I had a discussion yesterday, and I found my understanding of entropy lacking. I know that entropy is not exactly the same as the degree of disorder in a system, but I also know that outside of specifically designed experiments, it's quite difficult to find examples where the two are not intimately linked.
A hydroelectric power plant works by taking water from one basin and pouring it out into another. If these two basins are the same and placed at the same height, but one has a higher water level, then we see that after outputting electric power, the end state is a bit more disordered than the initial state (it goes from one basin having all the water and the other basin having no water to both the basins having some water).
However, if the basins are smaller, but one is filled with water and placed higher than the other, which is empty, so that you may empty the top one completely of water and fill the bottom one entirely, then the degree of disorder seems to be much closer.
In both of these two examples, if I were to just move the water without passing it through a generator, then the disorder has increased because the potential energy of the water has become chaotic movement and heat within the water, so it's not nearly as "available to do useful work", to quote the entropy tag. If the generator is used, the water slows down, but you make electric power which is spent to make something that eventually turns into heat somewhere else.
On the other hand, in the second example we still have one basin full of water and one basin with no water after using it all, so that contribution to the total disorder seems to disappear without the generator noticing any difference.
How come the generator doesn't notice any difference? Have I misunderstood something, and the state "the water is in the lower basin" actually has higher disorder than "the water is in the upper basin"? Or is this one of the places where I have to discard the "entropy = disorder" notion that popular science loves so much?