- #1

- 560

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[tex]P(i) = \frac{1}{Z} e^{-\beta E(i)}[/tex]

where

[tex]Z = \sum_i e^{-\beta E(i)},[/tex]

but how does one actually establish that

[tex]\beta = 1/kT?[/tex]

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- Thread starter center o bass
- Start date

- #1

- 560

- 2

[tex]P(i) = \frac{1}{Z} e^{-\beta E(i)}[/tex]

where

[tex]Z = \sum_i e^{-\beta E(i)},[/tex]

but how does one actually establish that

[tex]\beta = 1/kT?[/tex]

- #2

- 17,449

- 8,439

[tex]U=-\frac{\partial \ln Z}{\partial \beta}[/tex]

and compare with the definition of the temperature,

[tex]U=\frac{3}{2} N k T.[/tex]

- #3

- 3

- 0

I think that Leonard Susskind does this derivation in one of his lectures on statistical mechanics that is available on youtube.

http://www.youtube.com/watch?v=H1Zbp6__uNw"

http://www.youtube.com/watch?v=H1Zbp6__uNw"

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- #4

- 560

- 2

Ah, yes that is certainly a way to go. But how could that result possibly be general? Doesn't the distribution apply to any combination of systems who shares a total energy E and a number of particles N?Take a monatomic ideal gas and derive the mean energy

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