In class we showed that the difference in free energy between the superconducting state and the normal state
is given by
F_(s)(T)-F_(N)(T)=-(1)/(2)V\mu _(0)H_(c)^(2)
We aslo derived from Ginzburg-Landau theory that that the critical field H_(c) is related to the free energy
parameters a and b through the relation,
H_(c)=((a^(?)))/((\mu _(0)b)^((1)/(2)))(T_(c)-T)
Show that at the phase transition temperature, T_(c), the entropy is continuous, but there is a change in the
heat capacity. Obtain an expression for the heat capacity change in terms of a,b, and T_(c).