The motion of air masses through atmosphere can be approximated as adiabatic and reversible. Air can be treated as an ideal gas with average molar mass 29 g mol-1â and average heat capacity 29 J K-1 mol-1.
b. Suppose the average atmospheric pressure near the earth's surface is P0 and the temperature is T0â. The air is displaced upward until the temperature is T and the pressure is P. Determine the relationship between P and T. (Hint: consider the process as occuring in two steps, equate the sum of the two entropy changes to (delta S total=0))
c. In the lower atmosphere, the dependence of pressure on height, h, above the Earth's surface can be approximated as ln(P/P0â)= -Mgh/RT
Where M is the molar mass, g the acceleration due to gravity, and R the gas constant. If the air temperature near the equator is 38 degrees C (roughly 100degrees F) calculate the air temperature at the summit of Mount Kilimanjaro, roughly 5.9km above sea level.