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.
Have heard different views on this which I will coarsely summarize. To do so I will use the rough analogy of a green house. In fact a glass box.
Imagine if you will a glass box in your back yard on a cloudless day. Inside the box we place a candle and two devices to measure temperature and CO2 levels. We won’t light the candle yet. Outside the box we will place an environmental scientist and a physicist.
So we leave it for a while and notice that the temperature in the box rises initially and then comes into thermal equilibrium. The temperature inside the box is certainly higher than outside, but it is no longer changing.
If we light the candle we notice the temperature inside the box rises and the CO2 level rises.
The environmental scientist tells us that the byproducts of the candle are modifying the inside of the box. In a rough sense the CO2 is adding to the properties of the glass so that less energy is transmitted from the box due to the CO2 layer.
The physicist says “that may be so” but the increase in temperature is the same as the thermal energy released by the candle and corresponds to the CO2 produced by the candle so I must conclude that it is the candle heating up the box.
The environmental scientist says nonsense. The heat from the candle is insignificant compared to the total heat coming into the box from the sun. The additional heat from the candle is simply being mixed with the sunlight and being radiated away. Of course less of it is being radiated away because of the extra insulation, but it’s contribution will be proportional to its ratio to the total input energy.
The physicist asks the environmental scientist; “The fact that the temperature rise matches the heat given off by the candle?”
“Coincidence” is the response.
So who is correct?
The physicist is, but why?
The intuitive answer is to wait for night time and notice that most of the candles heat is still inside the box. Apart from the removal of the external source, nothing has changed. If you ran the whole thing at night, the temperature in the box would rise, hit equilibrium and then remain constant.
The environmental guy is correct that there is a lot more energy coming into the box from the sun than the candle produces. But to correctly compare the solar energy entering the box with the energy released by the candle we would have to “replace” the candle with the equivalent solar source required to raise the temperature by the amount of heat released by the candle. The big question mark is that the energy from the sun is not coming in as kinetic energy, whereas the candle is pumping heat directly into the box.
In one dimension we can imagine light coming into one face of the box and out the other side leaving a residual amount of energy behind that balances the cooling of the gas in the box so that we maintain a reasonable 14 degrees C average temperature. Now the energy in and the energy out over time have to be equal, but it doesn’t mean it can’t change form. So if you imagine a photon, hitting an atom, releasing an electron and another photon. The input and output spectra would be different. The output spectra would have a spike at lower frequency than the input spectra, with the difference being the residual kinetic energy of the electron that is still bouncing around the box.
In this case the “heat” in the box is in effect the residual kinetic energy left behind after incoming photons interact with the atmosphere. The atmosphere also loses energy over time so for a single photon entering the box, it would take a while for all the residual kinetic energy to be burned off. In effect we would have to integrate the output spectra over time to match the power of a single input pulse.
Anyway to work out how the candle was effecting the system compared to sunlight, we would need to replace the candle with an equivalent solar source to create the same residual kinetic energy.
Alternatively we could replace the sunlight with an equivalent number of candles to create the same kinetic energy as the sun created.
But I think it is improper to compare apples to oranges.
Making bold claims about the huge wattage of solar energy entering the box compared to the source energy is dangerous. Particularly as not all that solar flux is converted to kinetic energy of the atmosphere. Even more complicated is that there are lots of layers in the atmosphere where all the real action takes place. When you do see figures about the solar flux interacting the atmosphere you really need to ask and how much of that was the troposphere (the warm wet and cuddly bit we live in) and how much energy was lost in the various more exotic layers above us compared to how much of the residual flux was lost in our warm wet layer.
The fact that the atmosphere we live within is not glowing to a large extent suggests to me that not a lot of photons are being released by energetic electrons so I would suspect that absorption is not high and most of the heat is from the ground and oceans rather than direct absorption.
The more I look at this the, less trivial it becomes.
If we wanted our box to match reality we would need to wrap the box in various layers of material, each of different material properties and place our candle in the middle. It could be reasonably modeled using a time domain analysis such as that used in electromagnetism.
And I still have not had an answer of what the process is that has flattened temperature variation through the Holocene. Something has dampened temperature variation and I don’t know what it is. Arrrgh!
Following on from my somewhat tongue in cheek ‘Thoughts of Thor” post below I decided to take this a little more seriously and rework it backwards to see if everything all added up. It appears to. The brief summary is that assuming the validity of the CO2 graphs if you work backwards from the CO2 levels to the amount of heat that should have been added to the atmosphere you get a pretty good match with the observed temperature rise.
The problem is that the causality would seem to be
“Burn Coal”, produce “CO2″ and “Heat”
NOT
“Burn Coal” produce “CO2″ which produces “Heat”.
The problem being is that if you replace “Burn Coal” with anything else you will drop out the “CO2″ bit, but you will still get energy released into the atmosphere.
So yes you will improve air quality, but that is about it.
Anyway you can work it out for yourselves. The math is easy. If the presentation below doesn’t work – it had trouble with equations you can get a PDF here or a Power Point Show here
some constant. As such the residual energy would be per unit time
.
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.
