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The work function of a thermionic emitte...

The work function of a thermionic emitter is `4.5 eV`. By what factor does the thermionic current incease if its temperature is raised from `1500 K to 2000 K`?

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If `i_1 and i_2` represent the thermionic currents at temperatures `T_1 = 1500 K and T_2 = 2000 K` respectively,
`i_1 = AST_1^2 e^((-varphi)/(kt_1))`
and `i_2 = AST_2^2 e^(-varphi)/(kt_2)`.
Thus, `i_2/i_1 = (T_2/T_1)^2 e^(- (varphi)/k N2 (1/T_2 - 1/T_1)`.
Putting the value of `T_1, T_2, varphi and k`
`i_2/i_1 = 10625`.
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