ฝัง
- เผยแพร่เมื่อ 8 ก.พ. 2025
- Short physical chemistry lecture on the partition function.
The probability of the system being in one of the possible energy states is 1 (100%). The normalization constant for the probabilities is the sum of the Boltzmann factors of each state. This quantity is the partition function, which contains all information about the properties of the system.
Notes Slide: i.imgur.com/zC5...
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this is 1000 times more clear than my professor
I think theres something wrong with your partition function notation Q, when you sum over the states and use index i, the E_i would also change , so you change/sum over the energy level and not the states which you say it will do? Confusing
in partition function if you sum over them with respect to states, all states would have different Ei. and this is different from when you sum over them with respect to E levels. I think there's something wrong with former equation. and from what i understood from this lecture, i get QC=1. hope you'd help me
Very small systems (like atoms and molecules) obey the laws of quantum mechanics, which means that their physical properties are quantized in certain allowed states. Each state has an average value for every physical property: position, momentum, energy, etc. If we do the sum over all states, each state has a value of E which we substitute in to its terms in the sum, giving us its Boltzmann factor, and summing up to the partition function. Some states have the same energy, i.e. they are degenerate. Instead of summing these states separately, we can lump them together into an "energy level", where all states with that energy E_i are included, and we multiply by the number of states with E_i, i.e. the "degeneracy" of the energy level, g_i. The partition function ends up being the inverse of our coefficient between probability of a state (level) and its Boltzmann factor (times degeneracy), so QC = 1 would be true.
Maybe it's because english isn't my first language so i'm having trouble with it. If # of E level is 3 and # of states is 10, there will be E1~E10 in the former equation and E1~E3 in the latter equation. and it seems wrong with me. am i getting this wrong? and former equation makes E of each states different, though in actuality there're states with same E level.
The indices are different in each summation. The first sum is over states, in which each term in the sum is a distinct quantum state. Every state has a different i. The second sum is over energy levels, in which each term in the sum is the set of all states with the given value of energy. Every state with the same energy is represented with a given energy level. Every energy level has a different i. If the index variables are causing the issue, then change the index variable in the second sum to a sum over j with the energies being E_j and degeracies being g_j.
TMP Chem then could E1 and E2 from the first sum be the same E value ?
Correct. Any two values of E_i could be equal in the first sum. All values of E_i are distinct in the second sum.
amazing video, just one thing that I can't get my head around, what is the difference between i and j?
Nothing, just a different subscript
How do I double-like the video?
Like it with another account ;)
I just did ;)
Degenerates
You have two p_i's that looks confusing. Is C = 1/Q ?
Yes, C = 1/Q in this case.
Hi @TMPChem. I want to ask why is 'C' = 1/Q? How do you get to the white line on the RHS? Thank you.
How do we know that partition function will be an integer?
It doesn't have to be
My professor should watch this video
Many professors do watch these videos. ;)
Is it me just wildly speculating or does this actually relate to your lecture?
Particle in a box model
Thanks for your well produced video.
Your viewers might enjoy seeing my personal amateur science project in the visual aid linked below.
It uses a sheet of spring-like material buckled from the ends to form a Gaussian curve. This is to represents a two dimensional field with the ends bounded.
Seeing the mechanical effect may also takes some of the mystery of what the math is showing.
See the load verse deflection graph in the white paper found elsewhere on my TH-cam channel.
th-cam.com/video/wrBsqiE0vG4/w-d-xo.htmlsi=waT8lY2iX-wJdjO3
Noice
Aye
If you use 'g' you are talking of a level.