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. ${10}^{-4}{/}^{o}C$
• B. $3\times {10}^{-4}{/}^{o}C$
• C. $6\times {10}^{-4}{/}^{o}C$
• D. $9\times {10}^{-4}{/}^{o}C$

Answer 1

The correct option is A ${10}^{-4}{/}^{o}C$

$\frac{1}{density}=\frac{Volume}{Mass}$

Hence $d^{-1}=V\times M^{-1}$

We know that $\gamma =\frac{V-V_0}{V_0\Delta T}$

Hence, $\gamma =\frac{V{M}^{-1}-V_0{M}^{-1}}{V_0{M}^{-1}\Delta T}$

Hence, $=\frac{d^{-1}-d_0^{-1}}{d_0^{-1}\Delta T}$

After substitution you will get $\gamma =3\times {10}^{-4}$

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