Question

A glass flask of volume $200{\text{cm}}^3$ is just filled with mercury at ${20}^{\circ }\text{C}$. The amount of mercury that will overflow when the temperature of the system is raised to ${100}^{\circ }\text{C}$ is

$({\gamma }_{\text{glass}}=1.2\times {10}^{-5}{}^{\circ }{\text{C}}^{-1},{\gamma }_{\text{mercury}}=1.8\times {10}^{-4}{}^{\circ }{\text{C}}^{-1})$

• A. $2.15{\text{cm}}^3$
• B. $2.69{\text{cm}}^3$
• C. $2.52{\text{cm}}^3$
• D. $2.25{\text{cm}}^3$

Answer 1

The correct option is B $2.69{\text{cm}}^3$

Due to increase in the temperature, both the mercury and the glass vessel will expand

Increase in the volume of mercury

$=V{\gamma }_{\text{mercury}}\Delta T$

$=\left(200\right)\times 1.8\times {10}^{-4}\times (100-20)$

$=2.88{\text{cm}}^3$

Increase in the volume of glass

$=V{\gamma }_{\text{glass}}\Delta T$

$=\left(200\right)\times 1.2\times {10}^{-5}\times (100-20)$

$=0.192{\text{cm}}^3$.

So, the amount as mercury that will overflow
$=(2.880-0.192)=2.688=2.69{\text{cm}}^3$

Hence, option $\left(\text{B}\right)$ is correct.

Volume of overflow $=V\Delta T({\gamma }_{mercury}-{\gamma }_{glass})$