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 0ºC then the length of the mercury column at 100ºC is

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

Answer 1

The correct option is D

4.5 cm

$V=V_0(1+\gamma △\theta )\Rightarrow$ Change in volume
$V-V_0=△V=A.△l=V_0\gamma △\theta$
$\Rightarrow △l=\frac{V_0\gamma △\theta }{A}=\frac{{10}^{-6}\times 18\times {10}^{-5}\times (100-0)}{0.004\times {10}^{-4}}$
$=45\times {10}^{-3}m=4.5cm$