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Substituting into eqn (El)
EARTH'S ATMOSPHERE
(E3)
dp/dz= -gM/RTp= -p/H
Introduction The Earth's atmosphere is a thin layer of gases that surrounds the planet. Dry air consists almost entirely of nitrogen and oxygen (99%). We feel the air as it blows around us, and we depend on it as we breathe. The warmth that we feel in the air is controlled by the greenhouse gases that make up a small fraction of the remaining I% of the atmosphere. The Earth's atmosphere can be characterized by its density, temperature and composition. We will consider these three characteristics and briefly discuss how human activities are changing atmospheric composition. The characteristics of the atmosphere change most significantly in the vertical dimension, less so in latitude, and even less in longitude. The changes of atmospheric temperature and other characteristics are small enough in longitude that in many cases the climate is similar for similar latitudes and varies considerably as we move from one latitude to another.
H is defined as RT/gM and is called the scale height of the atmosphere. If we assume for the moment that the temperature of the atmosphere can be taken as a constant average value (256 K), then the scale height has a value of about 8 km. More importantly, assuming H to be constant, allows us to write simple approximate expressions for the change of density and pressure of the atmosphere with altitude: P=P0 exp(-z/H)
and
p=p 0 exp(-z/H).
(E4)
This relationship shows that the density of the atmosphere decreases exponentially with altitude which also represents the change of density of most trace gases in the lower atmosphere. The simplified eqn (E4) can be used to evaluate several practical results including the total number of molecules in the Earth's atmosphere and the mass of the atmosphere. Using the density of air in eqn (E4) we can sum up the numbers of molecules over the whole atmosphere as: Noo = N0 /Mp 0 A
f exp( -z/H) dz = N /Mp 0
0
H
(E5)
Density
The density of the atmosphere, averaged over the year, is determined by hydrostatic equilibrium. This equilibrium results from the gravitational pull of the Earth on the atmosphere given by Newton's law and the ideal gas law that applies to the atmospheric constituents. The weight of a layer of air between altitudes z and (z + dz) is p · d V · g = p ·A· dz · g where p is the density of air, A is a unit surface area and g is the acceleration due to gravity. This weight adds a pressure on the layer below of weight/area or: dp= -p·g·dz
or
dp/dz= -p·g
(El)
The density of air is related to the pressure by the ideal gas law asp V = nRT Noting that p = nM/ V where M is the molecular weight of the air molecules, results in the following relationship between density and pressure: p=pM/RT
(E2)
where A is the surface area of the Earth and N 0 is Avogadro's number. Putting numbers into this equation we get about 10 44 molecules of air in the atmosphere (M = 28.98 g/mol; N0 = 6.03 x 10 23 molecules/mol; p0 = 1.293 kg/m 3 ; H = 8 km, A= 1.275 x 10 8 km 2 ). Thi
