Q. A glass flask of volume one $litre$ at $0℃$ is fille, level full of mercury at this temperature. The flask and mercury are now heated to $100℃.$ How much mercury will spill out, if coefficient of volume expansion of mercury is $1.82 \times 10^{- 4}/℃$ and linear expansion of glass is $0.1 \times 10^{- 4}/℃$ respectively
A) $21.2\ cc$
B) $15.2\ cc$
C) $1.52\ cc$
D) $2.12\ cc$
Explanation
(b) Due to volume expansion of both liquid and vessel, the change in volume of liquid relative to container is given by $\mathrm{\Delta}V = V_{0}\lbrack\gamma_{L} - \gamma_{g}\rbrack\mathrm{\Delta}\theta$
Given $V_{0} = 1000\ cc,\ \alpha_{g} = 0.1 \times 10^{- 4}/℃$
$\therefore\gamma_{g} = 3\alpha_{g} = 3 \times 0.1 \times 10^{- 4}/℃ = 0.3 \times 10^{- 4}/℃$
$\therefore\mathrm{\Delta}V = 1000\left\lbrack 1.82 \times 10^{- 4} - 0.3 \times 10^{- 4} \right\rbrack \times 100 = 15.2\ cc$
Reviewed by Dr. Abubacker
Physics Educator & NEET/JEE Specialist
Ph.D. in Physics with 19+ years of teaching experience.