Two bodies A and B emits radiant energy at the rate of `1.6xx10^(6)J//m^(2)//s` and `8.1xx10^(6)J//m^(2)//s` from its surface. If the temperature of A is `227^(@)C`, the temperature of B will be

Options

A. 500 K
B. 400 K
C. `524^(@)C`
D. `477^(@)C`

Answer

D

Explanation

According to Stefan's law
`E=sigmaT^(4)`
`(E_(1))/(E_(2))=((T_(1))/(T_(2)))` or `(T_(1))/(T_(2))=((E_(1))/(E_(2)))^(1//4)`
Substituting the values, we get
`(T_(2))/(T_(1))=((E_(2))/(E_(1)))^(1//4)=((8.5xx10^(6))/^(1//4))/(1.6xx10^6)=(3)/(2)`
As, `T_(1)=227^(@)C=500K`
`impliesT_(2)=(3)/(2)T_(1)=(3)/(2)xx500`
`=750K=477^(@)C`