A black body at a temperature of `227^(@)C` radiates heat energy at the rate of 5 cal/`cm^(2)`-sec. At a temperature of `727^(@)C`, the rate of heat radiated per unit area in cal/`cm^(2)`-sec will be

Options

A. `80cal//cm^(2)s`
B. `500cal//cm^(2)s`
C. `100cal//cm^(2)s`
D. `250cal//cm^(2)s`

Answer

A

Explanation

`T_(1)=500K," "T_(2)=1000K`
Rate of radiation, `R=(dQ)/(Adt)=sigmaT^(4)`
`thereforeR_(2)/R_(1)=(T_(2)/T_(1))^(4)`
`=((727+273)/(227+273))^(4)=(1000/500)^(4)=16`
`R_(2)=16xx5=80cal//m^(2)-s`