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10-2.Transmission of Heat
medium
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
A
$\frac{c}{{{r^3}\rho }}$
B
$\frac{1}{{{r^3}\rho c}}$
C
$3r^3\rho c$
D
$\frac{1}{{r\rho c}}$
Solution
$\left[\frac{-d T}{d t}\right]=\frac{\sigma A}{m c}\left[T-T_{0}\right]$
$=\frac{\sigma 4 \pi r^{2}}{\rho \times \frac{4}{3} \pi r^{3} c}\left[T-T_{0}\right]$
$\left[\frac{-\mathrm{dT}}{\mathrm{dt}}\right] \propto \frac{1}{\rho \mathrm{rc}}$
Standard 11
Physics
