Question

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

• A. 10^-4
• B. 10^-2
• C. 10^-3
• D. 10²

Answer 1

Answer: (A)

Initial temperature $(T_1)=0°C$
Initial density (${\rho }_1)=10g/cc$
Final temperature $(T_2)=100°C$ and
Final density (${\rho }_1)=9.7g/cc$.
Coefficient of volumetric expansion
$\left({\alpha }_v\right)=\frac{\Delta \rho }{{\rho }_1\times \Delta T}$
$=\frac{{\rho }_1-{\rho }_2}{{\rho }_1\left(T_2-T_1\right)}$
$=\frac{10-9.7}{10\left(100-0\right)}=\frac{0.3}{1000}=3\times 10^{-4}.$
Therefore coefficient of linear expansion,
${\alpha }_1=\frac{\gamma }{3}=\frac{3\times 10^{+-4}}{3}=10^{-4}.$