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`.

Explanation

` i= AST^2 e^(-phi/KT)`
`i' = SAST_(1)^2 e^(-e/KT_1)`
` i/i' = (T^2 /T'^2) (e^-(phi/KT)/e^(-phi/KT))`
` i/i' = (T/T')^2 e^(-phi/kT) + e^(-phi/kT)`
` = (T/T')^2 e^(phi/k) ((1/T') - (1/T))`
` i/i' = (2000/2010)^2 e^((4.5 xx 1.6 xx (10^-19))/1.38 xx (10^-23))(1/2010 - 1/2000)`
` = 40000/((201)^2) e^((4.5 xx 1.6)/1.38)(0.0248)`
` = 0.8786/(201)^2 xx 40000 = 0.8699`
` i/i' = 1/0.8699 = 1.1495 = 1.14` .