Question

A glass vessel measures exactly $10cm\times 10cm\times 10cm$ at $0^{o}C$. It is filled completely with mercury at this temperature. When the temperature is raised to ${10}^{o}C,1.6{cm}^3$ of mercury overflows. Calculate the coefficient of volume expansion of mercury. Coefficient of linear expansion of glass $=6.5\times {10}^{-6}{}^o{C}^{-1}$.

Answer 1

$V_0=10\times 10\times 10=1000cc$

$\Delta T={10}^{o}C$, $V_{HG}^{\prime }-V_g^{\prime }=1.6c{m}^3$

${\alpha }_g=6.5\times {10}^{-5}{/}^{o}C$, ${\gamma }_{Hg}=?$, ${\gamma }_g=3\times 6.5\times {10}^{-6}{/}^{o}C$

$V_{Hg}^{\prime }=V_{HG}(1+{\gamma }_{Hg}\Delta T)$ ...(1)

$V_g^{\prime }=V_g(1+{\gamma }_g\Delta T)$ ...(2)

$V_{Hg}^{\prime }-V^{\prime }g=V_{Hg}-V_g+V_{Hg}{\gamma }_{Hg}\Delta T-V_g{\gamma }_g\Delta T$

$\Rightarrow 1.6=1000\times {\gamma }_{Hg}\times 10-1000\times 6.5\times 3\times {10}^{-6}\times 10$

$\Rightarrow {\gamma }_{Hg}=\frac{1.6+6.3\times 3\times {10}^{-2}}{10000}=1.789\times {10}^{-4}\approx 1.8\times {10}^{-4}{/}^{o}C$