The barometric formula relates the pressure of a gas of molar mass $M$ at an altitude $h$ to its pressure $p_0$ at sea level. Derive this relation by showing that the change in pressure $\mathrm{d} p$ for an infinitesimal change in altitude $\mathrm{d} h$ where the density is $\rho$ is $\mathrm{d} p=-\rho g \mathrm{~d} h$. Remember that $\rho$ depends on the pressure. Evaluate the pressure difference between the top and bottom of a laboratory vessel of height 15 cm.
0.00017