Mod-01 Lec-21 Some probability distributions; isolated system

[@soumiksamanta10]

The beauty & essence of statistics and probability distribution in statistical mechanics was described through this video is really awesome. Best teacher ❤️

[@Akash_Tyagi_93]

He is the best teacher I've noticed in this NEPTELhrd series . Thank you very much Sir, FROM IIT Kanpur.

[@chanky1000]

17:55 It's a non trivial trick, and it takes a non trivial person to find it. Poisson found this in 1815. Beautiful!

[@arghyamazumder4368]

Yeah,I am impressed

[@maujo2009]

I have found these lectures EXTREMELY helpful! Thx NPTELHRD! If available, please upload Classical Electrodynamics lectures.

[@supern0is349]

this is priceless.Seriously.A guy this smart teaching for free?Unbelievable thanks a lot for the video

[@sanchayanbanerjee7623]

just GOD.... !!!!!! CAMERA WORK & sound is also outstanding

[@03Kabbotta11]

He finally forgot something! After hours and hours of this brilliant man's lectures he finally forgot some little factor in Stirling's Approximation. He is human after all ; )

[@Tyns19]

Michael Chapman where is the error plz!!

[@swapnilganeshpure]

May be becquse he looks unwell in this lecture.

[@elamvaluthis7268]

Very excellent explanation 😁😁😁.

[@kunalverma6940]

Around 26:00, Dr. Balakrishnan doesn't do a Stirling approximation for n! because it varies from 0 to \infty, but so does the number (N-n)! (from \infty to 0) , so why is the Stirling Approximation valid in that case?

[@shambhavimishra8928]

Actually, N>>n, so (N-n) doesn't go from infinity to zero.

[@abbeselhabib2435]

very helpful for me and 'الفيلسوف عبد الصمد"

[@sagarmalhotra4473]

I don't really get the reasoning behind taking the integral from negative infinity to plus infinity at 15:58 , whereas in the gamma function the limits are from 0 to infinity.

[@TheBobathon]

it's a valid approximation because the area under the gaussian for x0, when n is large. You can check this for a given value of n using normal distribution tables if you want to be sure

[@meonyoutube2977]

how is Stirling's approximation justified for (N-n)! when n is variable from 0 to infinity?

[@shambhavimishra8928]

Actually, N>>n, so (N-n) doesn't go from infinity to zero.

[@elamvaluthis7268]

Very nice thank you.

[@ayushpaliwal1880]

I didn't get the N^(2/3) thing (particles near the wall), how ?

[@jdidiieiee462]

N proportional to V => N ~ L^3 => N^(1/3) ~ L, also S ~ L^2 => S ~ N^(2/3) irrespective of number of dimensions

[@mayanksharma828]

I have a dout . I would be grateful if someone can clear it. In 20:51 , How can we assume that particles are moving independent of each other. I understand that there is no explicit interaction between particles ,but due to thermal energy particles will collide . I don't know what can such an event be considered statistically independent.

[@kunalverma6940]

From what I can understand, by "independently moving", Dr. Balakrishnan does not mean that they aren't colliding. Instead, it means that the probability of a particle to be inside the small volume v is "independent" of (or you could say isn't affected by) some other particle being inside that small volume v. A particle sitting inside that volume can't cause another particle to "not be" inside that volume.

[@alokkumar3703]

🙏🙏🙏

[@pankajkumarsah1013]

thanks sir

[@karabomothupi9759]

Indian Einstein

[@joshuayao6236]

Wonderful lectures