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Tufts OpenCourseware
Author: Fulcrum Institute Development Team

Challenge Solution/Discussion

As the air is cooled the average speed of the molecules in the air decreases. At some point the average speed of the molecules of oxygen gets low enough that when they collide they stick to one another forming liquid oxygen. [The same is true for the nitrogen in the air.]

This implies that something “funny” is going on. As long as the air is in gaseous form, we are comfortable with the idea of compressing it. But if it turns to liquid, it is hard to imagine compressing a liquid. Yet, our graph seems to show that if the temperature keeps going down the volume of the air will go to zero!

The problem here is that we have reached the edge of validity and applicability of our model of molecular motion and its relation to thermal phenomena of all sorts. In order to explain the behavior of matter at very low temperatures it becomes necessary to use a different theory, called quantum mechanics. Rather than thinking of molecules as little particles that simply collide quantum mechanics models the way molecules interact in ways that are complex mathematically and rather abstract. On the other hand, quantum mechanics as a theory correctly predicts the behavior of matter at extremely low temperatures. Moreover, at the kinds of temperatures we experience on earth quantum mechanics makes the same predictions as the theory we have been using until now.

Does this mean that what we have been doing up to now is “wrong”?