Question

3) Consider the hot air balloon problem described in Lecture 1, pp. 22-24. That problem assumed an outside air temperature of T- 300 K (27°C or 80.6°F), arn atmospheric pressure of 1.013 x 10 Pa (at sea level), and a spherical balloon shape. We would like to perform the same calculation but assuming atmospheric pressure in Albuquerque, NM, where the altitude is 1620 m wikipedia.org/wiki/Albuquerque_International_Balloon Fiesta) (a) First, we need to estimate the ambient pressure at an altitude of 1620 m from a model for the atmosphere. Because the pressure change dP due to an increase in altitude from h to h dh is the weight of the air in the slab of unit area and thickness dh (thus volume V- dh), then dP--gpVg pgdh where m, is the mass of the slab, p is the density of air at h, and g is the acceleration of gravity. The minus sign accounts for the fact that pressure decreases as the altitude increases. Use the ideal gas law to eliminate p and arrive at the barometric equation RT where Mw is the mass per mole of air. Integrate this equation assuming a fixed temperature versus altitude and substitute values to determine the air pressure at T 300 K and 1620 m altitude.

Answer 1