Question

A U-tube filled with a liquid of volumetric coefficient of ${10}^{-5}{/}^{\circ }C$ lies in a vertical plane. The height of liquid column in the left vertical limb is $100cm$. The liquid in the left vertical limb is maintained at a temperature $=0^{\circ }C$ while the liquid in the right limb is maintained at a temperature $={100}^{\circ }C$. The difference in levels in the two limbs in $mm$ is :

Answer 1

Let the area of the tube be $A$.

Height in left limb is $h_1=100cm=1m$

The total volume is given as $TotalVolume\left(V\right)=Volumeinleftlimb+Volumeinrightlimb$

$\Rightarrow V=(A\times 1)+(A\times 1\times 100\times {10}^{-5})$

Total height, $h=V/A=(1+{10}^{-3})m$

So, Difference in height is given as :

$\Delta h=h-h_1=1+{10}^{-3}-1={10}^{-3}mor1mm$