JAMB Physics 2022 Paper

Concept:For solids expanding uniformly, volume expansion is about three times linear expansion.Explanation:The linear expansion coefficient is $\alpha$.The volumetric expansion coefficient is $\gamma$.Consider a cube of side $L$. Its initial volume is $V = L^3$.When temperature increases by $\Delta T$, the new side length becomes $L(1 + \alpha \Delta T)$.So the new volume is $V' = L^3(1 + \alpha \Delta T)^3$.Expanding gives $V' = V\left(1 + 3\alpha \Delta T + 3\alpha^2 \Delta T^2 + \alpha^3 \Delta T^3\right)$.For small temperature changes, the higher-order terms are negligible.Thus $\Delta V \approx 3\alpha V \Delta T$, so $\frac{\Delta V}{V} \approx 3\alpha \Delta T$.By definition, $\frac{\Delta V}{V} = \gamma \Delta T$.Therefore, $\gamma = 3\alpha$.Answer:$\gamma = 3\alpha$, which is option C.