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 $Q^{\prime }$. The ratio $Q^{\prime }/Q$ is equal to

Answer 1

Answer: 1.50

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