Boltzmann.pdf

4
7/21/2019 Boltzmann.pdf http://slidepdf.com/reader/full/boltzmannpdf 1/4    

Transcript of Boltzmann.pdf

Page 1: Boltzmann.pdf

7/21/2019 Boltzmann.pdf

http://slidepdf.com/reader/full/boltzmannpdf 1/4

   

 

 

Page 2: Boltzmann.pdf

7/21/2019 Boltzmann.pdf

http://slidepdf.com/reader/full/boltzmannpdf 2/4

 

 

 

 

  N   

 

 

 

U ∗

 

i  

i   U R  

U R =  U ∗ − i  

i  

 

N   

 

 

 

 

 

 

 

gR(U R)  

  U R  

 

i  

  U R   =   U ∗ − i  

  gR

 

P i  

  i  

 

  i    gT   

P i  = gR(U R)

gT = CgR(U ∗ − i)  

  C  = 1/gT   

log [gR(U ∗ − i)]  

  U ∗  

i

log [gR(U ∗ − i)] ≈ log [gR(U ∗)]− i

  ∂ 

∂U Rlog [gR(U R)]

U ∗

 

 β  = 1/kT   

β  =

∂  log gR∂U 

V,N 

=  1

gR

∂gR∂U 

V,N 

 

log [gR(U ∗ − i)] = log [gR(U ∗)] − βi  

gR(U ∗ − i) = gR(U ∗)e−βi  

 

Page 3: Boltzmann.pdf

7/21/2019 Boltzmann.pdf

http://slidepdf.com/reader/full/boltzmannpdf 3/4

 

P i  

P i =  CgR(U ∗)e−βi = Ae−βi  

 

 

Page 4: Boltzmann.pdf

7/21/2019 Boltzmann.pdf

http://slidepdf.com/reader/full/boltzmannpdf 4/4