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=9\,cm $