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Previously, we saw how the abundance of a constituent cannot change over lengths of time much shorter than the lifetime 1 ¡L of a constituent. This leads us to a general definition of the terms "lifetime", "time-scale", and "time constant": the length of time over which a quantity can change or a process operates. For example, if one puts a pot of cold water on the stove and wants to know when it starts to boil, how often does one check the pot (remembering, of course, that a watched pot never boils)? One could check the pot every 5 s, or one could check the pot every 5 days. But we know from experience that it lakes a few minutes to boil water on a stove, and so you would likely check the pot about that often. In this example, we would say that the time-scale for water to boil is a few minutes. As another example, the time-scale for paint to dry is several hours. So if you are asked to determine when a painted surface has dried, you would not check every few minutes or every few weeks, but every hour or so. In both of these cases, the time-scale gives you an idea of about how long the processes under investigation take.

It turns out that a knowledge of the time constants of a problem is invaluable for isolating its important aspects. For example, we discussed in Chapter 1 that column O, declined over much of the Earth during the 1980s. It is also well known that the arrangement of the Earth's continents affects the circulation of the stratosphere and thereby helps determine the distribution and amount of stratospheric 05. We also know that the arrangements of continents can change. Could the decline in column 0( during the 1980s be caused by changes in the arrangement of the continents? Of course not, and the reason is based on time-scales. The topography of the Earth does change, and this might indeed change the distribution of stratospheric O,, but significant change takes tens of millions of years. Thus, over the time period of the 0-, changes under investigation (a decade), we know that there were no significant changes to the topography of the Earth. We can therefore neglect continental drift and mountain building as a cause of O, loss over the last decade or so. Instead, we search for those processes that can affect 0, and were changing on a time-scale of decades. This method—identifying relevant time-scales and ignoring processes whose time-scales are too long or too short—is a useful approach that is used throughout science.

In the previous section, the lifetime \/L of a constituent was derived from the solution of a simplified continuity equation (Equation (2.23)). However, there is a simpler way to define the lifetime of a chemical constituent: the "replacement lifetime". The replacement lifetime is equal to the total abundance of the constituent divided by the rate at which the constituent is produced or destroyed. One can therefore define a replacement lifetime with respect to loss, r,, or with respect to production, r,-

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