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.

Explanation

It is given that the temperature of ball is constant. This means that the rate at which it loosing heat by radiation must be equal to the rate at which heat is supplied to this the rate of heat loss by the ball is given as
`(dQ)/(dt)=eAsigma(T^4-T_s^4)`
`=0.3xx4pi(0.01)^2xx5.67xx10^-8xx[(1000)^4-(300)^4]`
`=21.1W`
Thus electrical energy must be supplied to the ball at a rate of 21.1 W.