Q. The density of a substance at 0$℃$ is 10 g/cc and at 100$℃$, its density is 9.7 g/cc. The coefficient of linear expansion of the substance is
A) $10^{- 4}\ ℃^{- 1}$
B) $10^{- 2}\ ℃^{- 1}$
C) $10^{- 3}\ ℃^{- 1}$
D) $10^{2}\ ℃^{- 1}$
Explanation
(a) As $\rho - \rho_{0}(1 - \gamma\mathrm{\Delta}T)$
$\therefore\ 9.7 = 10(1 - \gamma \times 100)$
$\frac{9.7}{10}\ \ = 1 - \gamma \times 100$
$\ \gamma \times 100\ \ = 1 - \frac{9.7}{10} = \frac{0.3}{10} = 3 \times 10^{- 2}$
$\gamma\ \ = 3 \times 10^{- 4}\ \therefore\ \alpha = \frac{1}{3}\ \gamma = 10^{- 4}℃^{- 1}.$
Reviewed by Dr. Abubacker
Physics Educator & NEET/JEE Specialist
Ph.D. in Physics with 19+ years of teaching experience.