Q.

A solid copper cube and a solid copper sphere, both of same mass & emissivity are heated to same initial temperature and kept under identical conditions.  What is the ratio of their initial rate of fall of temperature?

Moderate

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By Expert Faculty of Sri Chaitanya

a

6π13

b

6π23

c

6π3

d

answer is 1.

(Detailed Solution Below)

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Detailed Solution

If 'a' is the length of cube, surface area Scube=6a2 If 'r' is the radius of sphere, surface area  Ssphere=4πr2Both the cube and sphere have the same volume as given Volume  V=a3  ∵V=43πr3∴a3=43πr3⇒ar=4π313 Area cube  Area sphere =6a24πr2=64πar2=64π×4π323=6π13∵  mass are equal Rate of fall in temperature = Surface area∵Rate of fall in temperature= 6π13
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