1. Calculate the free energy decrease when a transition from the normal state to the superconducting state takes place.

See text for the working out. The final expression is

2. Is the transition from the normal state to the superconducting state in the absence of a magnetic field a first or a second order transition? What is the order in case a magnetic field is present ?

In the absence of a magnetic field, the superconducting transition is a second order transition. On the other hand, in a magnetic field the T_c reduces and there appears a jump in free energy as for a first order phase transition.