[extropy-chat] energy from osmosis

Tue Oct 4 23:10:21 UTC 2005

--- Dirk Bruere <dirk.bruere at gmail.com> wrote:

> Sat soln of calcium chloride or ammonium nitrate.
> Tube in a tube.

Actually it isn't anywhere near that simple. Assuming
that you have an ideal solution (low solute
concentration and the particles don't interact with
each other) Long derivation skipped, you get a pretty
simple equation for the "break even" depth. That is
the depth which you have to stick the "pipe" to cause
the higher density (and therefore higher hydrostatic
pressure) of the solution to overcome the osmotic
pressure and "push" the pure solvent (in our case
fresh water) up to the same level as the solution on
the outside of the pipe.

The equation is D=iRT/gM, where D is the "break even"
depth, i is the number of ions in your solute molecule
(for example for NaCl it would be 2, 1 sodium and 1
chloride), R is the gas constant, T is the temperature
in Kelvins, g is the acceleration of gravity, and M is
the molecular weight of the solute in kilograms/mole.

Now one can see that this makes intuitive sense in
that since we are relying on the solution to be more
dense than the solvent to provide the "push", then the
heavier the molecule employed, the higher the added
density per molecule to the solution. So the trick is
to get the heaviest possible molecule that will go
into solution. I have run some calculations using some
salts that I found data on and got the following
results:

Solute	Ions/molecule	MW(kg/mol)	breakeven depth (m)
NaCl	2	0.058443	8656.511875
CaCl2	3	0.110986	6837.518113
NH4NO3	2	0.0804	6292.444322
BaCl2	3	0.20827	3643.677847
PbAc2	3	0.325	2334.980878
sucrose	1	0.3423	738.9899555

Intestingly enough, in the derivation of the equation,
the concentration of the solution "fell out" as it
does not affect the "break even" depth, but instead
acts a multiplier that will exaggerate any effects
caused by being above or below the break-even depth.
Also note that the break even depth of NaCl, is not
the same figure as given earlier for the ocean (around
9800m) this is because the while the primary salt in
the ocean is NaCl, it is not the only one as there is
MgCl2 and other stuff as well, so the ocean is not a
"pure ideal solution" of salt.

So as you can see from the table, even the heaviest
salt I could find, lead acetate, is still on the order
of kilometers of depth. While sucrose, obviously not a
salt, brings it down 738 meters which still won't fit
in a lab and is not very practical. So at that point I
decided to say screw trying to keep my solutions
ideal, just go with the heaviest solute possible. That
lead me to proteins, which are gigantic compared to
most molecules yet still fairly soluble.

So if looked into using the cheapest solution of
protein I could think of which was milk. Milk has an
average density of 1031 kilograms/cubic meter and an
osmotic pressure of 700 kiloPascals. (Its amazing what
you can find on Google.) So for milk we would only
need a depth of 226.76 meters to break even. We are
getting better here, but this is still impractical. 

So I started to look for data regarding osmotic
pressures of individual proteins in purified form.
Unfortunately, because protein solutions deviate very
far from "ideal solutions", the osmotic pressure must
be measured empirically. So far, I have only found one
candidate where that was done. Bovine serum albumin in
this article linked to here:

http://www.sciencedirect.com/science?_ob=ArticleURL&_udi=B6TFB-3Y2FXCR-9&_user=4423&_coverDate=12%2F31%2F1995&_alid=319909975&_rdoc=1&_fmt=summary&_orig=search&_cdi=5222&_sort=d&_st=4&_docanchor=&_acct=C000059605&_version=1&_urlVersion=0&_userid=4423&md5=f113121eb5369c5cd0fdec71db534453

So to summarize, after reading the article, I was able
to determine that the break-even depth of BSA at
concentration of 120 grams/liter at a pH of 4.6 (the
osmotic pressure of proteins change wth pH), was only
3.333 meters. 

A huge improvement and practical to do, but pretty
useless in the end. Who cares if you can get fresh
water dribbling out of the end of a pipe thrust into a
long tube of BSA solution? It would be a novelty at
best and an expensive one at that. Even if you could
hook up a water wheel to it, the protein solution
would get pretty nasty over time with mold and such.
It may settle the debate about getting energy from
thrusting a 6 mile long pipe down the marinas trench,
but I will leave the actual building of the device to
somebody with more time and money. So consider this to
be now be in the public domain.

The Avantguardian 
is 
Stuart LaForge
alt email: stuart"AT"ucla.edu

"I don't want to achieve immortality through my work. I want to achieve it through not dying." - Woody Allen

"Our hope of immortality does not come from any religions, but nearly all religions come from that hope" - Robert G. Ingersoll

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