A long glass tube of uniform capillary bore contains a thread of mercury which at $0^{0}C$  is 1m long, at ${100}^{0}C$ it is 15.5 mm longer. If the coefficient of real expansion of mercury is $1.82\times {10}^{-4}$ per ${ }^{0}C$, what is coefficient of expansion of glass $(\mathrm{in} {10}^{-6}{/}^0\mathrm{C})$

Here apparent expansion of the liquid is considered, due to the expansion of the liquid in the glass tube

 ${\mathrm{\gamma }}_{\mathrm{a}}=\frac{{\mathrm{V}}_2-{\mathrm{V}}_1}{{\mathrm{V}}_1\left(\mathrm{\Delta \theta }\right)}{/}^0\mathrm{C}\simeq \frac{{\mathrm{l}}_2-{\mathrm{l}}_1}{{\mathrm{l}}_1\left(\mathrm{\Delta \theta }\right)}{/}^0\mathrm{C}$

(Assuming change in area of cross-section to be negligible) $\therefore {\gamma }_a=\frac{15.5mm}{\left(1m\right)\left(\mathrm{\Delta }\theta \right)}=155\times {10}^{-6}$

${\gamma }_a=155\times {10}^{-6}{/}^0\mathrm{C}$

$\text{ We have }{\gamma }_R={\gamma }_a+{\gamma }_{\text{glass }}\dots ..\left(2\right)$

$\Rightarrow 182\times {10}^{-6}=155\times {10}^{-6}+3{\alpha }_{\text{glass }}$

$\Rightarrow 3{\alpha }_{\text{glass }}=27\times {10}^{-6}\Rightarrow {\alpha }_{\text{glass }}=9\times {10}^{-6}{/}^0\mathrm{C}$