Boltzmann's entropy formula

<p>In <a href="/facts/Statistical_mechanics/6zMsNYYG">statistical mechanics</a>, Boltzmann's entropy formula (also known as the Boltzmann–Planck equation, not to be confused with the more general <a href="/facts/Boltzmann_equation/6oRPrApT">Boltzmann equation</a>, which is a <a href="/facts/Partial_differential_equation/DyPsBlv7">partial differential equation</a>) is a probability equation relating the <a href="/facts/Entropy/s52IXeFz">entropy</a> 
  
    
      
        S
      
    
    {\displaystyle S}
  
, also written as 
  
    
      
        
          S
          
            
              B
            
          
        
      
    
    {\displaystyle S_{\mathrm {B} }}
  
, of an <a href="/facts/Ideal_gas/80EfYGFj">ideal gas</a> to the <a href="/facts/Multiplicity_(statistical_mechanics)/8EcfDu2n">multiplicity</a> (commonly denoted as 
  
    
      
        Ω
      
    
    {\displaystyle \Omega }
  
 or 
  
    
      
        W
      
    
    {\displaystyle W}
  
), the number of real <a href="/facts/Microstate_(statistical_mechanics)/ArXuNn08">microstates</a> corresponding to the gas's <a href="/facts/Macrostate/ArXuNn08">macrostate</a>:
</p>
<table><tbody><tr><td>                    S        =                  k                                    B                                      ln        ⁡        W              {\displaystyle S=k_{\mathrm {B} }\ln W}  </td> <td></td> <td>1</td></tr></tbody></table>
<p>where 
  
    
      
        
          k
          
            
              B
            
          
        
      
    
    {\displaystyle k_{\mathrm {B} }}
  
 is the <a href="/facts/Boltzmann_constant/5DIejyR3">Boltzmann constant</a> (also written as simply 
  
    
      
        k
      
    
    {\displaystyle k}
  
) and equal to 1.380649 × 10−23 J/K, and 
  
    
      
        ln
      
    
    {\displaystyle \ln }
  
 is the <a href="/facts/Natural_logarithm/PnreKEzI">natural logarithm</a> function (or <a href="/facts/Logarithm/QeXaV97q">log</a> base <a href="/facts/E_(mathematical_constant)/coEtSBk8">e</a>, as in the image above).
</p><p>In short, the <a href="/facts/Boltzmann/xDeLroqt">Boltzmann</a> formula shows the relationship between entropy and the number of ways the <a href="/facts/Atom/FoQ4kGN5">atoms</a> or <a href="/facts/Molecule/N9ljSfFq">molecules</a> of a certain kind of <a href="/facts/Thermodynamic_system/VUr0kpWu">thermodynamic system</a> can be arranged.
</p>

Boltzmann's entropy formula open-in-new

Boltzmann's entropy formula