If the volume of a block of metal changes by 0 . 12 % when heated through 20 ° C , then find its…

If the volume of the block is $V=100$then change in volume $∆V=0.12,$therefore, $\frac{∆V}{V}=\frac{0.12}{100}$

Also, for volumetric expansion of the block, $\frac{∆V}{V}=\gamma ∆T$where $\gamma$is the coefficient of volumetric expansion.

$$\begin{gathered} \Rightarrow \frac{0.12}{100}=\gamma \left(20\right) \\ \Rightarrow \gamma =0.06\times {10}^{-3} °{\mathrm{C}}^{-1} \end{gathered}$$

The relation between coefficient of volumetric expansion and coefficient of linear expansion is, $\gamma =3\alpha$

$$\begin{gathered} \Rightarrow \alpha =\frac{\gamma }{3}=\frac{0.06\times {10}^{-3} °{\mathrm{C}}^{-1}}{3} \\ \Rightarrow \alpha =2\times {10}^{-5} °{\mathrm{C}}^{-1} \end{gathered}$$