Wednesday, 21 October 2015

quantum mechanics - Didn't we mess up with the temperature?


The following passage has been extracted from the book "The Feynman Lectures on Physics-Vol l":



The mean kinetic energy is a property only of the "temperature." Being a property of the "temperature," and not of the gas, we can use it as a definition of the temperature. The mean kinetic energy of a molecule is thus some function of the temperature. But who is tell us what scale to use to use for the temperature? We may arbitrarily define the scale of the temperature so that the mean energy is linearly proportional to the temperature. The best way to do it would be to call the mean energy itself "the temperature." That would be the simplest possible function. Unfortunately, the scale of temperature has been chosen differently, so instead of calling it temperature directly we use a constant conversion factor between the energy of a molecule and a degree of absolute temperature called a degree kelvin.


The constant of proportionality is $k=1.38\times10^{-23}$ joule for every degree. So if T is a absolute temperature, our definition says that the mean kinetic energy is $(3/2) kt$ (The $3/2$ is put in as a matter of convenience, so as to get rid of it somewhere else.)





From the above passage, at absolute zero, by definition, mean kinetic energy of a molecule should be zero-"completely frozen." There is a giant principle which stands against the view of atoms getting completely frozen; the following passage from the same book introduces the principle:



As we decrease the temperature, the vibration decreases and decreases until, at absolute zero, there is a minimum amount of vibration that the atoms can have, but not zero.....



Remember that when a crystal is cooled to absolute zero, we said that the atoms do not stop moving, they still jiggle. Why? If they stopped moving, we would know where they were and that they had zero motion, and that is against the uncertainty principle. We cannot know where they are and how fast they are moving, so they must be continually wiggling in there!





Aren't the above two passages in contradiction with each other? Didn't we mess up with temperature?




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