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)

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 $\Delta l=9cm$