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sm-mte3-04 - PHY 4523 Statistical Physics Mid-term...

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Unformatted text preview: PHY 4523 Statistical Physics: Mid-term Examination 3 Professor Mark W. Meisel, Department of Physics, University of Florida 19 April 2004 1. (15 points) For spin waves, the dispersion relation is w(k:) = akz. In a three dimensional system, how does the internal energy of the spin wave system vary with temperature? Show all of the relevant work, but you do not have to evaluate any temperature independent integrals (unless you want to do it). 2. (15 points) Given that the mass of the Sun is 2 x 1030 kg, estimate the number of electrons in the Sun given that it is mainly composed of atomic hydrogen. In a white dwarf star of one solar mass, the atoms are all ionized and contained in a sphere of radius 2 x 107 m. What is the Fermi energy of the electrons in eV? Are they relativistic? If the temperature of the white dwarf star is 107 K, are the electrons in the star degenerate? One might think that this type of star would collapse under its own gravitational pressure. What prevents this collapse from occuning? me = 9.109 x 10‘31 kg and m1, = 1.673 x 10‘27 kg 3. (20 points) When we discussed hemoglobin, we considered a situation in the lungs where the blood is in approximate diffusive equilibrium with the atmosphere. Under these conditions, I quoted a value for the chemical potential of oxygen, 02, namely a m —0.6 eV. Generate your own value for u and compare it to the one that was used in class. If they are different, describe what the difference may mean. If appropriate, you may start your work with the following equation from the formula sheet (but you must describe the limits where this formula is valid): I u=A+k3T1n<n) no, ...
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