Stefan–Boltzmann law

The Stefan–Boltzmann law, also known as Stefan's law, describes the intensity of the <a href="/facts/Thermal_radiation/1PD9jtCv">thermal radiation</a> emitted by matter in terms of that matter's <a href="/facts/Temperature/QyGe4gmj">temperature</a>. It is named for <a href="/facts/Josef_Stefan/CjkQUM7t">Josef Stefan</a>, who empirically derived the relationship, and <a href="/facts/Ludwig_Boltzmann/xDeLroqt">Ludwig Boltzmann</a> who derived the law theoretically.
For an ideal absorber/emitter or <a href="/facts/Black_body/f0fHghDy">black body</a>, the Stefan–Boltzmann law states that the total <a href="/facts/Energy/wd8PrQM7">energy</a> radiated per unit <a href="/facts/Area/KsNG1G9t">surface area</a> per unit <a href="/facts/Time/HceJKUGB">time</a> (also known as the <a href="/facts/Radiant_exitance/US1T54p8">radiant exitance</a>) is directly <a href="/facts/Proportionality_(mathematics)/xDQmfh6t">proportional</a> to the fourth power of the black body's temperature, T:

M
          
            ∘
          
        
        =
        σ
        
        
          T
          
            4
          
        
        .
      
    
    {\displaystyle M^{\circ }=\sigma \,T^{4}.}

The <a href="/facts/Constant_of_proportionality/xDQmfh6t">constant of proportionality</a>, 
 
 
 
 σ
 
 
 {\displaystyle \sigma }
 
, is called the Stefan–Boltzmann constant. It has the value

σ = 5.670374419...×10−8 W⋅m−2⋅K−4.<a class="footnote-ref" id="fnref:1" href="#fn:1">1</a>
In the general case, the Stefan–Boltzmann law for radiant exitance takes the form:

M
        =
        ε
        
        
          M
          
            ∘
          
        
        =
        ε
        
        σ
        
        
          T
          
            4
          
        
        ,
      
    
    {\displaystyle M=\varepsilon \,M^{\circ }=\varepsilon \,\sigma \,T^{4},}

where 
 
 
 
 ε
 
 
 {\displaystyle \varepsilon }
 
 is the <a href="/facts/Emissivity/LUxfMRRI">emissivity</a> of the surface emitting the radiation. The emissivity is generally between zero and one. An emissivity of one corresponds to a black body.

Stefan–Boltzmann law open-in-new

Stefan–Boltzmann law