Question

Tungsten body of diameter 2.3 cm is at 2000 degree celsius it radiates 30% of heat energy radiated by a black body of the same temperature and radius find the radius of the black body which will radiate energy at the same rate at the same temperature

Answer 1

The radius of the black body is 0.63 cm.

Explanation:

Given:

         Diameter of the tungsten body = 2.3 cm

          Temperature = 2000 ⁰C

 

We know that the radiation of a body depends only on its surface area as its temperature is same.

So,    compare their surface areas.

         30 % of surface area of tungsten sphere is,

                           

                               ⇒ 4 x π x $R^{2}$  =  0.3 x 4 x π x $r^{2}$

                               ⇒ $R$ = $\sqrt{0.3 \times r^{2} }$

                                 ⇒ R = 1.26 cm

                      Here, R is the radius of black body that radiate same radiation and r is the radius of original black body.

           

Answer 2

The radius of the black body which will radiate energy at the same rate at the same temperature r = 2.32 cm

Explanation:

30% × σT^4 tungstun × 4π (1.35)^2 = σT^4 black × 4πr^2

as T (tungstun) = T (black)

so, 30 / 100 × (1.35)^2 = r^2

so r = 2.32 cm

Thus the radius of the black body which will radiate energy at the same rate at the same temperature r = 2.32 cm