Question

A glass vessel of volume $200{\text{cm}}^3$ is filled with mercury and is heated from ${25}^o\text{C}$ to ${75}^o\text{C}$. What volume of mercury will overflow? Coefficient of linear expansion of glass = $1.8\times {10}^{-6}{/}^o\text{C}$ and coefficient of volumetric expansion of mercury is $1.8\times {10}^{-4}{/}^o\text{C}$.

• A. $0.87{\text{cm}}^3$
• B. $1.764{\text{cm}}^3$
• C. $2.764{\text{cm}}^3$
• D. $1.374{\text{cm}}^3$

Answer 1

The correct option is B $1.764{\text{cm}}^3$

Since the coefficient of linear expansion of glass is $1.8\times {10}^{-6}{/}^o\text{C}$, and assuming glass to be isotropic in nature, the coefficient of volumetric expansion of glass will be $3\times 1.8\times {10}^{-6}{/}^o\text{C}$
Mercury will spill if the coefficient of volume expansion of glass is lesser than that of the mercury.
Let $\Delta V$ be the volume of the mercury spilled,
$\Delta V=V_0({\gamma }_m-{\gamma }_g)\times \Delta T$
where $\gamma$ is the coefficient of volume expansion
Putting the values
$\Delta V=200\times (1.8\times {10}^{-4}-3\times 1.8\times {10}^{-6})\times 50$
$\Delta V=1.764{\text{cm}}^3$