Beyond the Plumber's Nightmare

The Plumber's Nightmare drawing is just the tip of the ice box.  The reason someone like me made a drawing like that is because there is some serious confusion about the basic physics.  Carl Sagan proposed the "Faint Young Sun Paradox".  Had Carl started at the basic physics of water, there would never had been a paradox.  The system is perfectly understandable which does not particularly bode well for the current crops of "Geniuses".  A paradox is a problem to be solved not embraced.

If Sagan's basic theories resulted in a paradox, then his basic theories are questionable.  If Hansen's basic theories are based on Sagan's basic theories which resulted in a paradox, then Hansen's basic theories are also questionable.  Science does not advance without addressing problems, in this case, the Faint Young Sun Paradox.  The solution of the paradox is simple.  Ein=Eout only over a significantly long period of time and then is likely not to last long.  Entropy rules the universe, that is rule number one of physics.

Entropy is in the eye of the beholder.  An object at a higher energy state will attempt to find a lower energy state.  If that object can convert its energy into another form that results in a lower state, then that conversion may be useful in some way, then it is called work not entropy.  That was Carl Sagan's basic misunderstanding.

Sagan's paradox was that there was not enough apparent energy to melt and maintain liquid water on the Faint Yound Sun Earth.  Our current sun provides approximately 1360Wm-2 of energy at the top of the Earth atmosphere.  1360Wm-2 if it were absorbed by one object perfectly could produce a temperature of (1360/5.67e-8)^.25=393K degrees or 120 C degrees.  That is plenty of energy to melt ice.  Since the orbit of the EArth is not perfectly circular, the available solar energy can exceed 1400Wm-2.  With the Faint you Sun at 50% of today's sun there would be 700Wm-2 available capable of heating an object to 333K or 60 C degrees.  There is not issue with the ability of the faint young sun to provide energy, just the ability of the Earth to retain enough energy until the next sunrise.  The evidence said that water existed, the sun is not the issue, then Sagan's logic is likely the flaw.

What Sagan may believe is that the average energy available at the surface of the Earth is 1/4th the available solar or 175 Wm-2 for my example.  Actually, at the equator, 350Wm-2 would be available during the day with a peak of 700Wm-2  at some equatorial point for some period of say one hour's time.  If some surface of water had a low enough albedo to not reflect a significant amount of that energy, then the surface would warm.

If that surface absorbed 350Wm-2 time 12 hours there would be 4200 Watts per meter square which neglecting the fineries of the calculations could be converted into 1000Joules of energy during that period, call it Joules per day if you like.  If the surface did not release all of that 1000Joules in the 12 hours of darkness, then water would exist, energy would accumulate and the Earth would be warmer.  This has absolutely nothing to do with any greenhouse effect or scientific mumbo jumbo, it is just water has thermal mass and only radiates energy from its surface.

If you would prefer to get fancier, then consider a line by line estimate of the solar spectrum and the absorption spectrum of water.  Water absorbs most of the solar spectrum and a fair percentage at depth.  The sun's rays can penetrate water, some of that energy is absorbed, that absorbed energy is not radiated from beneath the surface it has to move via convection and diffusion to the surface or surroundings to escape.  The water gained energy and since we think that is a good thing, work was done.  If the energy makes it to the surface and to space it is lost, what does not make it back to space is converted to work.

Water under goes phase changes which have to be considered.  If the surface freezes, then the temperature maintains that freezing point until all the energy is lost.  The freezing point of fresh water is 273.15K degrees or 316Wm-2 if it were a true black body.  It is not a true black body so ice has a higher albedo or reflectivity than liquid water.  So if the water absorbed 1000Joules via 350Wm-2 of radiation for 12 hours and only can release 316Wm-2 of energy for the 12 dark hours, then it would have retained 350-316=34Wm-2 squared per hour or about 8 Joules per gram.  Well, you say, the energy would be conducted away beneath the surface.  So, that energy is still contained within the system.

Well, Ein Has to Equal E out!  Eventually it will.  But if that surface retained more that it lost it will move toward an equilibrium, then Ein will equal Eout for that surface, not until then.  The assumption of equilibrium is a powerful tool if used correctly and monstrous mistake if misused.

In my opinion, it is not worth the effort to "solve" a paradox that never should have existed.  Science based on that type of logic is flawed, simples.  Energy is fungible, but the work done is not.

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