Subsection 10.2.3 Volumetric (Cubic) Expansion
If a cuboid of original volume \(V_{o}\) [Figure 10.2.1.(c)] is heated for a temperature difference of \(\Delta T\text{,}\) then we can find that the change in its volume,
\begin{equation*}
\Delta V \propto V_{o}\times \Delta T
\end{equation*}
\begin{equation*}
\text{or,}\quad \Delta V =\gamma V_{o}\times \Delta T
\end{equation*}
where \(\gamma \) is a proportionality constant called coefficient of volumetric expansion or volumetric expansivity. It is a material property.
\begin{equation*}
\text{or,}\qquad \gamma =\frac{V-V_{o}}{V_{o}\left(T-T_{o}\right)}
\end{equation*}
\begin{equation*}
\therefore \quad V= V_{o}\left(1+\gamma\Delta T\right)
\end{equation*}
Most materials expand on heating and possess positive coefficient of expansion, e.g., metals, glass, etc. However, some materials contract on heating and possess negative coefficient of expansion, e.g., water, bismuth, welding rods, etc.
