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STD 11 - 10.2. transmission of heat — NEET STD 11 Science — Question

Gujarat BoardEnglish MediumSTD 11 ScienceNEETSTD 11 - 10.2. transmission of heat4 Marks
MCQ
There are two spherical balls $A$ and $B$ of the same material with same surface, but the diameter of $A$ is half that of $B$. If $A$ and $B$ are heated to the same temperature and then allowed to cool, then
  • A
    Rate of cooling is same in both
  • B
    Rate of cooling of $A$ is four times that of $B$
  • ✓
    Rate of cooling of $A$ is twice that of $B$
  • D
    Rate of cooling of $A$ is $\frac{1}{4}$ times that of $B$
✓

Answer

Correct option: C.
Rate of cooling of $A$ is twice that of $B$
c
(c) Rate of cooling ${R_C} = \frac{{A\varepsilon \sigma ({T^4} - T_0^4)}}{{mc}}$$ = \frac{{A\varepsilon \sigma ({T^4} - T_0^4)}}{{V\rho C}}$

==> ${R_C} \propto \frac{A}{V} \propto \frac{1}{r} \propto \,\frac{1}{{({\rm{Diameter)}}}}$        $(\because \,m = \rho V)$

Since diameter of $A$ is half that of $B $ so it's rate of cooling will be doubled that of B

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