The barometric formula relates the pressure of a gas of molar mass M at an altitude h to its pressure Po at sea level. Derive this relation by showing that the change in pressure dp for an infinitesimal change in altitude dh where the density is P is dp=-pgdh. Remember that P depends on pressure. Evaluate a) the pressure difference between the top and bottom of a laboratory vessel of height 15cm, and b) the external atmospheric pressure at a typical cruising altitude of an aircraft (11km) when the pressure at ground level is 1.0 atm.