- #1
Mayan Fung
- 131
- 14
- TL;DR Summary
- Why can we use the low-temperature limit to study Fermi gas in the ultra-relativistic limit?
In a statistical mechanics book, I learned about the degenerate pressure of a Fermi gas under the non-relativistic regime. By studying the low-temperature limit (T=0), we got degenerate pressure is ##\propto n^{5/3}## (n is the density).
And then I was told that in astrophysical objects, the fermions are in the relativistic regime so if we deal with an ultra-relativistic fermi gas: ##\epsilon = chk##, and also the low-temperature limit(T=0), then we can arrive at degenerate pressure ##\propto n^{4/3}##
My question is: If the fermions are in the ultra-relativistic limit, then it mush be very hot. How can we use the low-temperature limit to solve the problem?
And then I was told that in astrophysical objects, the fermions are in the relativistic regime so if we deal with an ultra-relativistic fermi gas: ##\epsilon = chk##, and also the low-temperature limit(T=0), then we can arrive at degenerate pressure ##\propto n^{4/3}##
My question is: If the fermions are in the ultra-relativistic limit, then it mush be very hot. How can we use the low-temperature limit to solve the problem?