Question

How high does a mercury barometer stand on a day when atmospheric pressure is 98.6 kPa?

Answer 1

Hint:We all have seen and studied mercury barometers, and mercury is widely used in barometers because its density is very high. It means that for an arbitrary volume of mercury, the weight of the mercury is relatively high.

Complete step by step answer:
We know that the expression for pressure is given as,
$P = \rho gH$
Here, P is the pressure, g is the acceleration due to gravity, $\rho $ is the density of mercury, and H is the height to which the mercury rises in the tube.
We can now substitute, $P = 98.6\;{\rm{kPa}}$ , $g = 9.8\;{\rm{m/}}{{\rm{s}}^2}$ , $\rho = 13600\;{\rm{kg/}}{{\rm{m}}^3}$ in the above equation to find the value of H.

$\left( {98.6\;{\rm{kPa}}} \right) = \left( {13600\;{\rm{kg/}}{{\rm{m}}^3}} \right)\left( {9.8\;{\rm{m/}}{{\rm{s}}^2}} \right)\, \times H\\
\left( {98.6\;{\rm{kPa}} \times \dfrac{{1000\;{\rm{Pa}}}}{{1\;{\rm{kPa}}}}} \right) = \left( {13600\;{\rm{kg/}}{{\rm{m}}^3}} \right)\left( {9.8\;{\rm{m/}}{{\rm{s}}^2}} \right)\, \times H\\
H = 0.739\;{\rm{m}}$

Therefore, the height till which the mercury rise is 0.739m.

Additional Information:
Also, we can say that one crucial point to note is why water is not used in place of mercury in a barometer. We can simplify this as, since the density of water is significantly less as compared to mercury, the height it will rise in the tube is around 10.3 m which is not practically feasible.

Note: We all have seen that the meniscus of mercury is concave upwards and this is because the cohesive force between mercury molecules is greater than the adhesive force between the glass and mercury when mercury is put inside a glass tube. Since the cohesive force is greater than the adhesive force, that is why mercury rises in the tubes. That is why the contact angle at the glass mercury interface is more than 90 degrees, and its value is equal to 130 degrees.