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Question

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.

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Solution

Given:
Work function of tungsten = 4.5 eV
Initial temperature of tungsten filament, T = 2000 K
Final temperature of tungsten filament, T' = 2010 K
Let the emission current at (T = 2000 K) be i.
Let the emission current at (T' = 2010 K) be i'.
The emission currents are given by
i=AST2e-ϕ/kT
i'=AST'2e-e/kT'
Dividing i by i', we get:
ii'=T2T'2e-ϕ/kT'e-ϕ/kT'ii'=TT'2e-ϕ/kT+ϕ/kT'=TT'2eϕk1T'-1Tii'=200020102e4.5×1.6×10-191.38×10-2312010-12000.=40000(201)2e4.5×1.61.38(-0.0248)=0.8786(201)2×40000=0.8699ii'=10.8699=1.1495=1.14

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