Originally posted by: QuantumPion
The best idea for a perpetual motion machine, which took me considerable time to understand its failings, is this:
Imagine a very tall U-shaped container, one side filled with fresh-water and the other with salt-water. The bottom is separated by a reverse-osmosis filter, and the top ends of the tube are touching with a lid. The containers are tall enough such that the weight of the water provides sufficient pressure for the reverse-osmosis process to occur. Since salt-water is denser then fresh-water, its level will be lower then the fresh-water given a fixed system volume. As the salt-water passes through the filter, the level of the fresh-water side rises, causing the excess to spill back over into the salt-water side, thus forming a self-sustaining flow loop from which work can be extracted.
Start from an understanding of Potential Osmotic Pressure. Let's use your structure of a large U-tube with a semi-permeable membrane across the bottom, salt water on one side, and fresh water on the other. Let it sit there for a long time. Water molecules can flow through the membrane in both directions, but the salt molecules cannot. Because the concentration of water on the two sides is different (higher in the fresh water side), the net exchange will be that more water flows from the fresh side to the salty side. This means the volume on the salty side increases, thus increasing the height of the column of salty water and reducing the height on the fresh side. That produces a higher static pressure on the salty side of the membrane, which tends to push water through the membrane from salty to fresh side faster than if the pressures were equal (as it was at the start of the experiment). So the build-up of pressure (from column height) on the salty side creates a flow preference that opposes the tendency for water to prefer to flow from the high-water-concentration (fresh water) side to the salty side. At some point these two driving forces just exactly match each other and the two column heights stop changing. They have reached an equilibrium state. The difference in pressure between the two sides (because of the difference in column height) is called the Static Osmotic Pressure for that salty solution. The process that got us to the equilibrium state is called Osmosis.
Now, to change the equilibrium and cause a preferential flow of water molecules from the salty to the fresh water side we can apply an external force (pressure) on the salty side so that the net pressure at the membrane on the salty side is greater than the Static Osmotic Pressure. Since that causes flow opposite to the direction of the original "normal" Osmosis, we call this "Reverse Osmosis". It is widely used in lots of processes. In the system proposed here, this could be accomplished merely by adding more salt water to the salty side and increasing the column height to accomplish the required pressure difference. But look closely at what we have now. The height of the salty water column at equilibrium was higher than the fresh water column, and now we've just increased that even more to produce Reverse Osmosis. Over on the fresh water side, how do you expect to get the height of that column up to the top of the U-tube so it can overflow back to the salty side? You can't without providing an external source of energy to do that work. That is just the opposite of what was proposed.
The original proposition postulated that the water column heights would just naturally make the fresh water column side higher than the salty water side so that work could be done as water flowed over the top. The facts deny that.