Expansion of a Gas at the Molecular Level

The two molecules are colored red and blue to keep track of them. 

Four possible arrangements (microstates) once the stopcock is opened. 

A FIGURE 19.6 Possible arrangements of two gas molecules n two flasks. (a)Beforethe stopcock is opened, both molecules are in the left flask, (b) After the stopcock is opened, there are four possible arrangements of the two molecules. 

Now let s consider a mole of gas. The probability that all the molecules are in the left flask at the same time is ( A), where N = 6.02 X 10. This is a vanishingly small number Thus, there is essentially zero likelihood that all the gas molecules will be in the left flask at the same time. This analysis of the microscopic behavior of the gas molecules leads to the expected macroscopic behavior The gas spontaneously expands to fill both the left and right flasks, and it does not spontaneously all go back in the left flask. 

We win see this notion of increasing randomness helps us understand entropy at the molecular level. 

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