Superconductivity Critical B field, thermodynamical proof

[Cheetox]

Homework Statement

Use a thermodynamic argument to show that a strong magnetic field will cause a transition from a super-conducting to a normal state.

Homework Equations

The Attempt at a Solution

Most books seem to use, the fact that the gibbs function of the super-conducting and normal states are equal at the critical B field to then derive the change in entropy and heat-capacity between the two regimes. But assume the critical field from the meissner effect rather than prove in thermodynamically.

I'm guessing you need an expression for the gibbs function of the super-conducting state and the normal state, and comparing them you'll be able to see that the application of a large B will make them equal, but I don't know how to formulate a gibbs function for both sates in term of parameters that you can compare...any ideas? thankyou

 

[Jhero]

Thank you for your question. I would be happy to provide a thermodynamic argument for the transition from a super-conducting to a normal state when a strong magnetic field is applied.

First, we need to understand the concept of superconductivity and how it is related to magnetic fields. Superconductivity is the phenomenon where a material has zero electrical resistance and can conduct electricity with 100% efficiency. This is possible because of the formation of Cooper pairs, which are pairs of electrons that have opposite spin and are bound together by lattice vibrations.

In a superconducting material, the electrons are in a state of perfect order and are able to flow without any resistance. However, when a magnetic field is applied, it disrupts this order and causes the Cooper pairs to break apart. This is because the magnetic field exerts a force on the electrons, causing them to move in a circular motion, which disrupts the formation of Cooper pairs.

Now, let's consider the thermodynamics of this system. The Gibbs free energy, denoted by G, is a thermodynamic potential that takes into account the enthalpy (H) and entropy (S) of a system. In the case of a superconducting material, the Gibbs free energy in the absence of a magnetic field can be written as:

G = H - TS

Where T is the temperature and S is the entropy. In a superconducting material, the entropy is zero due to the perfect order of the electrons, so the Gibbs free energy reduces to:

G = H

Now, when a strong magnetic field is applied, the electrons are disrupted and the entropy increases. This means that the Gibbs free energy also increases, as shown in the equation above. At a critical magnetic field, the increase in entropy becomes equal to the enthalpy, and the Gibbs free energy becomes equal to zero. This is the point where the superconducting material transitions to a normal state, as the disruption of the Cooper pairs leads to the formation of resistance and the material can no longer conduct electricity with 100% efficiency.

In summary, the application of a strong magnetic field disrupts the order of electrons in a superconducting material, leading to an increase in entropy and a decrease in the Gibbs free energy. At a critical magnetic field, the Gibbs free energy becomes equal to zero and the material transitions to a normal state. I hope this explanation helps to answer your question. Let me know if you have