Dehydration, Osmosis
and the 2nd Law of Thermodynamics

T   
his past Saturday, I spent several hours in the pool with my grandsons. After this amount of time one needs to begin a series of unending treks to the bathroom to get rid of excess water. This is almost pure water urine. You could probably offer a cup to someone (cooled of course) and they would not notice anything out of the ordinary. I didn't try this and won't in the future though some people drink urine regularly (an ambassador from India caused a minor sensation when he candidly admitted to taking his morning whiz in a glass and straightway chugging it down his pie-hole ... for health reasons ... of course).

Back to the salt mine ... ;o)

The cause of this prodigious urination is of course that your skin drinks water in greater amounts than you might think. It just takes a few hours to start the flow, i.e. to get through your skin, into your system and over to your bladder where it must be expelled as excess.

This brought to mind a book I once read, Survive the Savage Sea, an excellent true story about the travail of some people yacht-sunk by a whale and then living on a dingy and a raft. The woman was a nurse and gave sea-water enemas to all in order to get water into their systems in spite of the salt content (the large intestine extracts water before 'dumping').

This in turn brought to mind another story in Reader's Digest about some Cuban boat people trying to get to Miami and wrecked on a small rocky isle. They had no water and a few kids died. Others tried to swim for help and were never seen again. This could have been prevented by enema or skin-drinking water. Thus, if you ever find yourself at sea saying, "Water, water everywhere but nary a drop to drink" ... you just need to immerse yourself in the ocean water and your skin will in time take the proper measure (though you will probably not have to urinate as is the case with fresh water).

The reason being ...

Osmosis

Because our bodies are the same as salt water concentration, if you are short of water your body will imbibe pure water from the salt ocean until the two water-salt concentrations once again equalize. If you are in fresh water they can't equalize in principle so you simply gain more and more water forcing you to urinate copiously and frequently. If you couldn't urinate, you'd blow up like a balloon and burst ... literally. Drinking and urinating are the way in which we maintain the proper salt-water concentration (among other things).

How it works ...

osmosis1.gif - 3kb

The water fits through the membrane but the salt doesn't. Therefore, more often water from the left, less salty side goes into the right salty side than vice versa. The saltier side obtains to a less and less salty concentration until it matches the other side of the membrane ... or ... until the osmotic pressure stops the influx (which would be the case if the inflow side were contained in a strong metal shell).

There are only four basic possibilities here ... get it?
And one of them dominates if the two sides are not symmetric.

  • 1) Water goes through membrane to left
  • 2) Water goes through membrane to right
  • 3) Salt attempts to go through to left, but can't
  • 4) Salt attempts to go through to right, but can't

Now for the interesting part

Suppose we set up this apparatus.

osmosis6.gif - 10kb

There is a tank with two sides ... one water and one side salt water. A semi-permeable membrane is between them so water flows to the salty side. It rises to a second semi-permeable membrane and ... what?

Well, it can't go through and drip back into the fresh water again because once a little water wets the other side of the membrane the flow would reverse ... and be just the same as the bottom membrane. The setup is self-stopping. If it didn't stop, we would have a perpetual motion machine ... right?

No, not exactly. A perpetual motion machine typically is said to create energy out of nothing which can be tapped for use. This one (if it worked) would supply us with energy only at the expense of cooling, i.e. we could take energy out of its total heat content ...

WITHOUT A HEAT SINK AT A LOWER TEMPERATURE
That would constitute a violation of the Second Law of Thermodynamics but not the First Law.

My question (which I haven't yet answered to my own satisfaction) is ... what if I put a rag on the left side and try to "wick" moisture off the membrane (after all, it can go through continuously as evaporation - energy supplied by the sun) ... then ... gravity pulls the wicked pure water down the rag and more is wicked off at the membrane? The rag gets too wet and starts to drip. If one drop falls ... the Second law is falsified because we could, in principle, install a water wheel to turn a generator thus producing electrical energy at the expense of the total heat of the water, i.e. because the drop was gently lowered into the pool by way of the water wheel, less heat would be generated into the pool and so the net temperature of the system would be lower.

Second Law defeated by Osmosis and Capillary Action!

Whenever I get to this impasse, I know I will learn something I didn't already know ... or ... knew it in a different form. What is the answer? It must be simple.

hmmmmm ... I'm thinking of maple trees and tree sap and dripping faucets with pails on them stuck in the tree and ... hmmmmmm.


Naaaahhhhhhh ...

Next Day: 7-18-02

Why it won't work ...

The water rises to a certain extent on the salty side. At that limit no more fresh water enters the salty side because the osmotic pressure has increased enough to stop it. If it goes higher the process would reverse and fresh water would go back to the left side from the salty side, i.e. you can force it to go in the opposite direction.

The amount of force necessary to reverse is equivalent to the height of the salt water column above the fresh water column.

Now, the center of gravity of the water raised on the salty side is slightly higher than you might expect. This is because the fresh water that went to that side isn't just sitting on the top of the salt water ... it's mixed in with it. Therefore the center of gravity of the entire system is somewhat higher than when the fresh and salt water were the same height (even though for every bit the fresh went down ... the salt side went up). Thus, energy has been stored as a potential. That energy was taken from the heat of the system (kinetic) which is now slightly cooler. So, if our experiment were to work out, it wouldn't necessitate a First Law violation (when the drop falls some potential energy is re-converted into kinetic - heat).

But as we shall see, the drop won't fall anyway so it doesn't matter unless you're book-keeping.

When we put the rag (or any other capillary device) to the upper semi-permeable membrane, some amount of force is needed to 'pull' the water off that membrane ... which in turn measured itself against the force required to pull the water against the tendency to return through the membrane (it's self-stopping remember?).

And ...

osmosis5.gif - 6kb The amount of force required to reverse the osmotic flow is proportional to the difference in height of the fresh and salt water. So we need a capillary mechanism which is at least capable of lifting water to that height ... which ... when inverted to pull the water down will exert that same force. But that length just makes it to equilibrium. So there is no capillary arrangement that will wick the water off the upper membrane and deliver it continuously to the fresh water body on the left side ... even though such a continuous transfer would not be forbidden by the First Law.

Nor can the membrane water be removed by siphoning as would be the case if we butted a soda-straw full of water up to the membrane which led to the fresh side. We could only manage to get enough force (once again) to reach equilibrium.

Suppose, however, that we replace the straw with an inverted funnel full of water. Would all the extra water in the wide part of the funnel serve to 'suck' harder on the membrane? Unfortunately, no. The force sucking would be proportional to the size of the hole touching the membrane same as before. There is no change regardless of the shape or constitution of the setup.

Can you see how hydraulics conspires to uphold the Second Law?

Every part of physics is like this. Everything works in perfect relationships with the conservation and symmetry laws. There are no faults. All is connected together as a seamless whole. If one conservation were to fail ... all the others would too. All are true ... or ... none are.



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