Posted by Steve Simon on January 24, 2014, 5:57 pm
A good question was asked today after lecture. If the fermi temperature of a metal is 80,000 degrees, why is it not hot?
The fermi temperature is just a measure of the kinetic energy of the electrons at the top of the fermi sea -- the most energetic states of electrons that are filled (at T=0). However, even though these electrons have a huge kinetic energy, they are still in the ground state. If I have N electrons with N large, I have to fill up a very big fermi sea -- a ball of filled states. If you fill all the states up to E_F, there is no lower energy configuration.
Now, when you touch a piece of metal, it will only feel hot if it can transfer heat to your hand. Since the electrons in the metal are already in their ground state, they cannot transfer any heat to your hand. So it does not feel hot, despite the fact that the electrons have a huge kinetic energy.
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