Subsection 10.2.2 Superficial Expansion
If a thin plate of original area \(A_{o}\) [Figure 10.2.1.(b)] is heated for a temperature difference of \(\Delta T\text{,}\) then we can find that the change in its area
\begin{equation*}
\Delta A \propto A_{o}\times \Delta T
\end{equation*}
\begin{equation*}
\text{or,}\quad \Delta A =\beta A_{o}\times \Delta T
\end{equation*}
where \(\beta\) is a proportionality constant called coefficient of superficial expansion or superficial expansivity. It is a material property.
\begin{equation*}
\text{or,}\qquad \beta =\frac{A-A_{o}}{A_{o}\left(T-T_{o}\right)}
\end{equation*}
\begin{equation*}
\therefore \quad A= A_{o}\left(1+\beta\Delta T\right)
\end{equation*}
Hence, superficial expansivity is defined as the change in area of a plate per unit original area per unit rise of temperature.
