A sphere of `3 cm` radius acts like a black body. If it is in equilibrium with its surrounding and absorb `30 K` watt of energy radiated to it from the surrounding. Then the temperature of the sphere will be:

Options

A. `816`
B. `916`
C. `1616`
D. `2616`

Answer

D

Explanation

Radius of sphere `r=3cm=0.3m` the energy absorbed
`E = 30kW = 30xx10^(3)` watt
Energy absorbed by black when the temperature of surrounding is `T`, is given by
`E= sigma AT^(4)`
or` 30xx10^(3)=5.672xx10^(-8)xx4 pi(0.03)^(2)xxT^(4)`
`30xx10^(3)=0.64xx10^(-8)xxT^(4)`
`T^(4) = (30xx10^(3))/(0.064xx10^(-8)) = 46.875xx10^(12)`
`=2.616xx10^(3) = 2616K`.