[extropy-chat] energy from osmosis
hal at finney.org
Wed Oct 5 06:57:25 UTC 2005
> Hal I disagree. In your thought experiment, the pressure difference
> between the seawater outside the pipe and the fresh water inside is
> maximum at the bottom end and decreases linearly to zero at the surface.
> Water flows into the pipe below 9600 meters and out of the pipe everywhere
> above 9600. Fresh water flows upward thru the pipe. The process is
> driven by the energy released by falling salt: the depths are getting
> more salty and the upper layers less so. Assuming no mixing of currents
> and tides, the process continues until such time as equilibrium is
> established, with the surface of the fresh water 240 meters below the
> surface and the salinity increasing all the way down such that there is
> no flow in or out.
[With some later corrections]
Actually I agree substantially with this. The key is that last part,
the reaching of the equilibrium. All of my analysis was with regard
to the equlibrium state. I focused on this because some arguments may
superficially suggest that the circulation can go on forever, violating
the laws of thermodynamics. I was analyzing the nature of the equilibrium
that will keep this from happening.
The point is that, neglecting wind and wave action (and solar heating),
the ocean is in equlibrium even before we put in the pipe. (I don't mean
our ocean, which is of course subject to all kinds of disturbances, I
mean a hypothetical ocean with the same salinity and temperature as ours
but which has been left to rest for a few million years so it reaches
its natural equlibrium.) That equlibrium before we insert the pipe must
be the same as the one that is reached after the pipe has been there a
while, because the presence of this one little pipe cannot change the
equlibrium state for the whole ocean.
Thus my conclusion that even before we add the pipe, an ocean in
equilibrium must have a salinity profile which exactly matches the
osmotic pressure difference between ocean water and a hypothetical column
of fresh water starting 240 meters below the surface. When we add our
permeable pipe to an ocean in equlibrium, once the pipe fills with fresh
water to the 240 meter mark, there will be no net flow at any depth.
Does that make sense?
BTW I've been googling for a description of gravity induced concentration
gradients, and the best I've found so far is this homework problem,
<http://gandalf.umd.edu/CHEM482/Exam2_answ.pdf>. Problem 3 describes
how the concentration gradient is created and shows its form, which is
an exponential function.
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