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Question

Two electric lamps A and B radiate the same power. Their filaments have the same dimensions, and have emissivities eA and eB. Their surface temperatures are TA and TB. The ratio TATB will be equal to

A
(eBeA)1/4
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B
(eBeA)1/2
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C
(eAeB)1/2
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D
(eAeB)1/4
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Solution

The correct option is A (eBeA)1/4
Powerradiatedduetoradiationis,P=eAσT4,wheree= emmisivityσ= Stefans constantA= SurfaceareaofthebodyNow,inthequestion,sinceP,AandσareconstantseT4=constanteATA4=eBTB4TATB=(eBeA)14

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