# To what extent do (man made) generators of heat from internal sources in earth's system cause climate change?

So I'm very far from a climate scientist but I've always wondered, why don't things like electric heaters, lightbulbs, etc, contribute to climate change, or even things like the accelerated decay of radioactive materials -- human caused factors. I'm fairly sure it's due to the equilibrium being very stable to relatively small factors that we humans contribute and it can simply radiate away into space, but I honestly have no idea.

A simple calculation I did just now after thinking about it in some more depth put it this way: If every human had 100x 100W fluorescent lightbulbs (5% efficiency) each and were to leave them on for a year. I feel this maybe an overshoot by a few order of magnitudes but my aim is to account for other heat sources that take the average over the humans average We'd have Power output as heat: $$E_{heat} = 0.95 * 100 * 100 * (60*60*24*365) * (7.5 * 10^9) = 2.2 * 10^{21} J year^{-1}$$ Then with maybe a too simple $$E=mc\Delta T$$ equation

The atmosphere has a mass of about $$5.15×10^{18}$$ kg (Wikipedia)

specific heat capacity of air:

$$E_{heat} = M c \Delta T$$

$$2.2 * 10^{21} = 5.15×10^{18} * 716 * \Delta T$$ $$=> \Delta T = 0.6K / year$$

Small amount for what I feel is still a gross overestimation of 100x 100W lightbulbs per person as an internal energy output, but why isn't this a factor especially as the world becomes more energy hungry? Is it 'heat neutral' I find it hard to imagine that something even like a wind turbine generating the electricity would decrease the heat energy in the air more than an electric heater powered off of it would. And why large nuclear energy sources human accelerated don't play a large effect.

The power involved does not represent a significant fraction of the total energy budget, so it can normally be ignored. Assuming (per Wikipedia Solar Energy) that the energy received on earth from the sun is about $$3\times 10^{24} \text{J/year}$$ and total energy production on earth is (per Energy Consumption) about $$6 \times 10^{20} \text{J/year}$$, worldwide energy production would represent a value of 0.02 of one percent -see this chart.

There's a huge amount of fudge there. The value really represents energy consumption, so the heat output of production will be greater. At the same time, production from water/solar/wind are counted, when they do not produce additional heat (since it's already counted in the solar figure). But the figures would need a 50x boost to even reach a 1 on the chart. • What are the units on that graphic? (Sorry, I've just been marking and it jumped out) – Chris H Feb 8 at 11:47
• @ChrisH I believe the numbers are expressed as percentages of the total solar irradiance, so for a number $n$ on the graphic, the corresponding energy flow rate is $(3\times 10^{24})\frac{n}{100}$ J/yr. – probably_someone Feb 8 at 14:10
• @probably_someone the 100 suggests that, I agree. The 116 emitted from the surface seemed high in comparison but most of that is circulating within the Earth system and anyway it would need something strange for that to represent anything other than a bit more than incoming solar. – Chris H Feb 8 at 14:21
• @probably_someone: Where is $3*10^{24}\mathrm{J/a}$ coming from? Assuming $1360\mathrm{W/m²}$ solar constant and $6370\mathrm{km}$ Earth radius, you can calculate the total solar irradiance to be ~$173.4 \mathrm{PW}$ or ~$5.5*10^{24}\mathrm{J/a}$. – Eric Duminil Feb 8 at 16:35
• > "The power involved does not represent a significant fraction of the total energy budget, so it can normally be ignored." This is misleading. The relative importance of effect of the human generated power on warming the planet is not given by its proportion to net solar input power. Most of the solar power is reradiated back to space and does not contribute to global warming. The power at question should be rather compared to power of radiative forcing due to $\text{CO}_2$ emissions, which is much less than net solar energy absorption;currently reported value around 3W/m2(see my answer). – Ján Lalinský Feb 8 at 18:37

The forcing due to CO$$_2$$ is much larger. For example "business as usual" is RCP8.5 (Representative Concentration Pathway) which will give 8.5 W/m$$^2$$ extra heat due to greenhouse gases in the future. Over the whole surface of the Earth, that is $$4.10^{15}$$ W or $$10^{23}$$ J/year.

With that calculation using heat capacity, that would create very a rapid rise in temperature of the atmosphere, year after year. It is not the proper way to analyze the effects of an extra forcing. Instead, one should look at steady state. Currently, the surface of the Earth radiates about 400 W/m$$2$$. An additional 8.5 W/m2 means a 2 % increase. Because of the Stefan-Boltzmann $$T^4$$ law, this would in steady state give a 0.5 % rise in temperature, about 1.5 degrees. (Very crude back-of-the envelope estimate)

• Current radiative forcing due to increasing CO$_2$ and other gases is reported as around 3 W/m$^2$, not 8.5 W/m$^2$. If we are to compare effects, let us compare them at the same time. By the time the forcing will be 8.5 W/m$^2$, global energy consumption will increase as well. The comparison now says energy production has around 1% of radiative forcing of the greenhouse gases emissions. – Ján Lalinský Feb 8 at 3:41
• @JánLalinský Not to mention that the forcing is highly sub-linear with respect to carbon dioxide proportion. Mind you, not enough to avoid the climate change we're facing right now; doubling carbon dioxide will still retain huge amounts of heat - doubling it again, not so much; but by that point, we're already in serious trouble. – Luaan Feb 8 at 8:54
• @Luaan I am not sure what do you mean - do you mean the effect of CO2 emissions will decrease in importance and effect of energy production will increase in importance? – Ján Lalinský Feb 8 at 18:40

Almost all household consumption of electric energy produces equivalent heat, and this does contribute to heating the planet, no matter how the electric energy was produced. Similar thing is true for many (probably most) industrial use of electric energy - most of it dissipates into heat in the atmosphere, ocean and Earth crust. This too contributes to heating the planet. (Part of this energy - from renewable sources - would heat the planet anyway, but in 2019 that is a small percentage of total energy consumed.)

Whether effect of energy consumption on global warming is substantial is not obvious. Should we compare it to the effect of $$\text{CO}_2$$ already present or $$\text{CO}_2$$ introduced during the same time the energy was consumed ?

As @Accumulation correctly points out, the forcing effect of energy added into the system in one year is only temporary, as the increased average temperature due to it will not remain after energy consumption is curbed because energy can get lost by radiation. On the other hand, the effect of $$\text{CO}_2$$ added to the system is more long term, because $$\text{CO}_2$$ cannot get out so easily as the surplus energy.

So, if we are to make this comparison, we should compare the effect of energy production to the effect of net $$\text{CO}_2$$ already in the atmosphere.

We can compare the two effects by comparing their contribution to net energy they contribute to yearly energy increase of the atmosphere, which manifests as increasing temperature.

Increasing $$\text{CO}_2$$ in the atmosphere at the current rate is reported to provide around 3 W (2016$$^*$$) of power per squared meter of Earth's surface more than in balanced radiative equilibrium state, thus $$4.8\text{e}22~\text{J}$$ per year (this number increases in time as concentration of $$\text{CO}_2$$ increases). On the other hand, net human energy production per year (2015) is estimated to be $$5.5\text{e}20~\text{J}$$ and this energy eventually ends up heating the planet too.

Comparing the two numbers, human energy production per year is around 1% (maybe it is higher, a value of 1.7 % is given by this paper for fossil fuels only: https://agupubs.onlinelibrary.wiley.com/doi/full/10.1002/2015GL063514) of energy stored in the system due to greenhouse gases pollution, which is not a substantial, but still a noticeable effect. In time, importance of energy production will probably somewhat increase (if $$\text{CO}_2$$ emissions get lower than they are today and radiative forcing will decrease).

Decreasing impact of energy consumption is very hard, especially in developing countries that play catch-up to the developed countries. Certainly it is much easier to convince people to limit/stop burning coal and fossil fuels and use other sources of energy, than to limit/stop consuming equivalent energy in electrical devices.

$$^*$$ https://en.wikipedia.org/wiki/Radiative_forcing

• Sorry, this is not correct. The important point for OP is that human energy use is absolutely tiny compared to the energy entering/leaving the atmosphere, as explained by the other answers from BowlOfRed and Pieter. The effect of human energy consumption is definitely not "substantial" compared to the effect of CO2. – craq Feb 8 at 1:33
• @craq that is quite possible, I did not claim I am sure. Do you have some reference to support your claim? – Ján Lalinský Feb 8 at 1:44
• Most of the absorbed solar energy is reradiated back to space, it makes no sense to compare this large energy to energy consumption considered by OP. It would make more sense to find net solar energy yearly surplus dumped into atmosphere due continuing emissions of CO$_2$ and compare that to energy consumption. – Ján Lalinský Feb 8 at 2:18
• Actually effectively ALL of the absorbed solar energy is reradiated back into space. If it didn't, then the temperature would continually increase... The way CO2 works is by changing the radiated energy by a small amount. Pieter estimates that the extra CO2 in the atmosphere now compared to pre-industrial times causes 2% less energy to be radiated. (As he says, that's a rough estimate, but good enough for now.) Human energy use is 0.02% (1/5000). – craq Feb 8 at 2:26
• "Almost all household consumption of electric energy produces equivalent heat, and this does contribute to heating the planet, no matter how the electric energy was produced." - In the case of hydro-electric energy, the energy is taken from the fall of water which would produce heat if the energy was not diverted to electricity. After the electrical energy is used, most of it is converted to heat So the net heat caused by a drop in water appears to be the same. – xxyzzy Feb 12 at 18:47

Power output as heat: Eheat=0.95∗100∗100∗(60∗60∗24∗365)∗(7.5∗109)=2.2∗1021Jyear−1

Presumably, that 0.95 refers to the lightbulb being 5% efficient. However, that is incorrect reasoning. Efficiency does not refer to how much is turned into useful work instead of turning into heat, it's how much is turned into useful work before turning into heat. If a lightbuld produces 95W of heat and 5W of light, that light is eventually absorbed by something, and that something will then be heated up. So all of the energy of the lightbulb eventually turns into heat. Pretty much every use of energy eventually turns into heat, with only a few exceptions (an example of an exception would be that any energy used to build a skyscraper that goes into lifting building materials doesn't turn into heat ... at least not unless the skyscraper is demolished), and those exceptions are a tiny percentage of energy usage.

The atmosphere has a mass of about 5.15×1018 kg (Wikipedia)
specific heat capacity of air:
SHC of air 0.716 https://www.ohio.edu/mechanical/thermo/property_tables/air/air_cp_cv.html

Both the mass, and heat capacity, of land/water is much larger than that of air, and for air to remain at a high temperature, the ground and water below it has to be brought up to that temperature. You can have a region with cold ground and warm air, but for that situation to persist, that warm air has to be coming from someplace else that does have warm ground/water.

Small amount for what I feel is still a gross overestimation of 100x 100W lightbulbs per person as an internal energy output, but why isn't this a factor especially as the world becomes more energy hungry?

Besides this being a tiny proportion of the total heat, it's not permanent. The main concern over CO2 is not that emitting CO2 in 2019 will make the Earth hotter in 2019, or even 2020 or 2021, but that all the CO2 emissions are cumulative, and thirty years from now we'll still be dealing with the effects of CO2 emissions from today. The urgency of anti-warming activists is based on the premise that global warming has a lot of momentum, and it will take a lot of time to turn around warming trends. Simply adding heat to the system, on the other hand, doesn't have the same long-term effects. Heat causes objects to radiate heat. Without the greenhouse effect, raising the Earth's temperature means that it radiates more heat, and so without a constant influx of new heat, it will cool back down. So even if we were to raise the Earth's temperature by turning all our heaters on full blast, this wouldn't be a threat to later generations the way that CO2 emissions are asserted to be. CO2 reduces the amount of heat that the Earth emits, and so can permanently increase the equilibrium temperature.

Is it 'heat neutral' I find it hard to imagine that something even like a wind turbine generating the electricity would decrease the heat energy in the air more than an electric heater powered off of it would.

If you stick a heater next to wind turbine, all of its energy is coming from the energy being taken from the wind, and all of that energy would have turned into heat anyway (see my first paragraph). For the heater to result in a net increase of heat would be a violation of conservation of energy. Same with renewal energy in general, such as solar, geothermal, hydroelectric, or wave.