Question

The volume of a metal sphere increases by 0.24% when its temperature is raised by 40°C. The coefficient of linear expansion of the metal is _____________°C.
(A) 2 × 10^–5 (B) 6 × 10^–5 (C) 18 × 10^–5 (D) 1.2 × 10^–5

Answer 1

Dear student

$$\begin{gathered} V_{new}=V(1+{\rm Y}\Delta T) \\ V+0.24\%ofV=V(1+{\rm Y}40) \\ 1.0024V=V(1+{\rm Y}40) \\ \frac{0.0024}{40}={\rm Y}=6\times {10}^{-5} \\ \Rightarrow 3\alpha ={\rm Y} \\ \Rightarrow \alpha =2\times {10}^{-5} \end{gathered}$$
Regards