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Consider an ideal gas of highly relativistic particles
Chapter 6, Problem 52P(choose chapter or problem)
Consider an ideal gas of highly relativistic particles (such as photons or fast-moving electrons), whose energy-momentum relation is E = pc instead of \(E=p^{2} / 2 m\). Assume that these particles live in a one-dimensional universe. By following the same logic as above, derive a formula for the single-particle partition function, \(Z_1\), for one particle in this gas.
Questions & Answers
QUESTION:
Consider an ideal gas of highly relativistic particles (such as photons or fast-moving electrons), whose energy-momentum relation is E = pc instead of \(E=p^{2} / 2 m\). Assume that these particles live in a one-dimensional universe. By following the same logic as above, derive a formula for the single-particle partition function, \(Z_1\), for one particle in this gas.
ANSWER:Step 1 of 3
Given energy-momentum relation of the ideal gas
For a one dimensional universe, the allowed momenta are
We have the relation between the energy and momentum
So the allowed energies are