# (a) Show that , in S1 units for B c - Because B c decreases with increasing temperature, the right side is negative. The superconducting phase has the lower entropy: it is the more ordered phase. As 0,

(a) Show that

,

in S1 units for B_{c}- Because B_{c} decreases with increasing temperature, the right side is negative. The superconducting phase has the lower entropy: it is the more ordered phase. As τ → 0, the entropy in both phases will go to zero, consistent with the third law. What does this imply for the shape of the curve of B_{c} versus τ?

(b) At τ = τ_{c}, we have B_{c} = 0 and hence σs = σ_{N}. Show that this result has the following consequences: (1) The two free energy curves do not cross at τ_{c} but merge, as shown in Figure (2) The two energies are the same: Us(τ_{c}) = U_{N}(τ_{c}). (3) There is no latent heat associated with the transition at τ = τ_{c}. What is the latent heat of the transition when carried out in a magnetic field, at τ < τ_{c}?

(c) Show that C_{S} and C_{N}, the heat capacities per unit volume, are related by

Figure 8.18 is a plot of C/T vs T^{2} and shows that C_{S} decreases much faster than linearly with decreasing τ, while C_{N} decreases as Tτ. For τ << τ_{c}, ∆C is dominated by C_{N}. Show that this implies

Experimental values of the free energy as a function of temperature for aluminum in the superconducting state and in the normal state. Below the transition temperature T_{c} = 1.180 K the free energy is lower in the superconducting state. The two curves merge at the transition temperature, so that the phase transition is second order (there is no latent heat of transition at T_{c}). The curve F_{S} is measured in zero magnetic field, and F_{N} is measured in a magnetic field sufficient to put the specimen in the normal state. Courtesy of N.E. Phillips.

**Transcribed Image Text:**

## 1 d(B?) (os-ON) Be dBc Ho dt 2Ho dt dt

## This problem has been solved!

- Tutor Answer

## a We saw in 8 56a that the free energy difference per unit volume between the normal and t…View the full answer

**Related Book For**

## Students also viewed these Solid State questions