Editing Lambert W function (section)

=== Thermodynamic equilibrium ===
If a reaction involves reactants and products having [[heat capacity|heat capacities]] that are constant with temperature then the equilibrium constant {{mvar|K}} obeys
: <math>\ln K=\frac{a}{T}+b+c\ln T</math>
for some constants {{mvar|a}}, {{mvar|b}}, and {{mvar|c}}. When {{mvar|c}} (equal to {{math|{{sfrac|Δ''C<sub>p</sub>''|''R''}}}}) is not zero the value or values of {{mvar|T}} can be found where {{mvar|K}} equals a given value as follows, where {{mvar|L}} can be used for {{math|ln ''T''}}.
: <math>\begin{align}
-a&=(b-\ln K)T+cT\ln T\\
&=(b-\ln K)e^L+cLe^L\\[5pt]
-\frac{a}{c}&=\left(\frac{b-\ln K}{c}+L\right)e^L\\[5pt]
-\frac{a}{c}e^\frac{b-\ln K}{c}&=\left(L+\frac{b-\ln K}{c}\right)e^{L+\frac{b-\ln K}{c}}\\[5pt]
L&=W\left(-\frac{a}{c}e^\frac{b-\ln K}{c}\right)+\frac{\ln K-b}{c}\\[5pt]
T&=\exp\left(W\left(-\frac{a}{c}e^\frac{b-\ln K}{c}\right)+\frac{\ln K-b}{c}\right).
\end{align}</math>

If {{mvar|a}} and {{mvar|c}} have the same sign there will be either two solutions or none (or one if the argument of {{mvar|W}} is exactly {{math|−{{sfrac|1|''e''}}}}). (The upper solution may not be relevant.) If they have opposite signs, there will be one solution.