Global Warming Simplified Even Further
Even Simpler
Trying to work out the argument that the additional heat pumped into the atmosphere as a consequence of energy use is insignificant yet an amount of the same order of magnitude that is proposed to be added by some CO2 driven process isn’t insignificant is annoying.
Anyway before looking at that. The simpler way to get the temperature left behind by burning a quantity of fuel required to produce a given amount of CO2 turns out to be.
where
E is the energy density in Joules Per Mol
R is the Gas constant 8.314
C is the CO2 density in ppmv (part per million by volume).
So at 890kj per mol and 30 ppmv we get a temperature 2.14 degrees C
If I take aboard the complaint that I should use a lower figure rather than methane to average out all fossil fuels, so lets say half. And remove the assumption that it all stays in the air by allowing half to end up in the ocean then we end up with a 0.53 degrees C change. But that is too close to be true and anyone would think I fudged it. So at least I will show where the fudge is.
Energy In Energy Out
Anyway on to the larger problem.
One of the complaints I keep getting is that it can not be the residual energy from heat, because the energy from the sun is so large. That seems to me to say that the outgoing energy is proportional to the incoming energy. Put more heat in, get more heat out. Also it should be noted we are not talking residual energy. It is all energy. The thing to keep in mid is that all kinetic energy released by any process winds up as heat. So taking your car as an example, it is not just the waste heat from the radiator. It is also all the energy burned off from braking, wind resistance, the indicators flashing, the headlights – everything ends up as heat.
What I cant understand for the life of me is why the heat that has been released as a consequence of producing energy is swept out of the atmosphere and should not be used in any calculations. Yet heat the client scientists study of the same magnitude doesn’t get swept away, but builds up.
When I went to uni there was “Heat” and “Kinetic Energy” used somewhat interchangeably at times, but apparently there is ‘now Heat” and there is “Global Warming Heat” that although similar have some decidedly different dissipation properties. You don’t count the former and you do the latter.
Anyway looking at the climate argument that the heat out is proportional to the heat in which is another way of saying my heat just gets mixed up with the mass of heat from the sun and is radiated away.
Mathematically that would say
for 
some constant. As such the residual energy would be per unit time
In the end I don’t like this one, because if we assume the incoming energy is more or less constant and we let it run for a long time,
unless 
.
How old is the earth by the way…
This tends to either plus or minus infinity unless is so close to one as to be insignificant over the integration time scale. Anything else and you end up with Venus or Mars. One bloody hot, the other bloody cold. Neither much use.
In words if you have an in-balance in the incoming and outgoing energy the system will blow up over time.
So how do you maintain a system such as a habitable planet that has the property that it maintains a reasonable mean temperature given that the balance between incoming and outgoing energy has to be so fine?
You can if you want differentiate the above to see what the relationship between 
and 
needs to be. You could try a general rational polynomial solution, but unless that solution was effectively a constant over time, things would get interesting to say the least.
Keep in mind we only have say 30 degrees to play with here. Anything outside an average planetary temperature between 0 and 30 degrees and life is going to have a hard time. In the range of temperatures that we could have, 0 to 30 is essentially dead flat.
The Blocked Kitchen Sink
Well the obvious solution is that you either set up a feedback loop between and so that if one increases so does the other. Or you whack a bloody great heat absorber into the middle of the system to smooth out the ripple. The oceans by the look of things will do the trick for a heat buffer.
If we assume a basic system where and are balanced then what we have is something like a kitchen sink with a partially blocked plug hole. If you adjust the flow in to match the flow out you can then add water or energy depending on which half of the analogy you have in mind, to raise the system to a desirable level where it will remain.
If the flow in or out increases or decreases by even a little, then the sink will overflow or empty over time.
With our walloping great heat sink in there to smooth out variations on either the input or the output, then you have something that pretty well looks like this dirt ball we live on.
OK so what happens when we release energy into our balanced system that normally has no net temperature gain?
This should raise the average temperature.
It would be identical to adding a cup of water to our blocked sink. The level would rise.
Now eventually the heat sink would pick up the excess heat – warming the heat sink and lowering the temperature. But it would not all be magically be swept away.
The analogy is a little coarse in the sense that there should be increased dissipation with higher temperature. Think of heating a metal ball with a blow torch. If you raised the temperature of the flame you would in fact get more heat out, but the ball itself would also heat up until a new equilibrium is found after which heat in and heat out would be equal.
December 09 2009 07:21 pm | Climate
