By Christopher J. Foot
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Extra info for ATMOSPHERIC THERMODYNAMICS - Elementary Physics and Chemistry
As an air parcel rises for whatever reason in the real atmosphere, it will almost instantaneously adapt its internal pressure to the external pressure exerted by the local surroundings, but the temperature and composition adjust more slowly. In convection, entrainment of neighboring air also speeds up the process of equalizing the temperature between inside and outside air. Still there is a huge separation of equalization times between pressure and temperature and/or trace gas concentrations. This time scale separation has made the parcel concept a useful and even powerful tool in the atmospheric sciences.
3 As a molecule moves a distance v t, it encounters all the point centers in the volume of the cylinder whose length is v t and whose cross-sectional area is 4πr02 . The number of point centers in the volume is n0 4π r02 v t. molecule centers in this cylinder is n0 ×σc v t (number per unit volume × volume of the cylinder). Then the number of collisions per unit time (the collision frequency) is fcoll = n0 σc v [collision frequency]. 3) We may calculate the average distance between collisions to be the [distance per unit time] = [velocity] × [the time between collisions] (this last factor is the inverse of collision frequency): λ=v× 1 1 = n0 σc v n0 σc [mean free path, approximate form].
The expansion need not be solely along the x-axis as shown in the ﬁgure, but can be a distortion in any or all directions. The formula W = p V still holds for inﬁnitesimal V . If the pressure is not constant during the expansion, we must sum the contributions from a sequence of inﬁnitesimal expansions WVA →VB = VB p dV [expansion work done by the system]. 2). This makes it clear that the amount of work done by the system on its environment depends on the path taken p = p(V ), which deﬁnes a curve in the plane.