A black body at `227^(@)C` radiates heat at the rate of `7 cal cm^(-2) s^(-1)`. At a temperature of `727^(@)C`, the rate of heat radiated in the same unit will be

Options

A. 50
B. 112
C. 80
D. 60

Answer

B

Explanation

`E_1 = sigma T_1^4`
`E_1 = sigma (227 + 273)^4`
`7 cal//cm^2 s = sigma (500)^4` …(i)
` E_2 = sigmaT_2^4 = sigma (727 + 273)^4`
` E_2 = sigma (1000)^4` ….(ii)
Dividing equation (ii) by (i)
`(E_2)/(7) = (sigma (10^12) )/(sigma (5^4 xx 10^8) ) = (10000)/(25 xx 25)`
`E_2 = 16 xx 7 cal // cm^2 s `
` = 112 cal//cm^2 s `