Speed (1000 cm/s)

Fig 23.18.

Maxwell-Boltzmann velocity distribution for hydrogen and oxygen molecules at T = 300 K. For each curve, the vertical axis is a relative probability of finding a molecule at a given speed. In each case, notice the large number of molecules with speeds greater than the average.

At first you might think that once the relatively small number of molecules moving faster than the escape velocity leave, the process is finished. However, the remaining molecules collide with each other, and re-establish the Maxwell-Boltzmann distribution. Since the escaping molecules took away more than the average energy per molecule, if there is no replacement of the energy, the new distribution will be at a lower temperature. The gas will be cooled by the escape of the faster molecules (just as a liquid is cooled by the evaporation of the faster molecules.) However, if there is a source of energy, such as sunlight or heat from the ground, the equilibrium can be established at the same temperature as before, and the same fraction of molecules will be moving faster than the escape speed. It is by this process that, over time, the atmosphere can escape. For the Earth, this escape has been much more rapid for the hydrogen than for the heavier molecules, such as oxygen. The Earth's atmosphere is indeed quite deficient in hydrogen. That is, the fraction of hydrogen in our atmosphere is much less than the fraction of hydrogen in the Solar System as a whole.

This escape can only take place from the highest levels of the atmosphere. A molecule lower down in the atmosphere might start out going faster than the escape speed, but it will collide with other molecules, losing energy before it can escape. The layer of the atmosphere from which the molecules can escape is called the exos-phere. The thickness of the exosphere is taken to be equal to the average distance between collisions in the gas at high altitudes.

23.3.4 General circulation

Just as local air flows are in response to temperature differences which cause pressure differences, global air flows are subject to the same processes. The general tendency is for air to be heated at the equator, rise, and then flow toward the poles, where it cools, falls, and returns to the equator.

This simple pattern is disturbed by the effects of the Earth's rotation. Since the rotating Earth is an accelerating reference frame, we observe pseudo-forces. One of these is the familiar centrifugal force. It doesn't play an important role; however, the coriolisforce does.

The origin of the pseudo-force is shown in Fig. 23.19. We are looking down from above the

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