Two bodies `A` and `B` having equal surface areas are maintained at temperatures `10^(@)C` and `20^(@)C` . The thermal radiation emitted in a given time by `A` and `B` are in the ratio

Options

A. `1 : 1.15`
B. `1 : 1`
C. `1 : 2`
D. `1 : 4`

Answer

A

Explanation

(1) `E (= ut) prop T^(4)`
`(E_(1))/(E_(2)) = ((T_(1))/(T_(2)))^(4) = ((273 + 10)/(273 + 20))^(4) = ((283)/(293))^(4)`
`= ((293 - 10)/(293))^(4) = (1 - (10)/(293))^(4)`
`1 - (40)/(293) = (253)/(293) = (1)/(293//253)`
`= (1)/(1.15)`