Thought Experiment - Buoyancy and Density

[Positron]

I have attempted a simple thought experiment with buoyancy and density
changes and have attempted to model the situation mathematically. The
main objective have been to investigate the relationship between
applied work and energy potentially harvested from the system by
changing the density of an object with with one mechanism and
harvesting the energy potential produced by this using another method.

Depending on the situation, my current mathematical model indicates a
theoretical net energy gain, depending on certain specifications such
as the relationship between size and weight of the object. Realizing
that this is widely considered to be impossible, I suspect that there
must be some mistake in my approach or model. I have been unable to
find it as yet, and would appreciate it if you could investigate the
situation and give your input.

I have made the spreadsheet I used to do my calculations as well as a
short explanatory slideshow available under the files section of the
the Google Group The Tied:
http://groups.google.co.za/group/thetied/files?hl=en

Thank you in advance.

[Uncle Al]

Positron wrote:
>
> I have attempted a simple thought experiment with buoyancy and density
> changes and have attempted to model the situation mathematically. The
> main objective have been to investigate the relationship between
> applied work and energy potentially harvested from the system by
> changing the density of an object with with one mechanism and
> harvesting the energy potential produced by this using another method.
>
> Depending on the situation, my current mathematical model indicates a
> theoretical net energy gain, depending on certain specifications such
> as the relationship between size and weight of the object. Realizing
> that this is widely considered to be impossible, I suspect that there
> must be some mistake in my approach or model. I have been unable to
> find it as yet, and would appreciate it if you could investigate the
> situation and give your input.

[snip]

1) Time is homogeneous.
2) Noether's theorems.
3) Mass-energy is locally conserved.

Modality is irrelevant. Tell us what path to take so that the center
of mass of a kilogram test mass positioned one meter above a surface
has a potential energy differing from mgh.

> I have made the spreadsheet I used to do my calculations as well as a
> short explanatory slideshow available under the files section of the
> the Google Group The Tied:
> http://groups.google.co.za/group/thetied/files?hl=en
>
> Thank you in advance.

--
Uncle Al
http://www.mazepath.com/uncleal/
(Toxic URL! Unsafe for children and most mammals)
http://www.mazepath.com/uncleal/qz4.htm

[Positron]

> Uncle Alhttp://www.mazepath.com/uncleal/

>  (Toxic URL! Unsafe for children and most mammals)http://www.mazepath.com/uncleal/qz4.htm

On what grounds do you claim that modality is irrelevant? If you
noticed, I only used standard gas laws, w = PV and PV = nRT and mgh.
No part of the process involves any mass above a surface, everything
occurs underwater, so I am not sure why you asked that I should
explain that? I never made any statement or assumption in that regard.

[jbriggs444]

I'm not in the habit of downloading binaries mentioned in Usenet
posts. So I have no clue about what your Rube Goldberg device does.

Under what circustances do you believe that w = PV?
Does your apparatus meet those conditions?

Hint: Adiabatic, isothermal, natural log of pressure ratio

[Positron]

I have assumed isothermal conditions during the pumping of the gas.
The gas is not compressed (which involved logs of pressures), I tried
a design that way first but found it more efficient to pump the gas
from an external storage tank, as the objective is change of volume
(bringing about change in density), and compression requires
exponentially more work to get a decrease in volume as the compression
progresses.
Somebody else also requested that I explain it without requiring
downloads of Excel and PowerPoint documents. I have saved the
slideshow as a series of images located here: http://sites.google.com/site/thetied/documents

The original files can also be retrieved from:
http://sourcequest.freeforums.org/density-buoyancy-harvester-thought-experiment-t3.html

Here follows the explanation in the PowerPoint document:

The design constitutes of a hollow container separated into two
compartments by a movable diaphragm, one containing gas and the other
containing water. The water side of the container has an opening that
allows for free passage of water into and out of the container. The
gas side of the container is connected to an external gas storage
tank.
Step 1: Container at minimum depth with gas pressure equal to water
pressure and overall density of container equal or greater than that
of water.
(Zero net force, gas compartment relatively small)
Step 2: Container moved to maximum depth. This step requires no work
to be done on the system as the density is equal to or slightly
greater than that of water. The gas compartment size decreases
further
due to increase in water pressure and loose diaphragm, resulting in
an
increasing downwards force as the compartment lowers.
Step 3: Gas pumped into container to give net upwards force. Density
equal or slightly less than that of water. This step requires work to
be input into the system. Size of gas chamber increases.
Step 4: Container moves to minimum depth, performing work on attached
cable and generator system. The net force acting upwards increases
with decrease in height as water pressure decreases leading to
greater
density difference. (Larger gas chamber)
Step 5: Gas pumped out of container to make overall density again
equal to that of water to allow container to move downwards.
Cycle is now complete and is repeated from Step 1.

If you require further explanation of the operation of the proposed
system, the accompanying spreadsheet that I used to model the
situation mathematically, want to know how I derived the equations I
used in the spreadsheet or want my explanation why I think it is
valid
for such a system to operate within the normal laws of
thermodynamics,
please let me know.

[G=EMC^2 Glazier]

To ya All Every scuba diver knows the deeper you go the smaller the
bubbles. You can get an idea of your depth from noting how much smaller
and slower your bubbles are. Pressure makes air more dense. More dense
less bouyancy. Bert