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.
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.
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.
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.
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?
@@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.
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
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 😊😊😊😊😊😊😊
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.
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
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.
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.
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!
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.
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.
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;
@@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..
@@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.
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
You have accurately summarized the relationship between quality videos like this one and UA-cam comments. I'm not sure if this applies to the Second Law of Thermodynamics, though ;-)
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
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.
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?
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... ;-)
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?)
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.
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.
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.
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.
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
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?
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.
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?
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?
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?
T changes, but no changes in S in both cases...since going through micro-states is a nonsense (in this case vibrations only)...besides if V=const of the total system then and S must be const and only T with P changes accordingly (PV=nkT because we have N=const and a subthermodinamical energy of the particle do not show up meaning that it is const and unknown).
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...?
I was expecting the total number of microstates from the system and the surroundings to increase, not decrease, as the heat spread from one bar to the next, but it went from 56+4 = 60 down to 20+20=40. Definitely not intuitive that the total number of microstates can decrease, and yet the total entropy still go up. In the end, it is stated that the entropy is proportional to the number of microstates, which seems counter to the total counts in the example given.
The total number of microstates would be the product rather than the sum: 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). I hope this helps.
s far so good, all makes sense but what I don't grasp is why entropy has units of Energy/Temp.? that doesn't make sense, heat should be simply defined as Q (Joule) as T (energy) x Entropy (no units). what does J/K entropy mean?
+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.
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
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
given entropy; or entropy is recognized defined concept ;idea; entropy proves universe cannot have boundaries; because energy; or mass; energy plus object; can expand; but universe cannot expand; becaise unverse = space x motion x mass; thus other side of equal sign; if it expands; then universe size has to expand; but there is no probable cause for universe to expand; universe is set defined paradigm; energy can expand; as shown entropy;and kinetic energy has entropy thus results entropy; but universe cannot have entropy; thus universe does not expand; but kinetic energy expands in universe; thus universe has no boundaries;
Once again: Misunderstandings in ideas about entropy 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 is established on a solid foundation of equilibrium thermodynamics - thermodynamics of Rudolf Clausius, JW Gibbs and other great scientists.
The best video I've seen on entropy/thermodynamics. I really liked the graphical illustrations and the clear and simple explanations. Thanks a lot.
same here!
Absolutely!
Someone at MIT received a credit for letting go of a balloon, and I'm here for it.
what have you done ?
@@bird9 here for someone at MIT received a credit for letting go of a ballon
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.
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.
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.
Yes
The best, the one and only true definition and demonstration of entropy. Sir, you are a gifted genius.
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.
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?
Thanks a lot!
@@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.
@@abrahamkassahun5847 So that was it. Thank you very much, that "+|+|++|+" was what I was missing.
@@gerasimosmelissaratos6058 Yw :D
Thank youuu sir !!!!!
I have been searching for the real meaning of entropy for a year ,once again thank you!!!
Wonderful. The entropy, being the most important yet difficult to explain, is marvellously explained in the video. Thank you.
Thanks a lot mr. Lienhard, very effective explanation, greetings by a mechanical engineering undergrad student from Italy!
Wow, best video ever on entropy. Thanks a lot to Prof Lienhard and MIT
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
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 😊😊😊😊😊😊😊
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.
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
hmmm got it. actually nothing is everything!
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.
So clear, so concise and dense, so usefull...Bravo bravo bravo...
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 to my teacher for uploading the link to this video, I understand much better now
Absolutely well done and definitely keep it up!!! 👍👍👍👍👍
Best explanatory video EVER!
It was so easy to understand rather than consuming some abstract equation about entropy
Best explanation I've ever heard!
actual understanding of entropy meaning understand by this video than any other video. thanks to mit professor.
Sir you so formal looking but still so informal, awesome, just awesome
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!
Brilliant! So education can be efficient after all.
Thankyou for your wonderful explanation with a humble voice sir....and best of luck to you too for here and after..
13:25 Gas molecules are animated by Jennifer E. 'French'
That's why at 7:31 , we see her country's flag!!!
😆😂
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.
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.
How... Can you please explain me? I'm an student.
It will be very helpful.
Best video on entropy
The key to understand entropy is that energy is quantized as well as the idea of micro and microstates
Very good video seen so far on microstates/ entropy.
It is fantastic, any normal person like me can understand about the defenition for ENTROPY. Thanyou very much.
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;
what is entropy again?
@@veronicanoordzee6440 That is INCORRECT.. Entropy is NOT a measure of energy at all..
@@veronicanoordzee6440 Ludwig Boltzmann says that..
@@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..
Entropy is a quantity proportional to the amount of energy of a system that can't do any work (sorta)
@@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.
Such an excellent explanation! Thank you!
the bessstttt lecture
how do you make it clean the room though ? lets put it to work ...
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
The only video I got some clarification
So if you increase the truth of the system, you also increase the bullshit of the surroundings.
You have accurately summarized the relationship between quality videos like this one and UA-cam comments. I'm not sure if this applies to the Second Law of Thermodynamics, though ;-)
Its the best explanation for entropy #mit 🤐
Make me a student of your peace
Can the formula on minute 10 be explained? Thanks
This is the 1st time I learned about entropy
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
Mit is the best
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.
KeysToMaths this is moving towards Information Theory. There’s it’s called Shannon Entropy.
Thanks for your reasoning
Awesome stuff guys
MITOCW rocks
Well done. Thanks for the explanation.
thanks professor now i got it entropy is the measure of disorder :ٍ] :D and really you are the best
This video was brilliant. Thank you
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?
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... ;-)
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?)
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.
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.
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.
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.
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.
Very well explained...I even emptied a bag of chips to this :D
And thank you for having me watch this video ie making it in the first place :D
It really helped me . Thanks for d effort 🙂🙏
S = 0 , meams equilibrium ; so no energy is transmitted .
*Is this means spontaneous process ?*
At 7:31 the atoms basically become French, right?
LOL. But you probably meant inverse french.
We can observe this process from OUTSIDE as we watch blackholes admit Hawking radiation it gives away the game of what blackholes truly are
this is very good explanation. Thanks
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
Fantastic Lecture
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?
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.
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?
when a molecule becomes "freer" during a phase change, it has more accessible microstates even if its kinetic energy is the same
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?
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?
T changes, but no changes in S in both cases...since going through micro-states is a nonsense (in this case vibrations only)...besides if V=const of the total system then and S must be const and only T with P changes accordingly (PV=nkT because we have N=const and a subthermodinamical energy of the particle do not show up meaning that it is const and unknown).
Egidijus Kuprusevicius PV = nkT is an ideal gas equation. That doesn’t even apply here.
Grate video. Thanks.
great explanation
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...?
I was expecting the total number of microstates from the system and the surroundings to increase, not decrease, as the heat spread from one bar to the next, but it went from 56+4 = 60 down to 20+20=40. Definitely not intuitive that the total number of microstates can decrease, and yet the total entropy still go up. In the end, it is stated that the entropy is proportional to the number of microstates, which seems counter to the total counts in the example given.
The total number of microstates would be the product rather than the sum: 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). I hope this helps.
Can you please share the link for this whole governing rules series.
Beautiful, Thank You for covering all the important details
Thanks! This helped clearing things up. Keep posting these videos :)
That is great. How we calculate the number of possible microstates (Gamma) of a system? is there is a rule for it?
s far so good, all makes sense but what I don't grasp is why entropy has units of Energy/Temp.? that doesn't make sense, heat should be simply defined as Q (Joule) as T (energy) x Entropy (no units). what does J/K entropy mean?
I have to write a commentary of a book about the second law of thermodynamics, which advices would you give me ?
How is the entropy of the earth's atmosphere changing if at all and why?
But how did he get 8 factorial in the numerator when there were only 5 microstates possible?
+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.
+Parth Sabharwal Ah yes! I had completely forgotten that. Thanks! :)
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
5000(4 times), 4100(4(1st position)x3(all other)=12), 3200(12), 3110(12), 2210(12) and 2111(4) totaling to 56
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
Guess I'm not MIT material, but I get the concept on entropy now now.
Great Explanation
the omega keeps confusing me, my mind keeps going to ohms law
😂
is entropy a state or process or noun or verb???
IN A BOUT WITH HIGH TENSION DISORDER THERE MIGHT BE A WORSE BOUT WITH ENTANGLEMENT: ENTROPY CAN MAKE SOME WICKED ENTANGLEMENT
PAYDAY
Thank you so much,
given entropy; or entropy is recognized defined concept ;idea;
entropy proves universe cannot have boundaries;
because energy; or mass; energy plus object; can expand; but universe cannot expand;
becaise unverse = space x motion x mass;
thus other side of equal sign; if it expands; then universe size has to expand; but there is no probable cause for universe to expand;
universe is set defined paradigm; energy can expand; as shown entropy;and kinetic energy has entropy thus results entropy; but universe cannot have entropy;
thus universe does not expand; but kinetic energy expands in universe; thus universe has no boundaries;
That's great video
it was awesome, thanks
Great video!
Once again: Misunderstandings in ideas about entropy
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 is established on a solid foundation of equilibrium thermodynamics - thermodynamics of Rudolf Clausius, JW Gibbs and other great scientists.
"the origin of life can be easily explained".. !! Really.. Please just give one reference that actually demonstrates..
MASS + ENERGY = INFORMATION
At 2:30, there is a liquid crystal solution in the pan. Does anyone know what exactly that liquid is?
Great video
Thank you.
please i cant understand why does equilibrium happen when evenly spread happens ?
MIT ❤️❤️
How 5 states can be distributed in 4 atoms 56 ways ,, please explain ,,why 8!/3!.5!