Alkali Metal Fuel (AMF) "Perpetual Motion Device" That would actually work to power boats or other water based things

The NAVY is working on a catalyst that would utilize carbon dioxide and hydrogen from seawater to power itself.  This would be a sort of perpetual motion device since just traveling through water might be able to ultimately generate more power that it consumes.  This actually could work since you are using the water as a fuel.  It would be like driving your boat on a lake of oil.  No one would have a problem saying the boat can travel forever (or at least until the lake of oil is used up) since the boat could just use the oil to power itself.

So here we are.  I don't think the NAVY idea is a good one.  I think we could do better.  Perhaps we could use a specially designed Alkali and/or Alkaline metal alloy (can include any metals and/or other ingredients including carbon or others) that is reactive to seawater but doesn't react too fast so that it can cause a sustained reaction  and/or it could be entirely composed of or partial of a natural mix like say from the reduction of sea salt and/or dead sea salt or whatnot.  Then instead of trying to harvest the CO2 and Hydrogen from the water (or in addition to), we can burn the catalyst by just letting it contact with water.  Alkali and alkaline metals are reactive to water so this property can be utilized, perhaps along with other properties like carbides burning into CO2 at elevated temperatures, to create not only heat from reacting with water, but also potentially break the water into hydrogen and oxygen which can also be used as fuel either as is and burned as well with the alkali fuel, or used later on and/or extracted and/or concentrated or stored or anything else.

So we are just using a special metallic fuel that is specially designed to burn with water.

The water can be pumped in or passively diffuse in or funneled in during craft movement or any combination.  Seawater is ideal but not exclusive, because the ions can help the water be broken into hydrogen and/or oxygen.  Catalysts including other metals and/or compounds and/or physical, chemical, electrical etc means can be use to help catalyze the splitting of the water and/or produce oxygen.

So the alkali metal fuel (AMF) would perhaps be in one tube under the boat or at an underwater base, or floating base or whatever.  Adjacent to it could be a tube with no catalyst.  Joining the two tubes could be a line of peltier devices (with or without heat blocks, insulation, etc).  So the heat produced by the AMF tube coupled with the cooling of the seawater itself, would create a voltage differential in the peltier devices, creating electricity.

Do I think that more energy can be made than the energy it took to make the AMF alloy fuel (likely a difficult reduction reaction)?  Yes because you are basically making a sort of chain reaction that will split the water, turning it into a fuel.  Also the sea or other water as a reservoir of "cold" gives us a free source of potential energy as well.  Just like a match when you ignite a piece of wood creates more energy than it took to create the match, so here the amount of energy from burning water will likely be greater than the AMF fuel match took to create.

Also more things, the heat can evaporate the water and the salts left behind could be used to create the alkali metal fuel.  Also the expansion of the water vapor from the heat could also help propel the craft or be used to create work/energy such as in a piston.

Here's another idea.  Say you make a diesel like engine.  You put a piece of AMF in the chamber or whatnot.  You inject water in and the AMF causes the water to vaporize creating motion in the piston and also the hydrogen (and perhaps some oxygen) gas is produced which is also combusted in the chamber.

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