Question

A glass vessel of volume $100c{m}^3$ is filled with mercury and is heated from ${25}^{\circ }Cto{75}^{\circ }C$. What volume of mercury will overflow? Coefficient of linear expansion of glass $=1.8\times {10}^{-6}{/}^{\circ }C$ and coefficient of volume expansion of mercury is $1.8\times {10}^{-4}{/}^{\circ }C$.

• A. $0.67c{m}^3$.
• B. $0.87c{m}^3$.
• C. $1.74c{m}^3$.
• D. $0.98c{m}^3$.

Answer 1

Answer: (B)

$0.87c{m}^3$.

Initial volume of both the glass vessel and mercury is $V_o=100c{m}^3$

The coefficient of volume expansion for mercury is ${\gamma }_m=1.8\times {10}^{-4}/{}^{o}C$

The coefficient of volume expansion for glass is ${\gamma }_g=1.8\times {10}^{-6}/{}^{o}C$

Change in temperature be $\theta =75-25={50}^{o}C$

So final volume of of glass vessel is $V_1=V_o(1+{\gamma }_g\theta )=100(1+90\times {10}^{-6})c{m}^3$

and final volume of of mercury is $V_2=V_o(1+{\gamma }_g\theta )=100(1+90\times {10}^{-4})c{m}^3$

Amount overflowed is $V_2-V-1=100\times (90\times {10}^{-4}-90\times {10}^{-6})=0.89c{m}^3$