The volume of metal sphere increases by $0.24 \%$ when its temperature is raised by $40^{\circ} \mat

Question

The volume of metal sphere increases by $0.24 \%$ when its temperature is raised by $40^{\circ} \mathrm{C}$. The coefficient of linear expansion of the metal is .... per ${ }^{\circ} \mathrm{C}$.\

Professor PC Thomas Classes · Answer

$\gamma=\frac{\Delta \mathrm{V}}{\mathrm{V} . \Delta \mathrm{t}} \Rightarrow \gamma=\frac{0.24}{100 	imes 40}$ and $\alpha=\frac{\gamma}{3}$\ $\alpha=\frac{24 	imes 10^{-5}}{4 	imes 3}=\frac{24}{12} 	imes 10^{-5}=2 	imes 10^{-5}$ per ${ }^{\circ} \mathrm{C}$\