# Accounting for the thermal excitation in the Richardson-Dushmann equation or the work function equation

When accounting for thermal excitation in a system that is not in thermal equilibrium, heat is constantly flowing through a material, should I account for the thermal excitation in the work function equation as well as the Richardson-Dushmann equation? Due to the fact that the Fermi level will change when accounting for thermal excitation, which variables should I alter in accounting for heat? Here's an equation which may be relevant: $$J=A_G T^2 \cdot\exp{\cfrac{-W}{kT}} \, .$$

• Titles should not have a question mark unless it's actually an English question, and should only capitalize the first word and any proper nouns. See this meta post for information on titles. Also, I modified the last part of the question to be a complete sentence. Please modify to make it more clear what that equation actually is. – DanielSank Jul 31 '15 at 21:07