9.3 Consider a relativistic gas of N particles of spinį obeying Fermi statistics, enclosed in volume V, at absolute zero

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9 3 Consider A Relativistic Gas Of N Particles Of Spini Obeying Fermi Statistics Enclosed In Volume V At Absolute Zero 1 (103.86 KiB) Viewed 75 times

9.3 Consider a relativistic gas of N particles of spinį obeying Fermi statistics, enclosed in volume V, at absolute zero. The energy-momentum relation is E = (pc)2 + (mc2)2, where m is the rest mass. (a) Find the Fermi energy at density n. (b) Define the internal energy U as the average of E - me?, and the pressure P as the average force per unit area cxerted on a perfectly-reflecting wall of the container. Set up expressions for these quantities in the form of integrals, but you need not evaluate them. (c) Show that PV = 2U/3 at low densities, and PV = U/3 at high densities. State the criteria for low and high densities.