Question

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

Answer 1

Heat radiated (at same temperature) $\propto A$
$\Rightarrow Q \propto 4 \pi R^{2}$ and $Q' \propto\left(4 \pi R^{2}+2 \times \pi R^{2}\right)$
$\Rightarrow \frac{Q'}{Q}=\frac{6 \pi R^{2}}{4 \pi R^{2}}=1.5$
Here, $\pi R^{2}$ is extra surface area of plane surface of one of the hemispheres.