Two black bodies at temperature `327^(@)C` and `427^(@)C` are arranged in a box of `27^(@)C` variable temperature of free space, the ratio of their rate of radiant energy is . . . . ..

Options

A. `6/7`
B. `(36)/(49)`
C. `(464)/(243)`
D. `(243)/(464)`

Answer

D

Explanation

From Stefan-Boltzmann law,
`(dQ)/(dt)=eAsigma(T^(4)-T_(S)^(4))`
`:.((dQ)/(dt))_(1)/((dQ)/(dt))_(2)=(T_(1)^(4)-T_(s)^(4))/(T_(2)^(4)-T_(S)^(4))` `T_(1)=273+327=600K`
`T_(2)=273+427=700K`
`:.((dQ)/(dt))_(1)/((dQ)/(dt))_(2)=((600)^(4)-(300)^(4))/((700)^(4)-(300)^(4))`
`:.((dQ)/(dt))_(1)/((dQ)/(dt))_(2)=(10^(8)[(6)^(4)-(3)^(4)])/(10^(8)[(7)^(4)-(3)^(4)])`
`=(1296-81)/(2401-81)`
`=(1215)/(2320)`
`=(243)/(464)`