It is said that ACs are counterproductive in fight against global warming, in that while they may make the local environment temporarily livable, the greenhouse gases produced while making the electricity needed to operate them heat up the rest of the Earth by much more than the relief from the AC itself. By how much exactly is that? Note that here I am interested in the global impact of greenhouse gases specifically, not in the local heat island effect (given how ACs do not destroy heat but only move it from inside to outside, and add extra heat from running the compressor itself). Let’s also assume all electricity comes from fossil fuels (ACs might become a viable solution if 100% of AC electricity came from renewable solar, which is actually a reasonable goal to strive for given how both AC and solar are most active during the day, but at the moment most of electricity delivered to me specifically, for example, comes from natural gas.)
Here’s my estimate. Let me know if it is reasonable! Methane has energy density of 891 kJ/mol, burnt into CO2 at 1 mol : 1 mol. Gas turbines have efficiency up to 60%. The radiative forcing of CO2 can be calculated as: ln(new ppm/old ppm)/ln(2)*3.7 W/m**2. For example the 131 ppm increase in CO2 since 1750 up to 411 ppm has a radiative forcing of 2.05 W/m**2 (is that across the entire Earth’s surface? or only its crosssection?), and CO2 has persistence in atmosphere for at least 1000 years. The atmosphere composition is 78% nitrogen 21% oxygen 0.9% argon so its molar mass is:
.78 * 28 g/mol + .21*32 g/mol + .009*18 g/mol = 28.7 g/mol
And total atmospheric mass:
4*3.14*(6.37e6 m)**2 * ~10000 kg/m**2 * 1000 g/kg / (28.7 g/mol) = 1.78e20 mol
Suppose 8 billion people each run 1kW AC for 1 year, with electricity from natural gas. (That’s similar to our total current global energy consumption of 20TW, though of course we use power for things other than just AC or electricity, but also most energy comes from coal and gasoline not just gas, and 80% comes from fossil fuels not renewables.)
8e9 people * 1000 W/person * 60*60*24*365 s / (891e3 J/mol * 0.6) = 472e12 mol
That’s 472 teramols of CO2 (20.8 gigatons) added to the atmosphere each year, or 472e12 / 1.78e20 * 1e6 = 2.65 ppm (parts per million). It is believable that having done so for a hundred years we have raised CO2 concentration from pre-industrial levels up to 411 ppm. The radiative forcing is:
ln((411 ppm + 2.65 ppm)/(411 ppm)) / ln(2) * 3.7 W/m**2 = 0.0343 W/m**2
Or for the whole earth:
4*3.14*(6.37e6 m)**2 * 0.0343 W/m**2 = 17.5 TW
What is my individual contribution for 1 hour?
17.5e12 W / 8e9 / (24*365) = 0.25 W
That is, if I run my 1kW air conditioner for 1 hour, the entire Earth will be solar heated by an extra 0.25 W for the next 1000 years. That doesn’t sound like much, but it adds up over time: I spent one kilowatt-hour in one hour on cooling, but the rest of the Earth will be heated by an extra 0.25 W * 24*365 hours = 2.2 kilowatt-hours in the next year, and again every year thereafter. Multiply that by 8 billion people or a hundred years and it adds up a lot, even considering the heat is distributed across entire planet surface not just areas where people live.
So my answer is 1 kWh of cooling = 2.2 kWh of heating per year for the next 1000 years. By same calculation in terms of mass, 1 kg of CO2 = 7.4 kWh of heating for every year thereafter. Is this accurate?
A/C for cooling is one of those things that highly correlates with the availability of solar power.
So your assumption that they are running on coal is suspect.
Heatpumps running in the winter are a more pressing concern, since those are highly correlated with the unavailability of solar and therefore often run on coal or gas (unless wind or hydro is available)
Even so, burning gas in a power plant and then running a heat pump is more efficient than burning gas to warm a house.
You are probably talking about US. For instance, in Europe, places where A/C is more needed and used have also lower share of energy produced from renewable sources.
It’s not about current usage it’s about AC is needed at times that are sunniest.
More sun? More AC usage.
Solar supplies this energy usage well.
I need the AC right now and it’s middle of the night in September 🤮
Turn it on. You need it. Don’t put it too low though
Unfortunately currently most A/C in many countries runs with energy from fossil fuels. In Europe for sure. Solar production still lags behind too much
Yes, ideally all AC will be running off solar, but that’s not the case at the moment. My state has thankfully closed its last coal powerplant, but also shut down one of its nuclear plants, using gas to replace both. We are now running at 50% gas 20% nuclear 20% hydro and 10% wind/solar. Which is why I wanted to focus on methane in this specific calculation: when deciding “is it OK for me to run the AC now, or is the longterm global heating side-effect too great?” natural gas is what is relevant to me.
How “great” that is is precisely the question here, and apparently it’s 2.2x. If you are really a stickler for exact real-life electricity production piechart distribution, multiply that by 50% gas and call it 1.1x. That is, for every year that I run my 1kW AC, that’s as if I am airdropping a 1.1kW heater to a random location on Earth that will heat it up at 1.1kW forever. 10 years = 11 random heaters. 8 billion people = 88 billion random heaters. Is that “too great”? I dunno.
Winter heating is its own problem, but at least cold can always be dealt with by more insulation and clothing. Heat can literally make whole areas of Earth unsurvivable without electrical cooling. Would I rather feel more comfortable now or choose to be able to survive without mechanical aids later?
Using a static model is too simplistic.
An A/C consumes more energy when the temperature difference is higher, which is when it’s sunny outside. At those points in time, the grid is receiving a lot of solar power.
So just saying a grid has 10% solar is too simplistic. That grid probably has 30% solar during summer noon and 0% solar on a winter morning.
If your goal is to save emissions, your best bet is to get some solar panels if you can, run the A/C when the sun is shining. Have a well insulated house that acts as a thermal battery and turn the A/C off during the peaks of the duck curve.
I won’t comment on the final accuracy, but I will note that this is an extremely roundabout path to your final answer, and some of the intermediate steps are…weird. Most notably, the speculation that every man, woman, and child on the planet might run a 1 kW appliance 24/7/365. This is 7e13 kWh or 70k TWh, about 3x current global energy use (not just electicity) before accounting for efficiency. The equation you cite for radiative forcing, specifically its ln(new/old) term is very non-linear, so you should get a much lower marginal effect from 70k TWh than from 1 kWh.
A simpler approach is to calculate the CO2 required for your 1 kWh AC, i.e.: 1kWh * 3600 kJ/kWh / 0.6 efficiency / 890 kJ/mol = 6.7 mol CO2. Current atmospheric CO2 is 75 Pmol. From that, I get radiative forcing of ln((7.4e16 + 6.7)/7.4e16)/ln(2)3.7 * 4pi*(6.4e6^2). Numpy won’t tell me what ln(74000000000000006.7/74000000000000000). It will tell me the forcing from 10 kWh is ~2.5W, or the same 0.25W/kWh you got. I guess ln is not that nonlinear in the 1+1e-16 to 1+1e-4 range, after all.
0.25W/kWh seems improbably high. 1 kWh is about 0.1 W running 24/365. At 60% efficiency, that’s burning 0.2W of natural gas and implies that the radiative forcing from CO2 is much greater than the energy to produce the CO2 in the first place. I get that the energy source for heating is different from the energy source for electricity, but it feels wrong, even without the 1000 year persistence. I don’t know where the radiative forcing equation came from nor its constraints, so I’m suspicious of its application in this context. There’s a lot of obscenely large numbers interacting with obscenely small numbers, and I don’t know enough to say whether those numbers are accurate enough for the results to be reasonable. Then there’s the question of converting the energy input to temperature change.
Numpy won’t tell me what ln(74000000000000006.7/74000000000000000).
Ran into exactly this problem for individual calculation 😆. Which is also why I multiplied by 8 billion and divided in the end - make the calculator behave.
lnis linear enough around 1±epsilon to allow this.implies that the radiative forcing from CO2 is much greater than the energy to produce the CO2 in the first place
That’s what I wanted to find out and it does appear to look exactly that way. Makes sense in retrospect since the radiative forcing is separate from the energy content of CO2 itself, same way as a greenhouse gets hot for no energy expended on its own.
Numpy won’t tell me what ln(74000000000000006.7/74000000000000000). Ran into exactly this problem for individual calculation
Trouble is that 74000000000000006.7/74000000000000000 ~ 1.000 000 000 000 000 1 and double-float precision is 0.000 000 000 000 000 2. Needs a 96 or 128 bit float. The whole topic of estimating one’s personal contribution to global phenomena is loaded with computer precision risks, which is part of what makes me skeptical of the final result, without looking far more closely than my interest motivates. Like calculating the sea level rise from spitting in the ocean - I believe it happens, but I’m not sure I believe any numerical result.
Your skepticism is excessively cautious 😁. You can work around precision limits perfectly fine as long as you are aware they exist there. Multiplying your epsilon and then dividing later is a legitimate strategy, since every function is linear on a small enough scale! You can even declare that ln(1+x) ~= x and skip the logarithm calculation entirely. Using some random full precision calculator I get:
ln((74e15+6.7)/74e15) = 0.000000000000000090540540...Compare to the double-precision calculator with workaround:
ln((74e15 + 6.7*10e9)/74e15) / 10e9 = 9.0540499...e-17Or even:
ln(1+x) ~= x 6.7/74e15 = 9.0540540...e-17You are worried about differences in the final answer of less than 1 part in a million! I try to do my example calculations in 3 significant figures, so that’s not even a blip in the intermediate roundoffs.
Problem as discussed: Fossil Fuel for Electricity. Your solution: No more AC!
zero out of ten points
Electricity isn’t decarbonized yet, so it is a problem in practice. Exceptions exist.
Nope, it is a symptom and waste of resources to treat. Spend the time and money on an actual solution.
I know this is kind of off topic but I wanted to point out that the refrigerant that escapes from air conditioners when they leak or are thrown away, is a bigger contributor to climate change than the electricity they use.
Good point! Freon (CFC-12, with 10800x warming potential of CO2) has thankfully been banned by Montreal Protocol of 1987, and HCFC-22 (5280x) is being phased out. We are using what now, HFC-32 at 2430x? How much refrigerant does an AC contain, about a mole? I’ve been taught that refrigerant should normally never leak throughout the lifetime of the appliance (technicians are even prohibited from “recharging” refrigerant without identifying and fixing the point of the leak first) and that all gas must be recovered after end-of-life, but we can’t be sure that’s really what happens every time.
In that case leaking 1 mole of HFC-32 would be equivalent to… running the 1kW AC for 360 hours?
1 (mol HFC-32) * 2430 (mol CO2/mol HFC-32) * 1 (mol CH4/mol CO2) * 891 kJ/mol * 0.6 / 1 kW * (1 h / 3600 s) = 361 hIn my experience with the automotive industry. AC systems leak frequently and it is very common for the leak to be so small that it is not always possible to find the source.
So the majority of the time a fluorescent dye is added to the system and it is recharged with refrigerant to help find the source when it gets low again.
It’s common to have a leak so slow and undetectable that no one notices a system is low on refrigerant until a year later when it is summer again.
Also, auto parts stores sell cans of refrigerant so anybody can just recharge a leaking system, which is often cheaper than actually fixing the leak. So these AC systems are just constantly leaking refrigerant and being recharged.
I wouldn’t be surprised if AC systems in buildings are handled similarly.
Even if a law is made that a failed part must be identified before the system can be recharged, the technician who can’t find a leak is going to just pick a part (randomly or educated guess) to replace if he can’t find the leak.
The answer is 1:1, conservation of energy means that 1kWh of energy going into the AC you introduce near as makes no difference 1kWh of heat energy into the world. The wonderful thing AC does is amplify that cooling or heating by moving heat from one place to another meaning modern systems can move 5kW of heat using only 1kW of energy. In this example 6kW is outside but you have removed 5kW from inside so it’s still just 1kW net.
If you want to reduce the impact of using your AC you need firstly insulate the crap out of your house to prevent heat escaping or entering. Then you can delve into the world of Mechanical Ventilation Heat Recovery (MVHR), sealing all the air gaps in your home, at least quad-glazing, and finally passive cooling (sun shades over your windows).
Edit: sorry forgot to say for solar powered AC - which is 100% of my systems. I’m ignoring the grid for the above as the only systems I install are combined with at least 3x kW of solar and batteries so they never use grid power.
Let’s also assume all electricity comes from fossil fuels
If that’s your assumption, the ACs are the smallest problem when it comes to dealing with the climate crisis.
I just stumbled upon this video with a very similar topic: Can We Solve the Air Conditioning Paradox? (Be Smart)
Relevant excerpts:
- an estimated additional 2000 GW of electricity could be required to satisfy growing AC demand (6:40)
- HFCs are the fastest growing GHG (?). At this rate, they could add 40 years worth of carbon emissions or +0.55°C (7:45)
- Ideas and solutions exist (e.g. 10:30)
Your oversimplifying. No offense, but your calculation is a bit of a spherical cow in vacuum.
I am not gonna do the math, but the concept is simple: to cool a small amount of air you must heat a larger amount of air somewhere else. A/C is basically a heater overall, that consumes more “fuel” (whatever is your fuel) than normal, winter heating per identical volume of heated air.
That is why they say it is not great. Regarding the calculations, all co2 based calculations are not really accurate. It depends on the energy source, on the efficiency of energy production, on location of production, of supply chain… CO2 measures for a given product are extreme, inaccurate approximations not really meaningful on large scales. I won’t worry too much. I’d use A/C only when needed, with target temperature between 25 and 28, and you’ve done your part
Zero! I already have excess solar and planning to buy AC that runs purely on solar.