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There are two sphers of same radius and ...

There are two sphers of same radius and material at the same temperature but one being solid while the other hollow. Which sphere will expand more if they are given the same amount of heat ?

Text Solution

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(a) As thermal expansion of isotropic solids is similar to true photographic enlargement, expansion of a
cavity is same as if it had been a solid body of the same material i.e. ` DeltaV= Vgamma Deltatheta`
` (##ALN_PHY_C07(I)_S01_008_S01.png" width="80%">
As here V, `gamma ` and ` Deltatheta` are same for both solid and hollow spheres treated (cavity), so the expansion of both
will be equal.
(b) If the same heat is given to the two spheres due to lesser mass, rise in temperature of hollow sphere will be more [as `Deltatheta=(Q)/(mc)]` and hence its expansion will be more in hollosphere [as`DeltaV=VgammaDeltatheta].`
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