If the volume expansion coefficient of a solid is $7.2\times {10}^{-5}{/}^{0}C$. What is the value of its linear expansion coefficient?

Step 1:

Given data:

The volume expansion coefficient = $7.2\times {10}^{-5}{/}^{0}C$

Step 2:

Formula used:

The volume expansion coefficient (γ) is three times the linear expansion coefficient (α).

That is,

$$\begin{gathered} \mathrm{\gamma }=3\mathrm{\alpha } \\ \mathrm{We}\mathrm{can}\mathrm{rewrite}\mathrm{it}\mathrm{as}, \\ \mathrm{\alpha }=\frac{\mathrm{\gamma }}{3} \end{gathered}$$

Step 3:

Calculation of linear expansion coefficient:

Using the above formula,

$$\begin{gathered} \mathrm{\alpha }=\frac{7.2\times {10}^{-5}{}^0{\mathrm{C}}^{-1}}{3} \\ \mathrm{\alpha }=2.4\times {10}^{-5}{}^0{\mathrm{C}}^{-1} \end{gathered}$$

Thus, the linear coefficient is 2.4 x 10^-5 °C^-1.