An Introduction to Thermal Physics
An Introduction to Thermal Physics
1st Edition
ISBN: 9780201380279
Author: Daniel V. Schroeder
Publisher: Addison Wesley
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Chapter 7.2, Problem 9P
To determine

The temperature when quantum statistics become relevant for this system.

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Consider a free Fermi gas in two dimensions, confined to a squarearea A = L2. Because g(€) is a constant for this system, it is possible to carry out the integral 7.53 for the number of particles analytically. Do so, and solve for μ as a function of N. Show that the resulting formula has the expected qualitative behavior.
For a gas trapped in a two-dimensional harmonic oscillator, E = hf (nx+ny), sketch the positions of states in the n-plane and draw a couple of curves of constant energy. Calculate U/N at T = 0 and express it as a multiple of the Fermi energy. What is the density of states?
What properties of a nonideal gas do the van der Waals constants a and b represent?
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