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Unformatted text preview: dimensions μ ( T ) + k B T ln[1 + e-μ ( T ) /k B T ] = μ (0) . (4) (e). Estimate From this result the amount by which μ ( T ) di²ers From μ (0) at a temperature k B T ≪ μ (0). 1 4. The specifc heat at constant volume satisfes the thermodynamic iden-tities C V = p ∂U ∂T P N,V = T p ∂S ∂T P N,V . (5) Show, using these identities, the Nernst postulate (S → 0 as T → 0), and the relations f ( E ) = 1 exp[ β ( E − μ )] + 1 U = V 4 π 3 i d 3 kǫ ( k ) f ( ǫ ( k )) , (6) , that S = − V 4 π 3 k B i d 3 k [ f ln f + (1 − f ) ln(1 − f )] . (7) Here ǫ ( k ) is the energy oF an electron in state k . 5. Calculate the Pauli paramagnetic susceptibility, in the low temperature limit, oF an ideal gas oF Fermions with intrinsic magnetic moment μ * and spin angular momentum J ¯ h , with J = 3 / 2. 2...
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This note was uploaded on 07/15/2011 for the course PHYSICS 847 taught by Professor Stroud during the Spring '10 term at Ohio State.
- Spring '10