Question

The air pressure at the base of a mountain is 75.0cm of mercury. Given that the average density of air is 1.25kg/m³ and the density of mercury is 13600kg/m³,calculate the height of the mountain. [Take g=10m/s²]

Answer 1

The hydrostatic pressure is given by

$$p=g\rho h$$ $$g\rho_{\rm Hg}h_{\rm Hg}=g\rho_{\rm Air}h_{\rm Air}$$

Hence

$$h_{\rm Air}=\frac{\rho_{\rm Hg}h_{\rm Hg}}{\rho_{\rm Air}}$$

$$h_{\rm Air}=\frac{1360\rm \: kg/m^3*0.75\rm \: m}{1.25\rm \: kg/m^3}=8160\:\rm m$$