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In statistical mechanics, Boltzmann's equation is a probability equation relating the entropy S {\displaystyle S} , also written as S B {\displaystyle S_{\mathrm {B} }} , of an ideal gas to the multiplicity , the number of real microstates corresponding to the gas's macrostate:
where k B {\displaystyle k_{\mathrm {B} }} is the Boltzmann constant and equal to 1.380649 × 10 J/K, and log {\displaystyle \log } is the natural logarithm function.
In short, the Boltzmann formula shows the relationship between entropy and the number of ways the atoms or molecules of a certain kind of thermodynamic system can be arranged.
Equation in statistical mechanics Boltzmann's equation—carved on his gravestone. S = k B log W {\displaystyle S=k_{\mathrm {B} }\log W}