[extropy-chat] energy from osmosis
hal at finney.org
Wed Oct 5 00:20:37 UTC 2005
There are two different questions raised by this thought experiment.
One sees the experiment as a paradox and asks whether it violates the
laws of thermodynamics. The other asks whether it would work in practice
in the oceans of Earth.
I am mostly looking at the first question. An interesting variant on
the experiment sheds light on that issue. Imagine that the entire pipe
is made of a semipermeable osmotic membrane, instead of just the cover
at the bottom. The whole pipe allows water molecules to pass through
freely, while blocking salt.
If we again assume an ocean at equilbrium, without surface heating, wind
or wave action, it should be clear that once the pipe fills with fresh
water to the initial depth, nothing more will happen. At each depth,
fresh water moves between the pipe and the ocean, in equal amounts.
There is no net inflow at some depths which is balanced by a net outflow
at other depths. That would involve a constant circulation of water
even though we are at equilibrium, which would violate the second law.
In order for this to work, then, it is clear that the pressure difference
across the pipe walls at each depth must be precisely what is necessary to
match the salinity at that depth. When we go deeper by some amount, the
pressure difference increases slightly due to the difference in density of
fresh and salt water. At the same time, the salinity increases slightly
as well, due to the fact that salt is heavier than water. These two
effects will be precisely balanced so as to cancel each other out.
Any imbalance would violate thermodynamic law.
Since this is the condition which will obtain after we have inserted the
pipe and allowed it to fill, and since the pipe is small compared with
the ocean, clearly this condition will be met before we insert the pipe
as well. In equilibrium (again sans solar influence) the ocean's salinity
gradient will be such that the density of water molecules increases
exactly as fast (with depth) as if the salt were not present at all.
This surprising result is what comes from this thought experiment. It is
amazing to me that the salt distribution, which is due to a balance
between upward diffusion and the downward effects of gravity, will come
out to exactly what is needed to produce this effect on the water density.
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