Question

Density of a substance at $0^{o}C$ is $8gm/cc$ and at ${100}^{o}C$, its density is $7.8gm/cc$. The coefficient of linear expansion of substance will be?

• A. $8.33\times {10}^{-5}{/}^{o}C$
• B. $4.2\times {10}^{-6}{/}^{o}C$
• C. $8.33\times {10}^{-6}{/}^{o}C$
• D. zero

Answer 1

Answer: (A)

$8.33\times {10}^{-5}{/}^{o}C$

Coefficient of volumetric expansion $=3\times$ Coefficient of linear expansion

$\gamma =3\alpha$

$\frac{\Delta V}{V}=\gamma \Delta T$

$⟹\frac{0.2}{8}=\gamma \times 100$

$⟹\gamma =2.5\times {10}^{-4}$

$⟹\alpha =\frac{2.5\times {10}^{-4}}{3}$

$⟹\alpha =8.33\times {10}^{-5}{/}^{o}C$