Question

The volume of mercury in the bulb of a thermometer is ${{10}^{-6}}{{m}^{3}}$ . The area of cross- section of the capillary tube is $2\times {{10}^{-7}}{{m}^{2}}.$ If the temperature is raised by $100{}^\circ C$ , the increase in the length of the mercury column is $\left( {{\gamma }_{Hg}}=18\,\times \,{{10}^{-5}}{{/}^{0}}C \right)$

• A. 18 cm
• B. 0.9 cm
• C. 9 cm
• D. 1.8 cm

Answer 1

Answer: (C)

9 cm

Answer 2

By cubical expansion relation. $\Delta V=V\times \gamma \times \Delta T$ where $\gamma$ is coefficient of cubical expansion and $V={{10}^{-6}}{{m}^{3}}=$ initial volume $\gamma =18\times {{10}^{-5}}/{{\,}^{o}}C$ $\Delta T=100{{\,}^{o}}C$ $\therefore$ $\Delta V={{10}^{-6}}\times 18\times {{10}^{-5}}\times {{10}^{2}}$ $=18\times {{10}^{-9}}$ Since, $\Delta V=A\times \Delta l$ $\therefore$ $18\times {{10}^{-9}}=2\times {{10}^{-7}}\times \Delta l$ or $9\times {{10}^{-2}}=\Delta l$ or $\Delta l=9\,cm$