Question of conservation of energy in this thought experiment

[Low-Q]

Hi,

I have a somewhat silly question about something I cannot figure out properly.

I have a cylinder with a piston inside. The cylinder is sealed and filled with air. The piston is free to move back and forth inside the cylinder, but are also sealed so no air can escape no matter how much the piston compress the air inside the cylinder.

If this system is submerged into a fluid, water for example, the water pressure will push the piston further into the cylinder so the air inside becomes compressed according to the water column above.

When I pull the system up to the water surface, the air inside the piston finally expands to initial volume.

So to the question:
If the piston is a magnet, and the cylinder is a coil, and I repeat the experiment, the moving magnet piston will generate an electric current through the coil if the coil is shorted or loaded.

We all know that energy is allways conserved, so:
What difference in work, and how would it "feel like", to put the system in and out of the water if the coil is:
1. Not loaded
2. Loaded

Br.

Vidar

 

[Dale]

No load case:

The piston has a certain amount of buoyancy, so it will take work to push it under water. The change in volume will reduce that buyoancy as the cylinder goes further down and therefore reduce the amount of energy per meter it takes to push it down. On the way up work can be extracted from the piston. The amount of energy extracted per meter will increase as the piston expands and the buoyancy increases. Neglecting friction and viscous losses, the energy required to push the coil down will equal the energy recovered in raising it.

With load:

In this case the energy removed through the coil will cause a back emf on the piston, meaning that it will require more force to compress it than if the coil were not there. This will make the cylinder remain larger than it was previously on the way down, increasing the work required to push it down. On the way up, the back emf will work the other direction, meaning that it will require more force to expand it than if the coil were not there. This will make the cylinder remain smaller than it was previously on the way up, decreasing the work extracted in pulling it up. The difference in work from the previous case is equal to the energy delivered to the load.

 

[Dale]

Btw, in general, making complicated scenarios is counter-productive to understanding. It is far better to make a scenario as simple as possible. Here, the water is simply a complicated and non-intuitive mechanism for squeezing the piston, full of viscous losses etc. It is far better to use a simpler scenario where you simply push on the piston directly with whatever force you are using to push it underwater.

In such a simplified scenario it should be clear that the back-emf causes a force opposing the change in the size of the piston.