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A spherical ball of radius 1cm coated wi...

A spherical ball of radius 1cm coated with a metal having emissivity 0.3 is maintained at 1000 K temperature and suspended in a vacuum chamber whose walls are maintained at 300 K temperature. Find rate at which electrical energy is to be supplied to the ball to keep its temperature constant.

Text Solution

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It is given thatthe temperature ofball is constant. Thismeans that the rate at which it is loosing heat by radiation must be equal totherate atwhich heat issupplied tothis ball externally to keep its temperature constant.
The rate ofheat loss by the ball is given as
`(dQ)/(dt)=eAsigma(T^(4)-T_(s)^(4))`
`=0.3xx4pi(0.01)^(2)xx5.67xx10^(-8)xx[(1000)^(4)-(300)^(4)]`
`=21.1W.`
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