The filament temperature of a light bulb is 2 000 K when the bulb delivers 40 W of power. If its emissivity remains constant, what power is delivered when the filament temperature is 2 500 K?

1 Answer
A08
Mar 8, 2018

We know from Stefan's law that radiating power #P# of a black body is proportional to the 4th power of its absolute temperature #T#.

#=>Pprop T^4#

#:.P_"2000"prop(2000)^4# .......(1) and
#" "P_"2500"prop(2500)^4# .......(2)

Dividing (2) with (1) and inserting given value we get

#P_"2500"/40 = (2500/2000)^4#
#=>P_"2500"= 40xx(5/4)^4#
#=>P_"2500"= 97.66\ W#

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