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Let's say you have an object travelling between two immiscible liquids like water and oil in an arrangement shown below. (water being blue and oil being yellow)

Oil being yellow, water being blue The object is a cubic meter weighing 999 Kg. It displaces one cubic meter of oil as it passes through it but it's weight overcomes the amount of oil it displaces or its buoyancy. When the object sinks to the bottom of the oil It's transferred into the water. In the water it displaces one cubic meter of water or 1 ton of water so it's buoyancy overcomes it weight and it should float up.

It's then easy for someone unversed in physics like me to conclude that some kind of perpetual motion machine would be possible. I can see the transfer of the object from one liquid to the other would probably cost some energy but it could be easily accounted for by making the pits very deep and generating energy from the moving object.

Now of course I know this isn't possible but I just don't understand why?

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For this to be a perpetual motion machine, you need to transfer the block between containers. It's easy at the top, you just pick it up, translate and drop down. At the bottom, removing the block with arbitrarily négligeable energy cost from the oil is conceivable. You can even recover a bit more energy as oil will fill the space left empty by the block. However, to insert the block in the water at the bottom, you will need to push the block against the pressure of the water or find another way to create an empty space to slide the block into by raising part of the water. Deeper containers don't help as the pressure at the bottom is larger and therefore require more energy.

Note that the block at the bottom of water is the highest energy state of the system. That is because to obtain it, you must raise a volume of water equal to the volume of the block the full height of the water column, and water is the densest thing in your system.

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