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Monday, December 24, 2012

How would you use the Carnot Efficiency?

Happy Holidays!  While something finishes baking in the oven, I thought of a quick post.  A denizen asked about using the Carnot Efficiency for validating climate models then automatically leaped to a comparison of Earth and Venus.  Apples to oranges in my opinion.

My example is peanut butter between two Ritz crackers.  Squeeze the crackers together and the peanut butter oozes out the cracks.  Since Venus is more isothermal, the cracks are much smaller so less peanut butter oozes out.  Carnot efficiency determines the ideal peanut butter ooze.

When you have a closed system, you have a pretty good idea of how much temperature is available and how much energy is lost or used for some purpose, but with an open system like Earth we really don't know much.  With what little we do know, we can compare a few things then use the things you know pretty well as boundaries.  Then you can compare a number of Carnot engines to see what makes sense.

One of the biggest problems is you have to have a pretty good idea of the Th and Tc or the maximum and minimum temperatures or energy available to the engines.  Since the engines interact, you can either overly simplify or overly complicate the interactions then instead of peanut butter, you end up with cheese and it can fall off your cracker :)

That may sound a little confusing or harsh, but the normal fluctuation in Earth climate is likely equal to or greater than the potential impact of a quadrupling of CO2.

My example of a rough use of Carnot efficiency was Th=306.5 to Tc=184.5, where Th is the warmest SST ever recorded and Tc is the coldest temperature ever recorded on Earth.  Using those temperatures, the Efficiency would be 1-(184.5/306.5)=0.398  which compares well with the top of the atmosphere emissivity or ~60 to 61.  That would imply that the peanut butter ooze is 60 to 61 percent and the work would be ~40 percent.  I used Ritz crackers for a reason though.  Ritz crackers are discs.

In space, the two disc radiant model works great.  There is little reason for any significant amount of energy to slip out from between the crackers.  Once there are more molecules to interact, peanut butter ooze has to be considered.  So the ~40 efficiency of the Earth, using 306.5 and 184.5K degrees, includes an ooze amount.  This ooze or energy transfer from the equatorial source to a uniform envelope of 184.5K that is mostly in the higher tropopause but can also be at the surface, is a pain in the Carnot Efficiency ass.

That is exactly why I concentrate on simple models with true isotropic energy flow.  This is also why I look at lots of ocean paleo data and the Selvam Self-organized Criticality work.  One engine's ooze is another engine's input.  I think we need to know a lot more about the normal ranges of the engines before we can predict much of anything.

That is just me though, how would you use the Carnot efficiency?

Times up!

How about assuming a standard efficiency?  Instead of about 40 and about 60 assume 38.2 and 61.8 percent.  Then Selvam's Golden Ratio would be the standard efficiency ratio.  

This may not be a crazy as it sounds.  A conventional gas turbine efficiency is close to 38.2 percent.  In combined cycle, 38.2 percent of the 61.8 heat loss is 23.6 percent yielding a total efficiency of 38.2+23.6=61.8 percent.  Then with a TOA Eout of 240 being 61.8 of the total energy available, the effective surface energy would be 388 Wm-2. Since that 388 Wm-2 would also have an efficiency penalty or work potential depending on your perspective, of 148 Wm-2, the "Golden Efficiency" may provide a baseline missing in the chaos of climate and climate data.  The only issue is that in the "Golden Efficiency" world, temperature and energy are not interchangeable.  

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