Two spheres of the same material have radii 1 m and 4 m and temperature 4000 K and 2000 K respectively. Ratio of the energy radiated per second by the first sphere to that by the second is . . . . . .

Options

A. `1:1`
B. `16:1`
C. `4:1`
D. `1:9`

Answer

A

Explanation

According to Stefan-Boltzmann.s law, the amount of radiant energy emitted from a surface of area A
`W=esigmaAT^(4)`
A = Area of a sphere of radius r
`r_(1)=1m,r_(2)=4m`
`T_(1)=4000K`
`T_(2)=2000K`
`A=4pir^(2)`
`W=esigma(4pir^(2))T^(4)`
`:.W propr^(2)T^(4)`
`:.(W_(1))/(W_(2))=((r_(1))/(r_(2)))^(2)((T_(1))/(T_(2)))^(4)=((1)/(4))^(2)((4000)/(2000))^(4)`
`=1/(16)xx16=`
`:.(W_(1))/(W_(2))=1:1`