A sphere of ice at $0^o C$ having initial radius $R$ is placed in an environment having ambient temperature $> 0^o C$. The ice melts uniformly, such that shape remains spherical. After a time $‘t’$ the radius of the sphere has reduced to$r$. Assuming the rate of heat absorption is proportional to the surface area of the sphere at any moment, which graph best depicts $r (t)$.
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Heat lost
$=\sigma A\left(T^{4}-T_{0}^{4}\right)=-\sigma 4 \pi r^{2}\left(T_{0}^{4}-T^{4}\right)$
$=\frac{d(m L)}{d t}=\rho L \frac{d v}{d t}=\rho L 4 \pi r^{2} \frac{d r}{d t}$
$\Rightarrow-\sigma 4 \pi r^{2}\left(T_{0}^{4}-T^{4}\right)=\sigma L 4 \pi r^{2} \frac{d r}{d t}$
$\Rightarrow$ radius decreases with time
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