A black body at a temperature of `227^(@)C` radiates heat at a rate of `20 cal m^(-2)s^(-1)`. When its temperature is raised to `727^(@)C` the radiated by it in cal `m^(-2)s^(-1)` will be closet to

Options

A. `320`
B. `160`
C. `40`
D. `640`

Answer

A

Explanation

From Stefan's law the rate at which an object radiates, energy (E) per unit surface area is proportional to the fourth power of absolute temperature of the body (T).
`P=sigma T^(4)`
Where `sigma` is Stefan's constant
Given `P_(1) = 20 "cal" m^(-2)s^(-1)`
`T_(1) = 227+273=500K`
`:. 20+sigma(500)^(4)` ...(1)
Also, `T_(2) = 727^(@)C = 727+273=1000K`
`:. P_(2) = sigma (1000)^(4)` ...(2)
`:. (20)/(P_2) = ((500)^(4))/((1000)^(4))`.