Question

1. Estimate the fall in height of the mercury column when the barometer is taken from sea level to a hill top of altitude $1.0km$. For this rough estimate take the density of mercury to be $13000kg{m}^{-3}$ and the density of air to be $1.3kg{m}^{-3}$. Assume the densities remain the same at such low altitude.
2. If the barometer reading at sea level is 760 mm of mercury, what is the reading at the hill top?

Answer 1

Step 1: Given data

$$\begin{gathered} Heightofaircolumn,h_{air}=1.0km=1000m \\ Densityofmercury,{\rho }_{Hg}=13000kg{m}^{-3} \\ Densityofair,{\rho }_{air}=1.3kg{m}^{-3} \\ Heightofmercurycolumn,h_{Hg}=? \end{gathered}$$

Step 2: Comparing the pressure in terms of mercury as well as air

$$\begin{gathered} P={\rho }_{Hg}\times g\times h_{Hg}={\rho }_{air}\times g\times h_{air} \\ \Rightarrow 13000kg{m}^{-3}\times g\times h_{Hg}=1.3kg{m}^{-3}\times g\times 1000m \\ \Rightarrow h_{Hg}=0.1m=10cm \end{gathered}$$

Step 2: Finding the mercury barometer reading at hill top

$$\begin{gathered} P_{top}=P_{atm}-P_{10cmofHg} \\ HeightofHgcolumnathilltop=760mm-10cm \\ =760-100mm \\ =660mm \end{gathered}$$