Gujarati
10-2.Transmission of Heat
medium

A hot metallic sphere of radius $r$ radiates heat. It's rate of cooling is

A

Independent of $r$

B

Proportional to $r$

C

Proportional to ${r^2}$

D

Proportional to $1/r$

Solution

(d) Rate of cooling ${R_C} = \frac{{d\theta }}{{dt}} = \frac{{A\varepsilon \sigma ({T^4} – T_0^4)}}{{mc}}$

==> $\frac{{d\theta }}{{dt}} \propto \frac{A}{V} \propto \frac{{{r^2}}}{{{r^3}}}$

==> $\frac{{d\theta }}{{dt}} \propto \frac{1}{r}$

Standard 11
Physics

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