Question

density of a substance at o^oC is 10.6 gm/cc and at 100⁰c is 10gm/cc. coefficient of linear expansion of solid is?

Answer 1

$$\begin{gathered} \mathrm{Given}, \\ \mathrm{Density}\mathrm{of}\mathrm{substance}\mathrm{at}0°\mathrm{C},{\rho }_0=10.6\mathit{}\mathrm{gm}{\mathrm{cc}}^{-1} \\ \mathrm{Density}\mathrm{of}\mathrm{substance}\mathrm{at}100°\mathrm{C},{\rho }_{100}=10\mathrm{gm}{\mathrm{cc}}^{-1} \\ \mathrm{Change}\mathrm{in}\mathrm{temperature},∆T=100-0=100°\mathrm{C} \\ \mathrm{From}\mathrm{the}\mathrm{relation} \\ {\rho }_{\mathit{100}}={\rho }_{\mathit{0}}\left(1+\alpha ∆T\right) \\ \Rightarrow {\rho }_{100}-{\rho }_{\mathit{0}}={\rho }_0\alpha ∆T \\ \mathit{\Rightarrow }\alpha =\frac{{\rho }_{100}-{\rho }_{\mathit{0}}}{{\rho }_{\mathit{0}}∆T}=\frac{10-10.6}{10.6\times 100} \\ \Rightarrow \mathrm{\alpha }=-5.6\times {10}^{-4}°{\mathrm{C}}^{-1} \end{gathered}$$