# Critical field for a type I superconductor

1. Sep 19, 2010

### quasar_4

1. The problem statement, all variables and given/known data

Consider a type I superconducting material with a parabolic coexistence curve separating the uniform superconducting and normal phases. H is the external magnetic field and T is temperature. Ignore the tiny magnetization of the normal phase. The critical field is
Hc = H0 +a*T + b*T^2.

a) Why must the coefficient a =0?
b) Find the latent heat per unit volume as a function of T along the coexistence curve
c) Calculate the discontinuity in the specific heat per unit volume at constant H along the coexistence curve

2. Relevant equations

Hc = H0 +a*T + b*T^2

3. The attempt at a solution

I'm mostly at a loss on this one. I know that with a type I superconductor, the Meissner effect vanishes instantly if the external magnetic field exceeds this critical field, Hc, but I have no idea why that means the coefficient a has to vanish. Is it just that we want the vertex of the parabola to lie on the field axis?

I'm guessing that for part b I want to use the Clausius-Clapeyron relation, but not sure... and as for c I'm afraid I can't say much until I do a and b. Any hints? Any good references that actually discuss this? This is supposed to be part of "thermodynamics review" from undergrad days, but my undergrad text says almost nothing about superconductors, so it's not helping too much.