Distance between sun and earth is `2 xx 10^(8)` km, temperature of sun 6000 K, radius of sun `7 xx 10^(5)` km, if emmisivity of earth is 0.6 , then find out temperature of earth in thermal equilibrimum.

Options

A. 400 K
B. 300 K
C. 500 K
D. 600 K

Answer

B

Explanation

For thermal equilibrium
energy received by earth = Energy emmited by earth
`(T_(s)^(4) xx R_(s)^(2))/(4 xx d^(2) xx e) =T_(e)^(4) `
`rArr ((6000)^(4) xx (7 xx 10^(8))^(2) )/( 4 xx (2 xx 10^(11))^(2) xx 0.6)=T_(e)^(4)`
`rArr (36 xx 36 xx 7 xx 7 )/( 4 xx 4 xx 0.6) xx 10^(6)=T_(e)^(4)`
`rArr 66.15 xx 108 =T_(e)^(4)`
`T_(e)= 300K`