Thank you so much for these videos! I am attempting to get the jump on concepts in physical chemistry before the semester starts and this is so easily digestible and useful
I may predict that your video is going to get some what viral, as algorithm is now suggesting it in India and your views may rise to 10K As expected of such a high quality content.
@@PhysicalChemistry for reference see this video ua-cam.com/video/Ez2EaGNt-u8/v-deo.html , sir started making video at the time when there was no other person was making, even though his concept might not be at that level, but there is a demand in India for educational content.
@@PhysicalChemistry Just a Suggestion If You would make videos on some of the good olympiads(ICHO) and JEE Advanced Questions (a exam in India for class 12 th student , very tough exam) and do concept linking of these questions with the video you already made., then In can bet that within a month your subscriber count can go more than 10 fold, and once there are subscriber more than 10K then you must launch a discord channel, as it will form a community where students can discuss and resulting in some content for you to make video on , questions which are confusing or some concepts which may need further clarification.
@@lakshaymission548 Thanks for the suggestions. I'm in the US, so I don't know anything about the JEE. You'll probably have to rely on some engineering or chemistry profs in India to make that content.
Prof. Stuart, thank you so much for these amazing videos, they are definitely the best lectures I've found on statistical mechanics! I just have question about the Boltzmann Distribution: in your previous video you defined it as the probabilities that maximize S_molar/k(that constant that multiplies -sumPi*lnPi). Isn't this constant k in the entropy equation supposed to be the Boltzmann constant (Kb)? When I tried to derive the distribution as dS/dPi, keeping k on the equation, I've obtained the Boltzmann factor as e^(-beta*Ei/k), so when I try to define beta as a function of the temperature I get that beta = k/T, k being, thus, 1/Kb, the inverse of what it was supposed to be in the entropy equation. Could you please help me figure out what I am doing wrong?
You've done everything right, at least up to finding that your Boltzmann factor is exp(−βEⱼ/k), where this k is the one in the entropy expression. Essentially, you have changed the scale of your function to be maximized by a factor of k, but without changing the scale of your constraints, so the Lagrange multiplier gets scaled by a factor of k as well. Your β is proportional to my β, but differs by a factor of k. Then, solving for β should eventually give you β = 1/T, not k/T. So you might have an algebra error here. Again, your new β differs from my β by a factor of k.
You don't have to maximize S/k to get it **correct**. But if you maximize S instead of S/k, then you just have to keep in mind that your β will have a different value than the one that you see conventionally. Once all of the β are replaced by k_B and T, however, you'll end up with the same result either way.
Great as your other videos. thanks for spending time for us
My pleasure!
Thank you so much for these videos! I am attempting to get the jump on concepts in physical chemistry before the semester starts and this is so easily digestible and useful
That's a great use for these videos. Good job planning ahead
How'd PChem end up going?
I may predict that your video is going to get some what viral, as algorithm is now suggesting it in India and your views may rise to 10K
As expected of such a high quality content.
I'm not sure how viral any PChem video could ever get, but I certainly appreciate your enthusiasm!
@@PhysicalChemistry for reference see this video ua-cam.com/video/Ez2EaGNt-u8/v-deo.html , sir started making video at the time when there was no other person was making, even though his concept might not be at that level, but there is a demand in India for educational content.
@@lakshaymission548 3M views for a kinetics video! You're right, there must be plenty of PChem fans on UA-cam. Congrats to him.
@@PhysicalChemistry Just a Suggestion If You would make videos on some of the good olympiads(ICHO) and JEE Advanced Questions (a exam in India for class 12 th student , very tough exam) and do concept linking of these questions with the video you already made.,
then In can bet that within a month your subscriber count can go more than 10 fold, and once there are subscriber more than 10K then you must launch a discord channel, as it will form a community where students can discuss and resulting in some content for you to make video on , questions which are confusing or some concepts which may need further clarification.
@@lakshaymission548 Thanks for the suggestions. I'm in the US, so I don't know anything about the JEE. You'll probably have to rely on some engineering or chemistry profs in India to make that content.
Prof. Stuart, thank you so much for these amazing videos, they are definitely the best lectures I've found on statistical mechanics! I just have question about the Boltzmann Distribution: in your previous video you defined it as the probabilities that maximize S_molar/k(that constant that multiplies -sumPi*lnPi). Isn't this constant k in the entropy equation supposed to be the Boltzmann constant (Kb)? When I tried to derive the distribution as dS/dPi, keeping k on the equation, I've obtained the Boltzmann factor as e^(-beta*Ei/k), so when I try to define beta as a function of the temperature I get that beta = k/T, k being, thus, 1/Kb, the inverse of what it was supposed to be in the entropy equation. Could you please help me figure out what I am doing wrong?
Or is it that I actually must derive S/k to obtain the correct result?
You've done everything right, at least up to finding that your Boltzmann factor is exp(−βEⱼ/k), where this k is the one in the entropy expression.
Essentially, you have changed the scale of your function to be maximized by a factor of k, but without changing the scale of your constraints, so the Lagrange multiplier gets scaled by a factor of k as well. Your β is proportional to my β, but differs by a factor of k.
Then, solving for β should eventually give you β = 1/T, not k/T. So you might have an algebra error here. Again, your new β differs from my β by a factor of k.
You don't have to maximize S/k to get it **correct**. But if you maximize S instead of S/k, then you just have to keep in mind that your β will have a different value than the one that you see conventionally. Once all of the β are replaced by k_B and T, however, you'll end up with the same result either way.
@@PhysicalChemistry Thank you very much, professor! I actually had an algebra mistake somewhere, I've managed to correct it.
Butane? More like "Bro, the quality of these videos is off the chain!" 👍
(the *carbon* chain 😎)
Thank you so much. This was really helpful
Great video