Gibbs and Helmholtz energies of a superconductor

In summary, the Gibbs energy function has a superconducting-normal-state energy difference of $$G_n(T)-G_s(T) =\frac{1}{2} H^2_c(T) V$$.
  • #1
Botttom
15
0
Hello,
I consider an ideal superconductor with the gibbs-energy $$ d G=-SdT + VdP - \mu_0 M V dH$$
and helmholtz energy $$ dF = -SdT -P dV + \mu_0 V H dM$$
Assuming, that in the normal state the magnetization is too small, so that [itex]G_n(H) = G_n(H=0)[/itex] and at the transition point [itex]H_c[/itex] the superconducting phase energy equals to the normal state [itex]G_s(H_c) = G_n (H_c)[/itex] I get a continuous gibbs energy function with the superconducting-normal- states energy differency $$G_n (T)-G_s(T) =\frac{1}{2} H^2_c(T) V$$, when [itex]H_c(T)=H_c(0)(1-(\frac{T}{T_c})^2)[/itex].

Why one cannot use the helmholtz energy for the same calculation of the energy differences and would the function of the helmholtz energy would be continuous as well?

Thanks
 
  • #3
I suppose you could use Helmholtz energy, too, but which experimental setup would correspond to this situation? You assumed that the magnetisation in the normal state is very small, so if you want to keep M constant, it would have to be so in the superconducting phase, too. So basically you want to discuss the field free case.
 
  • #4
No, i just assume that the magnetization is small enough in the normal state, because the sample is not diamagnetic in normal state. The diamagnetism is only seen in the superconducting state with $$M=H,$$ and hence can not be assumed to be small enough to be neglected
 
  • #5
I understand this. But the Gibbs potential is so useful in this case because H is not changing on the transition, in contrast to M.
 
  • #6
But the helmholtz energy should still be continuous at [itex]T_c[/itex] like the gibbs energy, right?
 
  • #7
I don't think so. The two differ by a term MH. But below Tc, M=H, while below M=0. So if one is continuous, the other one jumps by ##H^2##.
 
  • #8
Just realsed that at Tc H=0, so both are continuous.
 
  • #9
Ok, thanks
 

What is Gibbs energy?

Gibbs energy, also known as Gibbs free energy, is a thermodynamic quantity that represents the maximum amount of work that can be obtained from a thermodynamic system at a constant temperature and pressure. It is a measure of a system's potential to do work.

What is Helmholtz energy?

Helmholtz energy, also known as Helmholtz free energy, is a thermodynamic quantity that represents the amount of internal energy that can be converted into work at a constant temperature. It is a measure of a system's available energy.

How are Gibbs and Helmholtz energies related to superconductors?

Superconductors are materials that have zero electrical resistance at very low temperatures. The Gibbs and Helmholtz energies of a superconductor are important in understanding the thermodynamic properties of these materials, such as their critical temperature and critical magnetic field.

What is the significance of the Gibbs and Helmholtz energies in the study of superconductors?

The Gibbs and Helmholtz energies play a crucial role in determining the stability of a superconductor and its ability to maintain its superconducting state. These energies also provide insights into the mechanisms behind superconductivity and can be used to predict and analyze the behavior of superconductors in different conditions.

How do Gibbs and Helmholtz energies affect the practical applications of superconductors?

The Gibbs and Helmholtz energies help determine the maximum amount of work that can be obtained from a superconductor, making them important considerations in the design and use of superconducting devices. They also influence the critical temperature and magnetic field, which are essential factors in the practical applications of superconductors in areas such as energy transmission and medical imaging.

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