Question

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

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

Answer 1

The correct option is A $4.5$ cm

We know that the change in volume due to heating can be given as:

$\Delta V=V_0\gamma \left(\Delta T\right)$

The initial volume of mercury will be equal to the volume of the bulb.

$\Delta V={10}^{-6}\times 18\times {10}^{-5}\times (100-0)$

Now change in volume can be written as a product of change in lenght and the area of crossection of the thermometer stem.

$A\Delta L={10}^{-6}\times 18\times {10}^{-5}\times (100-0)$

$\therefore \Delta L=\frac{{10}^{-6}\times 18\times {10}^{-5}\times (100-0)}{0.004\times {10}^{-4}}=4.5\times {10}^{-2}$ m

Therefore, the lenght of mercury column at $100$${}^{\circ }$C is $4.5$ cm.