deletions | additions       diff --git a/Convective Efficiency.tex b/Convective Efficiency.tex  index cfe93ca..10a4b2f 100644  --- a/Convective Efficiency.tex  +++ b/Convective Efficiency.tex 
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\end{equation}  with $\Delta T $ the temperature difference between the center of the turbulent element and the surrounding matter averaged over its lifetime. Given the area $A$ of the element and its lifetime $\lambda/\bar{v}$ the total radiated energy is   \begin{equation}  E_{rad} = -\frac{4ac}{3}\frac{T^3}{\kappa \frac{4ac}{3}\frac{T^3}{\kappa  \rho}\frac{\Delta T}{\lambda/2} \frac{\lambda A}{\bar{v}}. \end{equation}  The energy excess content carried by the convective element before dissolving is $\cp \rho \Delta T^{*} V$ with $\Delta T^{*}$ here being the temperature excess of the element over its surroundings at the end of its path. Obviously $\Delta T^{*} \simeq \Delta T$, and in the classic Bohm-Vitense work the choice $\Delta T^{*} = 2 \Delta T$ is made. Using these quantities one can define a convective efficiency $\Gamma$ as  \begin{equation}\label{eq:gamma}  \Gamma = \frac{2 \cp \rho \Delta T V}{\frac{4ac}{3}\frac{T^3}{\kappa \rho}\frac{\Delta T}{\lambda/2} \frac{\lambda A}{\bar{v}}}  \end{equation}