Question

Two identical solid spheres have the same temperature. One of the spheres is cut into two identical pieces. The intact sphere radiates energy $Q$ during a given small time interval. During the same interval, the two hemispheres radiate a total energy $Q^{\prime }$. The ratio $Q^{\prime }/Q$ is equal to

Answer 1

Heat radiated (at same temperature) $\propto A$

$\Rightarrow Q\propto 4\pi R^2$ and $Q^{{}^{\prime }}\propto (4\pi R^2+2\times \pi R^2)$

$\Rightarrow \frac{Q^{{}^{\prime }}}{Q}=\frac{6\pi R^2}{4\pi R^2}=1.5$

Here, $\pi R^2$ is extra surface area of plane surface of one of the hemispheres.