A thermometer bulb has volume 10⁻⁶ ~m ^3 and cross-section of the stem is 0.002 ~cm ^2 . The bulb is filled with mercury at 0^ C . If the thermometer reads temperature as 100^ C , then the length of mercury column is (coefficient of cubical expansion of mercury =18 10⁻⁵ / ^ C )

Step-by-step solution

To determine the height of the mercury column, consider the thermal expansion of mercury when heated from 0^ C to 100^ C . The initial volume is V₀ = 10⁻⁶ m ^3 , the cross-sectional area is A = 2 10⁻⁷ m ^2 , and the cubical expansion coefficient is = 18 10⁻⁵ /^ C . The change in volume is given by V = V₀ T = (10⁻⁶) (18 10⁻⁵) 100 = 18 10⁻⁹ m ^3 . This volume occupies the stem, so V = A L . Solving for the length: L = V A = 18 10⁻⁹ 2 10⁻⁷ = 9 10⁻² m = 9 cm . The correct answer is B .