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Unformatted text preview: Physics 880.06: Problem Set 1; Due Thursday, April 7, 2011 at 11:59 P. M. 1. (20) Thermodynamics of the Superconducting State: The equilibrium state of a superconductor in a uniform magnetic field is determined by the temperature T and magnitude of the field H. (Assume that the pressure P is fixed and that the superconductor is a long cylinder parallel to the field, so that demagnetization effects are negligible.) We write the differential relation for the Gibbs free energy density as dG =- SdT- MdH, (1) where G is the Gibbs free energy per unit volume, S is the entropy per unit volume, and M is the magnetization. The phase boundary between the S and N states in a magnetic field is defined by H c ( T ) (for a Type I superconductor). (a). Show, from the fact that G is continuous across the phase bound- ary, that dH c dT =- S n- S s M n- M s . (2) (b). Using the fact that the superconducting state displays perfect diamagnetism (B = 0) while the normal state has M 0, show that S n- S s...
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