Climate change due to combustion of fossil fuels

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The discussion centers on the impact of fossil fuel combustion on global warming, specifically questioning the significance of heat generated from this process. It highlights that while the combustion of fossil fuels does produce heat, its overall contribution to global warming is considered negligible compared to the vast energy received from the sun. The total energy consumption by humanity is approximately 16 terawatts, which is minuscule compared to the 176 petawatts from solar energy. The conversation references studies indicating that while local temperature increases due to energy consumption can be measurable, they do not correlate strongly with global temperature trends. Notably, climate models suggest that there is no significant correlation between CO2 emissions and temperature trends, indicating that the effects of greenhouse gases may not be as directly linked to temperature increases as previously thought.
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Has anyone ever researched what contribution, if any, the actual combustion of fossil fuels contributes to global warming? If you added up all the BTU's of energy which have been released in the last few decades, would it add up to something or is it negligible? Of course, all motion due to burning fossil fuels ends up as heat due to friction, etc (ok, maybe some EM energy leaves the system, and things like that), but is the capacity of the Earth great enough to absorb this heat?

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I don't have the reference handy, but if I remember the actual heat produced is negligible. It's supposed to be the effects of the gasses on incoming/outgoing heat that causes climate change.
 
Indeed, total "technical" energy use by humanity (meaning, not counting the sun that heats us and makes vegetables grow etc...) is about 16 TW. The total received power by the Earth from the sun is about 176 PW, 10 000 times more.
 
Yet, on local levels it is measurable.

http://www.knmi.nl/~laatdej/2006joc1292.pdf

in the conclusion:

The proposed physical mechanism is that energy – which is consumed in large quantities in these areas – is a conserved quantity in any physical system, and at some point this energy will be released into the atmosphere in the form of a direct near-surface temperature (energy) perturbation. By way of illustration, the average energy consumption for Germany is 1.3 Wm−2, for Japan it is 2.9 Wm−2, for the Netherlands it is almost 4 Wm−2, while for certain industrialized regions it can easily be 20–70 Wm−2 (IIASA, 2003; Crutzen, 2004). Temperature perturbations of up to 0.9 K were found by Block et al. (2004) for a 90-day simulation of a constant surface flux of 2 Wm−2 over Europe’s land areas, which suggest that the significant regional temperature trend enhancements discussed in this work and in Paper I could be partly explained by this process.

Note that it also find:

Our analysis of climate model simulations of GHG warming confirms our earlier results (Paper I), namely, that they do not show any kind of CO2 emission–temperature trend correlation. In fact, the modeled temperature trends are quite insensitive to the magnitude of the industrial CO2 emissions.
 
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