Volume of mercury in the bulb of a thermometer is  ${\text{10}}^{\text{-6}}{\text{m}}^{\text{3}}$, area of cross section of capillary tube is $\text{2}\times {\text{10}}^{\text{-7}}{\text{m}}^2$ . If the temperature is raised by ${100}^{\circ }\text{C}$ , the length of mercury is (${\text{γ}}_{\mathrm{Hg}}\text{=18}\times {{10}^{-5}}^{\circ }{\text{C}}^{\text{-1}}$ )

$\begin{array}{l}\mathrm{volume} \mathrm{of} \mathrm{mercury} \mathrm{in} \mathrm{the} \mathrm{bulb} \mathrm{of} \mathrm{thermometer} \mathrm{is}\\ {\text{V=10}}^{\text{-6}}{\text{m}}^{\text{3}}\text{:}\\ \mathrm{area} \mathrm{of} \mathrm{cross} \mathrm{section} \mathrm{of} \mathrm{capillarty} \mathrm{tube} \mathrm{is} \text{A=2}\times {\text{10}}^{\text{-7}}{\text{m}}^{\text{2}}\\ \mathrm{change} \mathrm{in} \mathrm{temperature} \mathrm{is} {\text{ΔT=100}}^{\text{o}}\text{C}\end{array}$

$\begin{array}{rcl}\mathrm{length} \mathrm{of} \mathrm{mercury} \mathrm{in} \mathrm{the} \mathrm{tube} \mathrm{is} \mathrm{l}& =& ?\\ \mathrm{real} \mathrm{expansion} \mathrm{of} \mathrm{mercury} \mathrm{is} {\mathrm{\gamma }}_{\text{reav}}& =& {\mathrm{\gamma }}_{\mathrm{r}}\text{=18}\times {{\text{10}}^{\text{-5}}}^{\circ }{\mathrm{c}}^{-1}\end{array}$

$\begin{array}{rcl} & & {\mathrm{\gamma }}_{\text{r }}\text{=}\frac{\text{ΔV}}{\text{V.Δt}}\\ & & {\mathrm{\gamma }}_{\mathrm{r}}\text{=}\frac{\text{A×l}}{\text{V.Δt}}\\ & & \text{l=}\frac{{\text{γ}}_{\mathrm{r}}\text{.V.Δt}}{\text{A}}\end{array}$

$\begin{array}{rcl} & & \mathrm{substitute} \mathrm{the} \mathrm{given} \mathrm{values}\\ \mathrm{l}& =& \frac{18\times {10}^{-5}\times {10}^{-6}\times 100}{2\times {10}^{-7}}\\ & & \mathrm{l}{\text{=9×10}}^{\text{-2}}\text{m}\\ & & \text{L=9 cm}\end{array}$