The picture compares the entropies (arbitrary units) of a piece of iron (say) magnetized and demagnetized, respectively, at same temperature.
The natural process is demagnetization, so entropy decreases on magnetization.
Ferromagnetism is due to tiny "elementary magnets". They are there whether the iron is magnetized or not. If it is, most elementary magnets are oriented in the same direction. If it is not, they are oriented randomly, thus mutually compensating their magnetic fields.
This remark is a first hint to the statistical interpretation of entropy. It will be elaborated elsewhere. Thermodynamical quantities are never defined statistically, because when thermodynamics was developed, atomistic theory of matter was not established yet. Thus one has to avoid carefully taking the metaphor for the concept. That is why I focused on the thermodynamic concept of entropy, avoiding to mention "order", which is also hard to quantify. Used with caution, these intuitive concepts certainly have their place in science, as they might help us wrapping our brains around unfamiliar quantities.
A better concept than "order" would be probability. In fact, a less probable state is said to be more "ordered". Why is the state of the magnet with all its elementary magnets heading in the same direction less probable?
Look at two elementary magnets. There is only one possibility to arrange them both heading north. But there are two possibilities to get heading one of them south and the other north.
Thus letting both magnets be oriented the same way is clearly less probable than having each of them directed in a different out of two directions. But who would say that the neat antiparallel arrangement is less "ordered"?
You now might want to go back to the examples and consider each of them in the light of of this new term. Read the examples and explain to yourself, why "order" is changed the way it is. Best is you write your explanations down. Then compare them with the suggestions you get by clicking here.
Is that system closed, isolated or open? Since the task was to magnetize the piece of iron at constant temperature, heat exchange with a thermal bath must be allowed. Thus the system is not isolated, but closed. Upon magnetization, heat is exported from the peace of iron.
This mechanism is used to reach very low temperatures. A sample is cooled down, then magnetized in contact to a heat bath. Heat is exported and entropy of the sample is reduced. After equilibrium is reached, the sample is isolated from the thermal bath and alowed to demagnetize. The loss of orientation of the elementary magnets consumes heat, so the temperature falls.
Last update Mar. 19. 1999, GVa