Einstein relation (kinetic theory) | Wikipedia audio article
Channel: wikipedia tts
Date: 2018-12-28

This is an audio version of the Wikipedia Article:
https://en.wikipedia.org/wiki/Einstein_relation_(kinetic_theory)


00:02:54 1 Special cases
00:03:04 1.1 Electrical mobility equation
00:04:26 1.2 Stokes-Einstein equation
00:07:44 1.3 Semiconductor
00:11:03 1.4 Nernst-Einstein equation
00:12:10 2 Proof of the general case
00:24:29 3 See also



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SUMMARY
=======
In physics (specifically, in kinetic theory) the Einstein relation (also known as Einstein–Smoluchowski relation) is a previously unexpected connection  revealed independently by William Sutherland in 1904,
 Albert Einstein in 1905, and by Marian Smoluchowski in 1906 in their papers on Brownian motion. The more general form of the equation is

  
    
      
        D
        =
        μ
        
        
          k
          
            
              B
            
          
        
        T
      
    
    {\displaystyle D=\mu \,k_{\rm {B}}T}
  where

D is the diffusion constant;
μ is the "mobility", or the ratio of the particle's terminal drift velocity to an applied force, μ = vd / F;
kB is Boltzmann's constant;
T is the absolute temperature.This equation is an early example of a fluctuation-dissipation relation.Two frequently used important special forms of the relation are:

  
    
      
        D
        =
        
          
            
              
                μ
                
                  q
                
              
              
              
                k
                
                  
                    B
                  
                
              
              T
            
            
              q
            
          
        
      
    
    {\displaystyle D={{\mu _{q}\,k_{\rm {B}}T} \over {q}}}
   (Electrical mobility equation, for diffusion of charged particles)
  
    
      
        D
        =
        
          
            
              
                k
                
                  
                    B
                  
                
              
              T
            
            
              6
              π
              
              η
              
              r
            
          
        
      
    
    {\displaystyle D={\frac {k_{\rm {B}}T}{6\pi \,\eta \,r}}}
   (Stokes–Einstein equation, for diffusion of spherical particles through a liquid with low Reynolds number)where

q is the electrical charge of a particle;
μq, the electrical mobility of the charged particle;
η is the dynamic viscosity;
r is the radius of the spherical particle.