Question

Consider a non-interacting relativistic Fermi gas at zero temperature. (a) Write down expressions for the pressure and the energy density in the rest frame of the gas. What is the equation of state? (b) Treating the system as a uniform static fluid, derive a wave equation for the propagation of small density fluctuations, and hence deduce an expression for the velocity of sound in the gas.

   Consider a non-interacting relativistic Fermi gas at zero temperature.
(a) Write down expressions for the pressure and the energy density in the rest frame of the gas. What is the equation of state?
(b) Treating the system as a uniform static fluid, derive a wave equation for the propagation of small density fluctuations, and hence deduce an expression for the velocity of sound in the gas.
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Problems and Solutions on Thermodynamics and Statistical Mechanics
Problems and Solutions on Thermodynamics and Statistical Mechanics
U.S.T. of China… 1st Edition
Chapter 2, Problem 178 ↓

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The energy \( E \) of a single particle is given by: \[ E = \sqrt{p^2c^2 + m^2c^4} \] where \( p \) is the momentum, \( m \) is the mass of the fermions, and \( c \) is the speed of light. At zero temperature, all states up to the Fermi momentum \( p_F \) are  Show more…

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Consider a non-interacting relativistic Fermi gas at zero temperature. (a) Write down expressions for the pressure and the energy density in the rest frame of the gas. What is the equation of state? (b) Treating the system as a uniform static fluid, derive a wave equation for the propagation of small density fluctuations, and hence deduce an expression for the velocity of sound in the gas.
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