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The process begins with the drawing below.

The freeze thaw pump is a heat exchanger for the adsorption of heat from water /
freezing of  water. It should have been labeled as a freeze pump in the drawing.

Its energy source could be a heat radiator and pump located above the water's surface,
in cold arctic air. A cooling fluid is circulated between the radiator and the adsorber.

Cyclically the Ice is discarded and new water taken in and frozen.

The water expands upon freezing, presses a hydraulic fluid through a piston cylinder
and moves a piston.  It is a water phase change driven, hydraulic press.

Note that, Only for simplifying of the math, did I assign a 1 square centimeter surface area to
the piston.  As a result, this give a very long piston stroke (caused by the hydraulic pressure
/ fluid) 80,000 centimeters length.  It will be more practical to have a larger piston diameter
and a shorter piston stroke.  This would however, necessitate the changing of all of the various
mathematical ratios given in the exemplary model of its operation.

The hydraulic press / piston's motion is used to draw / pull a vacuum in another piston and
cylinder. I have referred to that   other  piston and cylinder as a syringe (like unto a syringe used for hypodermic injections but obviously much larger).  That syringe pulls nothing into itself
as it expands. An empty space / vacuum in relationship to the surrounding water pressure
is created instead.  The syringe is
                                              LATCHED
                                                    in that position until it has arrived at the surface
 of the water.  I hope this helps for now.


                 EDIT
               And math checked

1280   kilograms of buoyancy  x 1101 meters of depth = 1,409,840 joules.
                                                                                   not 14,092,800 joules.