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A sphere of density p, 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:

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$\frac{c}{r^{3} ρ}$

$\frac{1}{r^{3} ρc}$

3r³pc

$\frac{1}{rpc}$

answer is D.

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Detailed Solution

$[\frac{- dT}{dt}] = \frac{σ A}{mc} [T - T_{0}]$

$= \frac{σ 4 {πr}^{2}}{ρ \times \frac{4}{3} {πr}^{3} c} [T - T_{0}]$

$∴ [\frac{- dT}{dt}] \propto \frac{1}{ρrc}$

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