Determine the factor by which the emission current changes when the temperature of a tungsten filament is increased from 2000 K to 2010 K . The work function of tungsten is 4.5 eV .

Step-by-step solution

According to the Richardson-Dushman equation, the emission current I is given by: I = A T^2 e^ - W kT Taking the natural logarithm on both sides: I = A + 2 T - W kT Differentiating with respect to T : dI I = 2 T dT + W kT^2 dT Given values are T = 2000 K , dT = 10 K , W = 4.5 eV , and Boltzmann constant k 1 11600 eV/K . Substituting these values: dI I = 2 10 2000 + 4.5 11600 10 (2000)^2 dI I = 0.01 + 522000 4000000 dI I = 0.01 + 0.1305 = 0.1405 The new emission current is I' = I + dI = I(1 + 0.1405) = 1.1405 I . Th