# Magnetic cooling question

1. Sep 21, 2005

### sniffer

in a book says cooling by demagnetization can be explained in terms of reduced entropy.

As far as I know, entropy is associated with order. More order we have (i.e. more spin alignment), then less entropy S. Demagnetization results in disorder, since spins are more disorder, thus higher entropy, doesn't it mean higher temperature???

i looked at the graphs and read the paragraphs in the book several times but still didn't get it.

2. Sep 22, 2005

### ZapperZ

Staff Emeritus
Again, if you are refering to a book to ask such questions, it is imperative that you clearly cite the book, or any external sources. Without such things, we can't tell if the books is wrong, if your interpretation is wrong, or both.

Without such reference, I will hazzard a guess here. At some finite temperature (not T=0), you will have a distribution of energies of the particles in the system. If such a system consists of particles with magnetic moment, then what you have will be a distribution of such moments. If you put this system in a magnetic field, depending on the strength of the magnetic field AND the temperature, you will have a number of moment alligned with the field, and a number that is anti-alligned with the field.

Let's assume for simplicity that the moment alligned with the field is in a lower energy state than the one anti-alligned to it. So due to the finite temperature, there will be a fraction that has enough energy to be anti-alligned. But I can always increase the external magnetic field. This will force the anti-alligned moments to be alligned, thus forcing it into a lower energy state. What I am essentially doing is sucking the thermal energy from that moment via its "magnetic" energy. The more moment that I can force to allign, the more energy that I will suck out of the system.

However, this is not the end of the story. I then cut off the magnetic field. What will happen is that the system wants to go back to its original state temperature. It wants to do this by making those moments that got force to allign themselves with the external field to go back to the way they were. But to do that, they have to absorb energy from somewhere, because remember that in a magnetic field, the anti-allign state has a higher energy. So it absorbs energy from the system itself, i.e. other particles. I then reapply the external field, and now, the fraction of the particles having antialligned moments will be smaller. The system temperature is dropping.

I repeat the pumping cycle continuously to go to lower temperatures or to maintain the equilibrium temperature.

So you can't just look at the entropy of the system because it is being acted upon by an external field. Here, what you typically want to use as your state variables are T and V, and not S and V. So you transform your system to look at the Helmoltz free energy.

Zz.

3. Sep 26, 2005

### shyboy

Another crude explanation is the following:
When you inverse the field, the spin system is immediately in the nonequilibrium postion. You may describe this position as a state with negative temperature. Indeed, at negative temperature the number of spins at higher energy should be bigger then the number of spins at lower energy.
Now as the system will drift toward equilibrium, its entropy will go up. But, because the intial "temperature" is negative, to have a positive change of the entropy we need to have a negative heat change. So the system will cool itself.