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Q.
The density of a substance at $0^{\circ}C$ is $10\, g/cc$ and at $100^{\circ} C$, its density is $9.7\, g/cc$. The coefficient of linear expansion of the substance is
Initial temperature $(T _1 ) = 0°C$
Initial density ($\rho_{1} ) = 10\, g/cc$
Final temperature $(T_2 ) = 100°C$ and
Final density ($\rho_{1} ) = 9.7\, g/cc$.
Coefficient of volumetric expansion
$\left(\alpha_{v}\right)=\frac{\Delta\rho}{\rho_{1}\times\Delta T}$
$=\frac{\rho_{1}-\rho_{2}}{\rho_{1}\left(T_{2}-T_{1}\right)}$
$=\frac{10-9.7}{10\left(100-0\right)}=\frac{0.3}{1000}=3\times10^{-4}.$
Therefore coefficient of linear expansion,
$\alpha_{1}=\frac{\gamma}{3}=\frac{3\times10^{+-4}}{3}=10^{-4}.$