Entropy

MIT RES.TLL-004 STEM Concept Videos
Instructor: John Lienhard

This video begins with observations of spontaneous processes from daily life and then connects the idea of spontaneity to entropy.

License: Creative Commons BY-NC-SA

0:00 Introduction
0:51 Prerequisite Knowledge
1:02 Learning Objectives
1:18 Spontaneous Processes
3:04 2nd Law of Thermodynamics
3:22 What is entropy?
3:31 Molecules interact and transfer energy
4:21 Distributing Energy
4:42 Possible sums for a pair of dice
5:18 Dice combinations for each sum
6:14 Heat Diffusion Set-up
6:54 Vibrations in a solid
7:24 Energy transfer
7:46 Evaluating entropy change
9:21 How many different microstates (2)?
10:32 Change in Entropy
12:25 To Review

[DawsJosh]

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

[benjamincordes]

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

[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.

[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.

[hooh]

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.

[omarfaruqi]

Best video on Entropy I've seen so far.

[adrient]

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.

[musaddikhossain]

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

[hassanazizi]

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

[vickybhandari]

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

[vittoriopiaser]

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

[robertsullivan]

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 😊😊😊😊😊😊😊

[christa]

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

[lucgootjes]

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

[brainstormingsharing]

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

[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!

[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.

[vikasmange]

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

[AnirbanMandal]

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

[randallreid]

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