Theory:

Areal expansions:
When we heat a solid, if there is an increase in the area of the body, this is called Areal expansion. It is also known as Superficial expansion

The amount by which the area of a material increases when the temperature is raised one degree is called the coefficient of superficial expansion. The unit of coefficient of superficial expansion is K1.

The coefficient of superficial expansion can be designated by the symbol β (beta).

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Areal expansion in solid

Consider a material with the area of A1 at t1o \(c\). And, the material is heated upto t2o \(c\). Now, the length of the material is A2.

Let β be the coefficient of linear expansion.

We know that,

The change in area \(ΔA\) is proportional to the original area A1, rise in temperature \(ΔT\), and material type.

ΔA=A2A1andΔT=t2t1ΔAA1ΔTΔA=βA1ΔT

Rearranging the above equation,

β=A2A1A1t2t1Where,A1andA2aretheareasofthematerialbeforeandafterheatingrespectively.t1andt2arethetemperaturesofthematerialbeforeandafterheatingrespectively.βistheArealcoefficientofexpansion

The β will vary for different materials.