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I'm curious about the climate impact of different heating solutions, particularly regarding the comparison between traditional fossil fuel heating sources and heat pumps. Traditional fossil fuel heating relies on the conversion of chemical potential energy to heat, which is then used to warm homes. This seems to lead to global warming in two ways: the conversion of chemical potential energy produces excess heat that goes into the atmosphere and the burning results in greenhouse gases (GHGs) that warm the atmosphere through the greenhouse effect.

Heat pumps seem to mitigate both of these effects, provided that the electricity they use is renewable.

However, I am curious to know which of these two factors—excess heat release or the greenhouse effect due to the release of GHGs—play a more significant role in contributing to warming due to traditional heating. Are there any order of magnitude estimates one can make comparing the contribution of the two?

Any insight would be appreciated!

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Excess heat release (often referred to as "waste" heat), can be a noticeable contributor to urban heat islands, but globally it has two orders of magnitude less heating effect than greenhouse gas releases. The critical factor is that greenhouse gases accumulate.

The effect of waste heat is discussed in the multiple Stack Exchange questions, e.g.

But let's work the rough numbers for a typical home heating requirement of about $10000$ kWh ($3.6$ GJ) per year. Since the Earth's total surface area is $5.1\times 10^8\,\mathrm{km^2}$, this one home contributes about $2.2\,\mathrm{pW/m^2}$ ($2.2\times 10^{-12}\,\mathrm{W/m^2}$) of heat averaged over the Earth.

We now need to estimate our greenhouse gas emissions. According to the U.S. Energy Information Administration, 53 kilograms of $\mathrm{CO_2}$ are produced per million British Thermal Units (Btu) of natural gas heating. In SI units this is $5\times 10^{-8}$ kg/J, so over a year our home will produce about 1800 kg of $\mathrm{CO_2}$. According to the IPCC, only about 44% of anthropogenic $\mathrm{CO_2}$ stays in the atmosphere, the rest being absorbed by the biosphere and oceans, so our house's $\mathrm{CO_2}$ contribution is reduced to 800 kg.

The radiative forcing for small additional amounts of atmospheric $\mathrm{CO_2}$ is

$$\Delta F = 5.35 \ln{\left(1+\frac{\Delta C}{C_0}\right)} \approx 5.35 \frac{\Delta C}{C_0}\, \mathrm{W/m^2}$$

where $C_0$ is the base $\mathrm{CO_2}$ concentration.

According to Wikipedia "Each part per million of $\mathrm{CO_2}$ in the atmosphere represents approximately 2.13 gigatonnes of carbon, or 7.82 gigatonnes of $\mathrm{CO_2}$." The Earth's atmospheric $\mathrm{CO_2}$ concentration (as of May 2022 was $421$ ppm, giving $C_0=3.3\times 10^{15}\,\mathrm{kg}$ of $\mathrm{CO_2}$. So the radiative forcing due to $\mathrm{CO_2}$ releases from our home's heating over a year is about $1.3\times 10^{-12}\,\mathrm{W/m^2}$, i.e. $1.3\,\mathrm{pW/m^2}$.

So per year, the effect of waste heat ($2.2\,\mathrm{pW/m^2}$) is actually about twice the greenhouse contribution ($1.3\,\mathrm{pW/m^2}$), but the crucial fact is that waste heat is transient while the green house contribution cumulates. Increases in atmospheric carbon dioxide have lifetimes of hundreds of years, so this year's greenhouse effect is not caused just by this year's gas releases, but also last year's, and the year before that, and so on. After 10 years our home's integrated greenhouse effect will be $13\,\mathrm{pW/m^2}$, and after a hundred years it will be $130\,\mathrm{pW/m^2}$, but its waste heat will still only contribute $2.2\,\mathrm{pW/m^2}$.

This cumulative effect manifests globally. Humanity's current annual energy consumption is about $5.8\times 10^{20}\,\mathrm{J}$, corresponding to an averaged heating effect over the Earth's surface of about $0.036\,\mathrm{W/m^2}$. The total anthropogenic greenhouse radiative forcing due to carbon dioxide since 1750 is estimated to be about $2.17\,\mathrm{W/m^2}$, $60$ times greater.

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The effect of the CO2 in the atmosphere is far more important than the heat generated. The reason is that the energy from the sun radiation is several orders of magnitude bigger than what is generated by burning fossil fuels.

Just to have an idea, an array of solar panels scattered around the world, covering a total area equivalent to the state of Connecticut, would produce all the present electric energy world consumption.

So, the big issue is the amount of this incoming radiation trapped in the atmosphere due to the greenhouse effect.

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  • $\begingroup$ Claudio Saspinski, we don't just need the solar panel installation that you referenced. We need dependable energy, on demand. Maximum solar power generation occurs at noon, but in the United States, the maximum demand occurs approximately between the hours of 5 p.m. to 8 p.m. Thus, there is a mismatch in the timing that must be met with some kind of large short-term storage (e.g., a HUGE battery bank). Such short term storage solutions are still in the prototyping stage. $\endgroup$ Dec 17, 2023 at 1:16
  • $\begingroup$ I agree. The example was only to show the power of the solar radiation on the earth surface. $\endgroup$ Dec 17, 2023 at 12:33
  • $\begingroup$ @DavidWhite Short-term storage is well beyond the prototyping stage. Commercial battery plants are already under construction. Much harder and less ready for commercialisation is seasonal energy storage, but it turns out that wind and solar are remarkably complementary on a seasonal scale. $\endgroup$
    – gerrit
    Dec 17, 2023 at 13:02
  • $\begingroup$ @gerrit, short term energy storage of just a few hours will not get the job done. For a practical solution, we need at least the following: 1) environmentally benign; 2) non-flammable; 3) composed of cheap and VERY abundant raw materials; 4) scalable; 5) VERY large storage capacity. Short term lithium ion batteries do NOT meet these criteria. I suspect that some type of flow battery will be the answer, but this technology is still in the development phase, especially given that we don't have enough real world experience to properly size such batteries. $\endgroup$ Dec 18, 2023 at 6:04
  • $\begingroup$ @DavidWhite sodium-ion batteries potentially tick all the boxes for overnight storage (they're large, but for stationary storage that is not a critical problem). For the rare Dunkelflaute it's acceptable to keep some gas plants on reserve; they won't spring the carbon budget if used for less than 5% of the time. $\endgroup$
    – gerrit
    Dec 18, 2023 at 7:30

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