Question

The coefficient of volumetric expansion of mercury is $18\times {10}^{-5}{/}^{o}C$. A thermometer bulb has a volume ${10}^{-6}{m}^3$ and cross section of stem is $0.004c{m}^2$ Assuming that bulb is filled with mercury at $0^{o}C$ then the length of the mercury column at ${100}^{o}C$ is :

• A. $18.8mm$
• B. $9.2mm$
• C. $7.4cm$
• D. $4.5cm$

Answer 1

Answer: (D)

$4.5cm$

The volume expansion at $100{}^{\circ }C$ is given as,

$\Delta V=V_0\gamma \times \Delta T$

$={10}^{-6}\times 18\times {10}^{-5}\times 100$

$=18\times {10}^{-9}{m}^3$

The length of the mercury column is given as,

$l=\frac{\Delta V}{A}$

$=\frac{18\times {10}^{-9}}{4\times {10}^{-7}}$

$=4.5\times {10}^{-2}m$

Thus, the length of the mercury column is $4.5cm$.