Physics 32.5 Statistical Thermodynamics (9 of 39) Number of Microstates Analyzed N=10

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In this video I will analyze the number of microstates when N=10.

Next video in the polar coordinates series can be seen at:

[岡安一壽-gy]

ni:the number of particles in energy level εi
gi:the number of quantum states in energy level εi
N=n1+n2+･･･+nk
E=n1ε1+n2ε2+･･･+nkεk
(n1, n2, ･･･, nk):the distribution
W = W(n1, n2, ･･･, nk):the number of states
P = P(n1, n2, ･･･, nk):the probability
【Assumption】P = W Π{exp(-α-βεi)^ni = W exp(-αN-βE)
ln P = ln W -αN-βE
In equilibrium, ∂(ln P)/∂ni = 0.
Therefore, ∂(ln W)/∂ni - α- βεi = 0 (1)
●FD statistics
W =
By using 【Assumption】 and (1),
ni/gi=1/{(1/N)exp(α+βεi)+1}
●BE statistics
W =
By using 【Assumption】 and (1),
ni/gi=1/{(1/N)exp(α+βεi)-1}

In equilibrium, by using (1)
∂(ln W)/∂ni = ∂(ln W)/∂N + {∂(ln W)/∂E}εi = α + βεi
Therefore, α = ∂(ln W)/∂N, β = ∂(ln W)/∂E
Since entropy S = kB ln(W/N!),
α = ∂(ln W)/∂N = (1/kB)∂(S +ln N!)/∂N = -μ/(kB T)+ ln N,
β = ∂(ln W)/∂E = (1/kB)∂(S +ln N!)/∂E = 1/(kB T).
Accordingly,
●FD statistics
ni/gi=1/{exp{β(εi-μ)}+1}
●BE statistics
ni/gi=1/{exp{β(εi-μ)}-1}

[kidamaroo]

I think you goofed when filling the table in. You wrote 254 for Wmax instead of 252.

[myzorro]

Very well done dear Michel. May I suggest a serie about two very important matters now a day. Informatics on a methematical and programmation point of vue and quantum physics on both precedent point of vue. If you find the necessary time of course....

friendly
Bernard v lierde.

[myzorro]

Ow.. quantum physics on a methematical (theoretical) and pratical applications way of course, sorry. Thanks a lot..

[fauziahbintisulaiman-]

can't wait for the rest of the video:-)