Question

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

• A. ${10}^{-2}$
• B. ${10}^{-5}$
• C. ${10}^{-3}$
• D. ${10}^{-4}$

Answer 1

The correct option is D ${10}^{-4}$

The coefficient of volume expansion
$\gamma =\frac{\Delta \rho }{{\rho }_1\times \Delta t}$
$=\frac{{\rho }_1-{\rho }_2}{{\rho }_1(T_2-T_1)}=\frac{10-9.7}{10(100-0)}=3\times {10}^{-4}$
Coefficient of linear expansion
$\alpha =\frac{\gamma }{3}=\frac{3\times {10}^{-4}}{3}={10}^{-4}$