A sphere of ice at 0^{circ}C having initial r | vedclass

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(B) The rate of heat absorption is proportional to the surface area $A$ of the sphere.$Q = mL$,where $m$ is the mass and $L$ is the latent heat of fus

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(B) The rate of heat absorption is proportional to the surface area $A$ of the sphere.$Q = mL$,where $m$ is the mass and $L$ is the latent heat of fusion.Rate of heat absorption $\frac{dQ}{dt} = L \frac{dm}{dt} = L \rho \frac{dV}{dt}$,where $\rho$ is the density and $V$ is the volume.Since $V = \frac{4}{3} \pi r^3$,we have $\frac{dV}{dt} = 4 \pi r^2 \frac{dr}{dt}$.Given $\frac{dQ}{dt} \propto A$,where $A = 4 \pi r^2$,we have $L \rho (4 \pi r^2 \frac{dr}{dt}) = -k (4 \pi r^2)$,where $k$ is a constant.Simplifying this,we get $\frac{dr}{dt} = -\frac{k}{L \rho} = -C$,where $C$ is a positive constant.Integrating this,$r(t) = R - Ct$.This represents a linear decrease in radius with time,which is depicted by graph $B$.

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