Areal (Superficial)l expansion — lesson. Science State Board, Class 10.

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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 $K^{- 1}$ .

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

Areal expansion in solid

Consider a material with the area of $A_{1}$ at $t_{1}^{o}$ $c$. And, the material is heated upto $t_{2}^{o}$ $c$. Now, the length of the material is $A_{2}$ .

Let $β$ be the coefficient of linear expansion.

We know that,

The change in area $ΔA$ is proportional to the original area $A_{1}$ , rise in temperature $ΔT$, and material type.

$\begin{array}{l} Δ A = A_{2} - A_{1} and \\ Δ T = t_{2} - t_{1} \\ Δ A \propto A_{1} Δ T \\ Δ A = β A_{1} Δ T \end{array}$

Rearranging the above equation,

$\begin{array}{l} β = \frac{A_{2} - A_{1}}{A_{1} (t_{2} - t_{1})} \\ Where, \\ A_{1} and A_{2} are the areas of the material before and after heating respectively . \\ t_{1} and t_{2} are the temperatures of the material before and after heating respectively . \\ β is the Areal coefficient of expansion \end{array}$

The $β$ will vary for different materials.

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14. Areal (Superficial)l expansion

Theory: