The density of a substance at $0^0\mathrm{C}$ is 10g/cc and at ${100}^0\mathrm{c}$ in its density is 9.7 g/cc. The coefficient of linear expansion of the substance is

The coefficient of volume expansion is given by

      $\mathrm{\gamma } = \frac{∆\mathrm{\rho }}{{\mathrm{\rho }}_1\times ∆\mathrm{T}}$

where ${\text{ρ}}_1 \mathrm{is} \mathrm{density}, \mathrm{T} \mathrm{is} \mathrm{temperature}$

       $\mathrm{\gamma } = \frac{{\mathrm{\rho }}_1-{\mathrm{\rho }}_2}{{\mathrm{\rho }}_1({\mathrm{T}}_2-{\mathrm{T}}_1)}$

           = $\frac{10-9.7}{10(100-0)} = 3\times {10}^{-4}$

Coefficient of linear expansion is

$\mathrm{\alpha } = \frac{\mathrm{\gamma }}{3} = \frac{3\times {10}^{-4}}{3}= {10}^{-4}$