Show that the coefficient of area expansions `(Delta A//A)//Delta T` of a rectangular sheet of the solid is twice its linear expansivity `alpha`.

Explanation

Consider a rectangular sheet of the solid
material of length a and breadth b.When the temperature increases by `DeltaT`, a increases by `Deltaa = (alpha_l)aDeltaT` and b increases by `Deltab = (alpha_l)bDeltaT`,the increase in area

`DeltaA = DeltaA_1
+DeltaA_2
+ DeltaA_3`
`DeltaA = a Deltab + b Deltaa + (Deltaa) (Deltab)`
`DeltaA= a (alpha_l)
b DeltaT + b (alpha_l)
...