Question

For a black body at a temperature of ${727}^{\circ }C$, Its radiated power is 60 watt and temperature of the surrounding is ${227}^{\circ }C$ If the temperature of the black body is changed to ${1227}^{\circ }C$, Then its radiating power will be

• A. $304W$
• B. $320W$
• C. $240W$
• D. $120W$

Answer 1

The correct option is B $320W$

Radiation power of a black body

$E_0=\sigma (T^4-T_0^4)A$

$T={727}^{\circ }C=1000K$

$T_0={227}^{\circ }C=500K$

$\therefore 60=\sigma ({1000}^4-{500}^4)A$

$E^{\prime }=\sigma (T^4-T_0^4)A$

$T={1227}^{\circ }C=1500K$

$T_0={227}^{\circ }C=500K$

$\therefore E^{\prime }=\sigma ({1500}^4-{500}^4)A$

$\frac{E^{\prime }}{60}=\frac{{1500}^4-{500}^4}{{1000}^4-{500}^4}$

$\therefore E^{\prime }=\frac{50000}{9375}\times 60=320W$