Question

A tungsten body of diameter $2.3cm$ is at ${2000}^{o}C$. It radiated $30$% of the energy radiated by a black body of same radius and temperature. Find radius of black body which will radiate energy at same rate at the same temperature ?

• A. $2.32cm$
• B. $1.26cm$
• C. $0.629cm$
• D. $0.123cm$

Answer 1

The correct option is B $1.26cm$

Diameter of the tungsten body $=2.3$ cm

$T={2000}^{0}C$

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

$4\pi R^2=0.3\times 4\pi r^2$

$R=\sqrt{0.3r^2}=1.26$ cm