If the temperature of a tungsten filament is raised from 2000 K to 2010 K, by what factor does the emission current change? Work function of tungsten is 4.5 eV.

Sol. i = AST^2 e^-∅/KT i’ = AST^12 e^-∅/KT i/I’ = T^2/T^12 e^-∅/KT/e^-∅/KT’ ⇒ i/i’ = (T/T’)^2 e^-∅/KT +∅KT’ = (T/T’)^2 e^∅KT’-∅/KT ⇒ = i/i’ = (2000/2010’)^2 e^-4.5*1.6*10^-19/1.38*T*10^23 (1/2010 – 1/2000) = 0.8690 ⇒ i/i’ = 1/0.8699 = 1.1495 = 1.14