(a) Photograph showing the Earth and its atmosphere from space; note how thin the atmosphere is. (b) Diagram showing the layers in the atmosphere. [(a) NASA]

Fig 23.10.

(a) Photograph showing the Earth and its atmosphere from space; note how thin the atmosphere is. (b) Diagram showing the layers in the atmosphere. [(a) NASA]

must have an equation of state. We can treat planetary atmospheres as ideal gases, so the equation of state is simply

temperature distribution, as we will discuss in

Section 23.3.2. The bottom layer, to which we are mostly confined, is called the troposphere. It is only 14 km thick. At the top of the troposphere is the thin tropopause. Above that is the stratosphere, in which some high altitude aircraft fly. At the top of the stratosphere is the ozone layer (which will be discussed below).

To relate the basic variables that describe a gas - temperature, density and pressure - we

In this expression, m is the average mass per particle. For the Earth's atmosphere, this is approximately 29 times the mass of the proton, reflecting the fact that the atmosphere is mostly N2 (molecular weight 28) and O2 (molecular weight 32). For a surface temperature of 300 K, the density at the surface is 1.1 X 10 ~3 g/cm3.

The pressure at the bottom of the atmosphere, near the surface of the Earth, is called one atmosphere or one bar. It is quite large, approximately 105 N for every square meter (106 dyn/cm2 or 15 lb/in2). Remember the weight of a typical person is about 750 N, so it is like having over 100 people stand on every square meter. We don't normally see the effects of this pressure because in most situations it tends to cancel. For example, for a wall, the air on opposite sides is pushing with equal and opposite forces, resulting in a net force on the wall of zero. We see the effects of the pressure if we remove it from one side, by using an air pump, for example.

The vertical distribution of pressure and density is governed by the condition of hydrostatic equilibrium, just as in stars. The weight of each layer is supported by the pressure difference between the bottom and the top of that layer. For stars, we treated the layers as spherical shells. We could do that for the Earth, also. However, the Earth's atmosphere is so thin that we can treat it as a plane parallel layer (see Problem 23.8).

The equation of hydrostatic equilibrium then becomes dP

We now have two equations, the equation of state and the equation of hydrostatic equilibrium. However, we have three unknowns, T, P and p. When we look at the temperature distribution, discussed later in this section, we find that, especially in the lower atmosphere, the temperature doesn't deviate by large amounts from its value at the ground, T0. We therefore make the approximation that the temperature is constant. Knowing T, we can use equation (23.9) to substitute for the density in equation (23.10), so that the only remaining variable is pressure. This gives dP dz mg kT0

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