Q. The coefficient of volume expansion of a liquid is $49 \times 10^{- 5}K^{- 1}$. Calculate the fractional change in its density when the temperature is raised by 30$℃.$
A) $7.5 \times 10^{- 3}$
B) $3.0 \times 10^{- 3}$
C) $1.5 \times 10^{- 2}$
D) $1.1 \times 10^{- 3}$
Explanation
(c) Variations of density with temperature is given by
$\ \rho ’ = \ \frac{\rho}{1 + \gamma\mathrm{\Delta}\theta}$
Fraction change is
$\frac{\rho^{'} - \rho}{\rho}\ = \left\lbrack \frac{1}{1 + 49 \times 10^{- 5} \times 30} - 1 \right\rbrack$
$= \ 1.5 \times 10^{- 2}$
Reviewed by Dr. Abubacker
Physics Educator & NEET/JEE Specialist
Ph.D. in Physics with 19+ years of teaching experience.