# There are two spheres of same radius and material at same temperature

There are two spheres of same radius and material at same temperature but one being solid while the other hollow. Which sphere will expand more if (i) they are heated to the same temperature (ii) same amount of heat is given to each of them?

(i) As thermal expansion of isotropic solids is similar to true photographic enlargement, the expansion of a cavity is same as if it were a solid body of the same material i.e. ∆V = $\gamma$V ∆T. As here V, $\gamma$ and ∆T are same for both solid and hollow spheres, so the expansions of both will be equal.
(ii) If same amount of heat is given to the two spheres, then due to lesser mass, rise in temperature of hollow sphere will be more (as ∆T = Q/Mc) and hence the expansion will bemore as ∆V = $\gamma$V ∆T.