all.

[@a.a.zviagin]

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.

[@NOBOX7]

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

[@vikasmange5204]

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

[@yisokolo]

Best explanation I've ever heard!

[@henryswan1374]

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

[@srushtinagargoje5604]

😂

[@yashvanthm1180]

The only video I got some clarification

[@maurocruz1824]

Best explanatory video EVER!

[@willz3222]

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]

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]

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]

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.

[@mdshahporan9069]

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

[@KeysToMaths]

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]

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

[@sundaranarasimhan58]

Thanks for your reasoning

[@theunknownscientist3249]

Best video on entropy

[@mathematicalmuscleman]

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!

[@BratPick]

Such an excellent explanation! Thank you!

[@jamesmonteroso824]

the bessstttt lecture

[@iagosoriano3734]

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

[@pintoguy]

LOL. But you probably meant inverse french.

[@mskEduTech]

Very good video seen so far on microstates/ entropy.

[@user-pk5rc4or2w]

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.

[@ibrahimhussaini2701]

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

[@jeffreypaten1234]

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

[@KnorpelDelux]

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

[@Arjun-zk2kf]

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

[@ahmedsoliman9594]

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

[@johntracy72]

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]

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

[@Catalanos33]

Well done. Thanks for the explanation.

[@mohansundaram100]

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

[@yolangielen1416]

Can the formula on minute 10 be explained? Thanks

[@Sillymarin]

This video was brilliant. Thank you

[@Gaitori]

Would someone be kind enough to explain the binomial expression in 10:02 to me? A secondary 4 student.

[@jonathanjollimore4794]

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

[@daedra40]

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

[@james6518]

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

[@_hrits_d_6249]

It really helped me . Thanks for d effort 🙂🙏

[@elranitya]

Fantastic Lecture

[@vinayseth1114]

But how did he get 8 factorial in the numerator when there were only 5 microstates possible?

[@ParthSabharwal719]

+Vinay Seth Number of ways of distributing n identical objects among r groups is (n+r-1)C(r-1). We have n=5 quanta to be distributed among r = 4 balls.

[@vinayseth1114]

+Parth Sabharwal Ah yes! I had completely forgotten that. Thanks! :)

[@Heizler]

What I don't understand why in the second case he calculated Ω separately for the two systems. Why not to calculate it for the whole system like: Ω = (8+6-1)!/(8-1)!/6!=1716

[@egidijuskuprusevicius4225]

5000(4 times), 4100(4(1st position)x3(all other)=12), 3200(12), 3110(12), 2210(12) and 2111(4) totaling to 56

[@egidijuskuprusevicius4225]

since initially they were two separate systems with different Ts (and in this case Energies too) ... but after they became twice larger system with Ω = (8+3-1)!/(8-1)!/3!=1320 number of states (3 probably corresponds to T and number of states to Energy, but should be only proportional) and this would mean that each having not 20 the final number of states, but 1320/2=660 each

[@josephpc3211]

this is very good explanation. Thanks

[@debalinasengupta9333]

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]

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

[@davidwalker5054]

Entropy is the universe slowly but surely erasing every sign of us humans ever having existed everybody is fighting it every day without realizing it. But it's a losing battle

[@bmanagement4657]

Is life itself possibly a 'resistance' to entropy? Our beings, including plants, as a distillation of energy that holds together overtime in a self-sustaining way? Like accessing our memory is a very efficient computer, it does an amazing amount of computation with what seems to be an intention towards conservation. Our development of language and now film is a continuation of an inheritance of the distillation of efficient energy storage.

[@michaelzimmermann3388]

no, life is no resistance to entropy. nothing can fool the laws of nature, there is no backdoor. Your mistake: you neglect the surroundings: if we are ordered, something else gets to a greater degree disordered. just an example: our body is 37° hot, therefore it glows in the infrared, creating the most "worthless" type of all energies, radiation.

[@ergbudster3333]

Naw. I heard the CIA has a backdoor. They can change the "Laws" of nature/physics/whatever whenever they like. 911 is the perfect example of that.

[@krisvarbenov900]

I just read in a book by Max Tegmark that you can look at life as a way to dissipate energy more effectively. Like how sugar crystals can sit on the ground for years without releasing it's potential energy if it weren't for ants. Same goes for coal, for example, and people. And yes, thinking of life as "resisting" entropy would totally be ignoring the surroundings, but also I think it's a neat trick on behalf of nature to make life in a way to accelerate the increase in entropy.

[@johnz.2907]

The transfer of knowledge from MIT to us is entropic in nature. Lol

[@athiest100]

How 5 states can be distributed in 4 atoms 56 ways ,, please explain ,,why 8!/3!.5!

[@albertkundrat5501]

5:43/13:32 All the microstates presented have an invisible conceptual AXIS of SYMMETRY about each microstate! For example, for row "8", there's (2+6) at the extreme left, yet its reversed equivalence is (6+2) at the extreme right! The extreme middle is (4+4) where the Axis of Symmetry is the + sign between the two 4"s! At the extreme minimum level is row 12, having only (6+6) but could this be really "reflexive" for actually two (6+6)'s that would be reflexive between the parentheses inserted to enclose the two sets of 6+6?, if presented as such: (6+6) (6+6)? Thus I "ASK" this question: if the axis of symmetry is taken away or becomes non-existent, could the property of entropy be gone as well? Could the irony of Entropy be: Entropy, customarily defined as disorder or the measure of disorder of a display of located "moving or inter-relating stuff, spreading from a concentrated state to an extremely expanded "de-concentrated"state, were it to have no "inherent" symmetrical balance within its field of manifestation, would no loner be Entropy in that situation? I ASK another Question: Why are there NO ZERO's in Parentheses with the Numbers in each row? Take again row 8: why is there no (0+8)at the extreme left, and (8+0) at the extreme right? Again, at row 12, why no (0+12) at one end, with (12+0) at the other end? Is it because there's no ABSOLUTE ZERO at that area-Point of Entropy?

[@TwelfthRoot2]

Albert Kundrat I’m not sure where you’re going with this one. It sounds like you’re trying to add the order of rolling dice instead of just considering the resulting sum. For example you could roll die one as a 6 and then roll die two as a 6 or do them in opposite order. And you’re calling this two different states. Well then all of the other states would increase by 2 also. So you don’t change the result of state 7 being most likely and the other possible states cascading to the extremes. So this “axis of symmetry” doesn’t change the result. In a weird way you can think of “ordering” the die roll as essentially “vectorifying” the particles. But entropy is a state variable and not a vector quantity. For example in a jar of particles there are many ways to arrange the particles with position and velocity that could achieve identical macrostates of the same temperature and pressure and entropy. That’s the whole point of state 7 having 6 different microstates. Hopefully this makes sense. I don’t really have the time or patience to break it down any further. Ps, and regarding your comment about zeros, I mean you have to roll the die and it cannot have a zero. In other words the “particle” has to exist in the environment somewhere. Now if you wanted to send that die to a different dimension then it would change the problem we’re considering. After all, the point of this physical discussion is rooted in the idea that a defined physical system is changing over time. The aren’t two different systems with different numbers of dice. We have to use the same number of dice to define every state or else you would have particles appearing and disappearing to other dimensions or something. If an absolute zero existed it means the die didn’t exist. Maybe you missed the fact that the entropy value is a function of the value of the macrostate (left column) and not the value of a microstate (right column).

[@tarunpurohit6522]

Beautiful, Thank You for covering all the important details

[@user-bd1bl8ue9g]

Awesome stuff guys MITOCW rocks

[@ajj-k2t]

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

[@amritanshusrivastava9625]

great explanation

[@bilbobaggins9321]

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?

[@angel_machariel]

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?

[@abelurbina2003]

The WORK OUTPUT is more than double the WORK INPUT. So the theory of entropy is misconception. A 15 ball billiard pool to be striked by white mother ball When I computed the work done in pool (billiard) the white mother ball break the 15ball. F = 30lbs (White Mother Ball); D = 3ft (Distance from the white mother ball to the first ball to strike) SOLVE FOR WORK INPUT W = F X D; W = 30lbs x 3ft = 90Ft.lbs SOLVE FOR WORK OUTPUT First two ball extreme corner of the billiard ball 2 out of 15 ball W = F X D; W = 30lbs x 3ft = 90ft.lbs X 2ball = 180 ft. lbs The remaining ball (13pcs ball) can produce more than 90 ft.lbs The computation shows that the output work done is higher than the input work done Appreciated for your reply Thank you. Abel Urbina

[@bobmoandfriend]

9:59 ; I got absolutely wrecked in the statistical mechanics portion of my PChem class because of this concept. I am having trouble seeing how the picture on the right relates to the equation 8!/(3!5!), yet I am almost certain the answer is quite simple, because whenever I ask about it I get funny looks. Would anyone out there be so kind as to explain this?

[@bobmoandfriend]

Or rather, how does one arrive at n = 8 for n!/[m!*(n-m)! ?

[@elenalabrecque]

I went looking for the answer to this question. I found this: (n+q-1)!/(q!)(n+q-1). That explains the 8!. But does not explain why he had 6!/3!3! at the end.

[@hooh5479]

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. I hope this helps.

[@GGlad100]

Misunderstandings in ideas about entropy and second law Many misunderstandings in understanding the problems of life and evolution from the standpoint of physics and physical chemistry are typically associated with misconceptions in understanding entropy. The term "entropy" coined Rudolf Clausius. According to his "model" of the world (universe), he presented a statement: "The energy of the world is constant. The entropy of the world tends to the maximum". Later this statement was chosen by JW Gibbs as an epigraph to the paper "On the Equilibrium of Heterogeneous Substances". These scientists have given this statement in relation to their model of the universe. This model corresponds to a simple isolated system of ideal gas, i.e. isolated system of ideal gas, energy and volume of this system are constant and in which only the work of expansion is performed. Entropy of such a system can only increase! It should be noted that when we say on ideal model, which would correspond to the real universe, it would be necessary to accept the unreal assumption that any form of energy real universe will be transformed into thermal energy. Only in this case, also under additional unrealistic assumptions, the real universe "would turn" into the model of ideal system of Clausius - Gibbs. However, lovers of science have applied representations on simple systems to systems of other types, in which the interactions takes place between particles of different nature (interactions of molecules or other objects of different hierarchies) and to systems which interact with the environment. Some scientists, who are not professionals in the relevant fields of knowledge, have not escaped such errors. This has led to unimaginable confusion. This has slowed down the development of science, more than on a century. There are thousands of publications in scientific journals and popular literature containing marked misunderstandings. To these were added incorrect ideas on the negentropy and on the dissipative structures in the living world, and the false identification of "the information entropy" with the thermodynamic entropy. The origin of life and its evolution can be easily explained from the standpoint of hierarchical near equilibrium thermodynamics of complex dynamic systems. This thermodynamics established on a solid foundation of equilibrium thermodynamics - thermodynamics of Rudolf Clausius, JW Gibbs and other great scientists. www.membrana.ru/particle/17266 See also: On General Physical Principles of Biological Evolution www.researchgate.net/publication/314187646_On_General_Physical_Principles_of_Biological_Evolution

[@ahmadeldesokey9844]

Mit is the best

[@بوفارسبونورا-ص7ه]

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

[@niravsavaliya823]

Great Explanation

[@fatima-gq3ot]

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

[@IntraFinesse]

2 comments 1 - the material is clear and gets the idea across. A good lesson. 2 - Prof. Lienhard was too robotic, and this detracted from the video. It reminded me of videos from the 60's. He knows his stuff, but would benefit from working on his presentation skills so he comes across as more natural and less stiff. Still a worthwhile video.

[@baz2033]

Grate video. Thanks.

[@davidyoung3288]

universe is in entropy; or continual entropy process; till end of time; universe has microstate and number of possible microstate is by each system's faceted or possible faceted; existence in its ability to form covelant bond for interaction to exist in seamless integration resulting entropy; if we calculate age of universe in rate of entropy; where visible universe is less than 10%; age of universe via entropy should be more than 100b years old;

[@QWRTYPSDFGHJKLZXCVBNM]

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

[@Yagyaansh]

great lesson👍

[@specmarteyecare]

it was awesome, thanks

[@Epiphone1964]

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?

[@km4hr]

Entropy must be one of the most explained concepts ever. Why isn't one explanation good enough? Does anybody really understand it? Let's face it, for most of us it's really just a topic for the Mensa society.

[@divvy1400yam600]

At 9:59 we are told that the hot bar has 56 micro states of energy. I cant understand this. I get 20 The 5 shown in the diagram arranged 4 times. Will someone explain my error? I think the vid. is excellent ! adding:I've just noticed some else has asked the same question.

[@divvy1400yam600]

Having read all comments it seems that few understand the derivation of the 56 microstates. One explanation posted is incomprehensible. So I am downgrading this vid to good.hehehehehehehe My tiny mind is never afraid to be judgemental. I am familiar with the concepts of Combinations. Permetations and Factorials.

[@divvy1400yam600]

divvy1400yam600 Referring to the equation. The use of 3 in 3! implies that one molecule can be at energy level 1 OR energy level 2 while the other 3 are at energy level 1 The use of 5(micro states) in 5! is consistent with that 1 1 1 1 1 1 1 2 1 1 2 1 1 2 1 1 2 1 1 1 8 in 8! represents the SUM of the energy levels (E) and the microstates (M) In words the equation then expresses: The number of combinations of 3 energy levels arranged 5 at a time from a total of 3 energy levels plus 5 micro sates. hehehehehehehehehe plus he

[@divvy1400yam600]

divvy1400yam600 Correction: The number of combinations of 3 energy levels arranged 4 at a time from a total of 3 energy levels plus 5 micro sates MIT here i come I don't think lol Took me a while to figure out and I'm not 100% sure I'm right.

[@divvy1400yam600]

divvy1400yam600 However there exist ONLY 2 energy levels. So why isnt the equation 7! / ( 2! * 5! ) it would be interesting to read a well written explanation from someone who really understands this. A time limited edit feature om utoob would be useful too.

[@julien6893]

+divvy1400yam600 You have 5 different Energy levels the formula for the number of possibilities is here: (n+k-1)!/((n-1)!*k!) with n being the Particles and k the Energy to distribute.

[@mohammedaliyualiyu1855]

Thank you so much,

[@NilanjanaLodh]

@10:01 how is the no. of ,microstates 56?

[@hui-yuanchen8454]

It's the result of "combination with repetition". You can think that the four atoms to be X1, X2, X3, X4, then it's like finding the possible solution combinations for the equation "X1+X2+X3+X4 = 5 ", where "5" comes from the five pairs of curved lines(quantized energies). In mathematical language, H(4,5)=C(4+5-1,5)=8!/(3!5!).

[@jilow]

陳薈元 Possible non-negative integer solutions.

[@CyberMew]

is entropy a state or process or noun or verb???

[@daedra40]

Sorry, I have no classmate at home right now :P

[@nedisawegoyogya]

especially right now

[@masterchief3247]

@@nedisawegoyogya lmao

[@bhavinsinyal8631]

but 56+4 > 20+20......how then we say entropy increased

[@andrzejgajewski359]

Think about dices. A total number of possible combinations in case of dices is not 6+6 = 12 but 6*6 =36. So you shouldn't be adding but multiplying 20*20 > 56*4.

[@bhavinsinyal8631]

ohh yes!!! got it

[@andrzejgajewski359]

Yes, but for two separate systems. A total number of combination in system A is X (i.e 56) and a total number of combination in system B is Y (i.e. 4), but a total number of combination in system A AND B is X*Y (56*4).

[@ShauriePvs]

Andrzej Gajewski you are truly genius!!

[@xaviervangorp4862]

exactly why logarithms are taken converting this multiplication into an addition

[@europaeuropa3673]

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

[@biggerthaninfinity7604]

Great video!

[@EliotMcLellan]

IN A BOUT WITH HIGH TENSION DISORDER THERE MIGHT BE A WORSE BOUT WITH ENTANGLEMENT: ENTROPY CAN MAKE SOME WICKED ENTANGLEMENT

[@EliotMcLellan]

PAYDAY

[@thomasdowe5274]

And so, how would our present system (unverse) reach a state of being a 'Singularity' that could go 'B A N G', and since that singularity, as a 'Mass' would be at absolute zero' Kelvin...?

[@soodehmoallemian]

Thanks for the information :)