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STD 11 - 10.2 , transmission of heat — JEE STD 11 Science — Question

Gujarat BoardEnglish MediumSTD 11 ScienceJEESTD 11 - 10.2 , transmission of heat4 Marks
MCQ
A solid cube and a solid sphere of the same material have equal surface area. Both are at the same temperature ${120^o}C$, then
  • A
    Both the cube and the sphere cool down at the same rate
  • ✓
    The cube cools down faster than the sphere
  • C
    The sphere cools down faster than the cube
  • D
    Whichever is having more mass will cool down faster
✓

Answer

Correct option: B.
The cube cools down faster than the sphere
b
(b)Rate of cooling of a body $R = \frac{{\Delta \theta }}{t} = \frac{{A\varepsilon \sigma ({T^4} - T_0^4)}}{{mc}}$
==> $R \propto \frac{A}{m} \propto \frac{{{\rm{Area}}}}{{{\rm{Volume}}}}$

==> For the same surface area. $R \propto \frac{1}{{{\rm{Volume}}}}$
( Volume of cube < Volume of sphere

==> ${R_{Cube}} > {R_{Sphere}}$ i.e. cube, cools down with faster rate.

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