A sphere of density $\rho $ , specific heat capacity $c$ and radius $r$ is hung by a thermally insulating thread in an enclosure which is kept at a lower temperature than the sphere. The temperature of the sphere starts to drop at a rate which depends upon the temperature difference between the sphere and the enclosure and the nature of the surface of sphere and is proportional to
Medium
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$\left[\frac{-d T}{d t}\right]=\frac{\sigma A}{m c}\left[T-T_{0}\right]$
$=\frac{\sigma 4 \pi r^{2}}{\rho \times \frac{4}{3} \pi r^{3} c}\left[T-T_{0}\right]$
$\left[\frac{-\mathrm{dT}}{\mathrm{dt}}\right] \propto \frac{1}{\rho \mathrm{rc}}$
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