32 Comments

AC is quickly becoming a survival necessity. I would go so far in saying that, at some point, it will be declared a fundamental human right that can't be denied, especially to those living in certain regions affected by extreme heat waves. Therefore, I don't believe it will help to ask people to give up AC, no more and no less than it would be to ask them to give up heating. Telling them to be parsimonious may help to postpone a bit the problem, but won't solve it. Whereas, we should face reality and accept that AC also will steadily pile up on the top of all the electric energy consumption. This is only a reason more to go all in with renewables, impose on new buildings efficient home insulation, heat pumps, green roofs, solar panels, energy storage systems, thermostats, ceiling fans, educate people how to optimize their homes’ thermodynamics, and for those who can’t afford it, create public facilities with air conditioning as “heat shelters,” etc.

So, can we air condition our way out of climate change? Of course not. Climate change will stay with us for generations to come and will have to be fixed on a completely different level. But I think it is time to stop preaching to people about “AC chastity,” telling them to “drink more water.” We must develop a serious and rational long-term plan that integrates it into the energy grid, without collapsing it. The first thing that must change are the simplistic and sterile narratives that surround this topic. Time is running out!

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Another problem I didn't see mentioned here. Right now air conditioners rely on Hydrofluorocarbons (HFCs). Which are a greenhouse gases that stay in the atmosphere for 15 years, and are 1,000-9,000 times more potent than CO2.

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Injecting more heat into the environment to stay cool, particularly as long as FFs are the primary source of electricity, is an exercise in nihilism. However, what choice do people have? As usual, the poorest and most marginalized are the most vulnerable. Clearly, we won't air condition our way out of this crisis. Nor will we continue to live as we have on so-called green energy in the form of solar arrays and wind turbines, dependent on fossil fuels to mine, process, manufacture, erect, and maintain. The energy and investment to extract FFs is quickly approaching the point of no returns.

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That’s encouraging. Of course, to begin with, solar and wind will cost some carbon. In the long run they will supply carbon neutral energy which will compensate for the carbon cost of extraction.

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Yes, the elimination of FFs needs to happen. It appears that the approaching economic non-viability of extracting them is the only thing that will stop the madness. However, that leaves other serious questions. We are approaching a world with less energy, not more. We also need to move to a post consumption world.

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None of that is true, and quite frankly counter productive.

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You are absolutely incorrect. Consider, the Permian Basin is tapping out.

https://blog.gorozen.com/blog/the-permian-basin?trk=article-ssr-frontend-pulse_little-text-block

And renewables depend on fossil fuels to create and have nowhere near the energy density of them.

https://thehonestsorcerer.substack.com/p/2019-peak-western-civilization?publication_id=1498475&post_id=146157349&isFreemail=true&r=putep&triedRedirect=true

Not seeing the truth is counterproductive.

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"we’ll rely on air conditioning” to address climate change."

That sounds pretty stupid, so stupid in fact that I really wonder if anyone ever said that. Cite?

Now if one means by "address" that air conditioning is one way of adapting to climate change -- a better way that, say, evacuating Phoenix -- and we take account of the cost of those adaptions in figuring out how much less climate change we are willing to pay for, then what's the problem with AC?

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I find it interesting that the claim here is an exponential cooling energy use versus the delta T (best described as degree-days in most cases, i.e. average degrees above 65F). Yet, when you monitor actual energy use for cooling in homes and businesses, the relationship is nearly perfectly linear. To the extent that all energy management professionals and all software I have ever seen uses the linear relationship. Any explanation why your theoretical conclusions do not match what is observed?

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I would urge a bit more caution when applying the Carnot efficiency formulas to real-world engines and air conditioners. It's worth remembering that these formulas apply only in the limit where the heat transfer processes occur infinitely slowly—when the device would become useless. Real-world devices are optimized to move heat much faster.

For a real-world air conditioner this means (for instance) that the work required will be nonzero even when Delta-T is zero (or negative). So it can't be accurate to say the work required to remove a given amount of heat is directly proportional to Delta-T, at least when Delta-T is sufficiently small. I'm not sure how large Delta-T would have to become to make the proportionality reasonably accurate, but since Delta-T for a household air conditioner is always much smaller than T, my guess is that the direct proportionality is never very accurate in practice.

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Yes, of course you're right — thermodynamics often only works for limits that you can never actually achieve. Nevertheless, calculations like this can still give you insight into the controlling factors in many systems. I think the essential message is that power consumption rises rapidly with outside temperature is robust.

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I was about to say that at least the other factor of Delta-T, from the rate of heat flow through the building envelope, is still there. But that assumes pure conduction, neglecting solar gain and neglecting any thermal energy production within the building. So it's conceivable to me that the Delta-T dependence could be weaker than linear.

Sure would be nice to have some data!

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Having lived and worked (running national climate and biodiversity programs) in hot African deserts for much of my life, I thank you for writing this justice-focused piece. A colleague of my filmmaker husband in Dubai lamented that without air-conditioning in those western-style glass skyscrapers, thousands of people would cook and the buildings would be abandoned. Our documentary series The Climate Restorers (forthcoming late 2024-25) includes an episode on the built environment and the traditional Arabic and other architectural styles that insulated and cooled people so much better than modern western buildings. We are such a clever species, but so often very lacking in wisdom. https://www.theclimaterestorers.com

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Thank you for sharing this Andrew. It's important for people to understand thermodynamic relationships and how it relates to home comfort and building performance. While these conclusions are correct about higher outdoor temperatures leading to much higher cooling electricity inputs, in practice the numbers are a little off. Proportionality is not necessarily equivalence. There are other thermodynamic factors at play here. The TL;DR is that heat pump (or AC) maximum theoretical efficiency is far from real world efficiency (it doesn't scale linearly), and Newton's law of cooling is not a great approximation of total heat gain in a house. Nonetheless and with much respect, thank you for getting this info out there!

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Thanks for this feedback. I certainly think that the assumption of Newtonian cooling is definitely a weak link. Do you have better numbers about how energy flow relates to the temperature differential?

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Heat gain/loss in a house is a tricky thing to model. The three methods of heat transfer all need to be accounted for. Conduction can be approximated using Fourier's Law and convection with Newton's law of cooling. Windows and doors need to be accounted for with a different number for thermal conductivity than the wall assembly. Also quantification of how much of the heat transfer is from which mechanism is difficult also. The good news is that conduction and convection have the same proportional dependence on the temperature difference. The two big kickers are radiative heat transfer (which has a fourth power dependence on temperature) and duct losses. Duct losses are major! I did several case studies on this if interested: https://energyresourcedynamics.substack.com/p/the-duct-problem-americas-building

Unfortunately it is difficult to estimate how all of this heat transfer works together. Ideally you would need to integrate 3 differential equations with codependent variables of questionable accuracy.

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Yes, thanks for this. I added an update emphasizing that this is an idealized calculation, along the lines of “assume a spherical cow spraying milk isotropically”. In many cases, I think this one included, the idealized calculation is actually good enough because it tells you what you ultimately need to know.

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> Very efficient coal-fired power plants tend to be around 40% efficient

GE helps build 47-48% efficient coal PPs. A new Chinese coal PP has achieved 49% efficiency.

https://www.gevernova.com/steam-power/coal-power-plant/usc-ausc

https://www.powermag.com/chinas-pingshan-phase-ii-sets-new-bar-as-worlds-most-efficient-coal-power-plant/

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Thanks for this. Engineers are indeed very clever.

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There are a LOT of things wrong with this article!

To mention a few :

(1)

Yes, Carnot's equations are basic physics. It is true that the Carnot efficiency is Tc/(Th-Tc), but Th and Tc are *not* "the temperature inside and outside of the home" but specifically the temperature of the condenser and of the evaporator. You may be able to estimate that the condenser temperature goes up with the outdoor temperature, but with an offset, and the evaporator temperature isn't your indoor temperature, either. There are several reasons they aren't the same as the indoor and outdoor temperatures. For the condenser (hot side), it's because there's an economic limit of how large you can make the condenser. Say on a hot day (100F), the condenser might be at 20F above ambient (120F). But much more importantly, the evaporator is going to be maybe 40F *below* the indoor temperature. That is for two main reasons: one is that let's say your target temperature is 78F, if you were to run the evaporator at 75F, you'd have to have a jet engine to move the air fast enough to maintain the target with such a small delta to your evaporator temperature; the other is that you *want* the evaporator a bit colder on a hot day because that is what gives you maximum dehumidification.

This is not a small detail!

If you use the author's method, if you target 78F with a 78F evaporator and the outdoors go from 96 to 100F, your COP goes from

(460+78)/(96-78) = 29.9

to

(460+78)/(100-78) = 24.4

[460 converts from F to Rankine degrees, absolute zero is -460F]

for a loss of about 20% in your AC efficiency.

In actual fact your evaporator temperature is probably 34F and the outdoors goes from 116 to 120.

(460+34)/(116-34) = 6.0

to

(460+34)/(120-34) = 5.7

which is just a 5% loss!

(2)

The Newton heat transfer formula is very wrong for the application. It's not just Bitcoin mining that is a fixed source of heat. One of the most important sources of indoor heat is insolation! Even on a relatively cool day you may want to turn on your AC because of the sunlight streaming in through your windows. And the sunlight doesn't magically get stronger because it's hotter outside.

(3)

The thing that's *really* wrong with the argument is neglecting the improvement to the climate in the winter.

Air conditioners can be run off solar power. Especially when the problem that's being solved is insolation heat.

But a 4F warming in the summer you'd imagine goes with a 4F warming in the winter. (This is certainly something that's been observed in Scandinavia---in fact the warming in the winter is *more* than the warming in the summer.) Even in Southern California, people use heat in the winter. And in most of the U.S., people heat their houses with fossil fuels! An overall heating trend will tend to lead to an electrification of HVAC systems, since winter heating loads, which are generally handled by burning fossil fuels, are shifted towards summer cooling loads, which are almost always handled by electric air conditioners, which are relatively easy to run off solar power especially since the demand for air conditioning is the highest on the sunniest days!

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apparently the comments are limited in length...

for a loss of about 20% in your AC efficiency.

In actual fact your evaporator temperature is probably 34F and the outdoors goes from 116 to 124.

(460+34)/(116-34) = 6.0

to

(460+34)/(120-34) = 5.7

which is just a 5% loss!

(2)

The Newton heat transfer formula is very wrong for the application.  It's not just Bitcoin mining that is a fixed source of heat.  One of the most important sources of indoor heat is insolation!  Even on a relatively cool day you may want to turn on your AC because of the sunlight streaming in through your windows.  And the sunlight doesn't magically get stronger because it's hotter outside.

(3)

The thing that's *really* wrong with the argument is neglecting the improvement to the climate in the winter.

Air conditioners can be run off solar power.  Especially when the problem that's being solved is insolation heat.

But a 4F warming in the summer you'd imagine goes with a 4F warming in the winter.  (This is certainly something that's been observed in Scandinavia---in fact the warming in the winter is *more* than the warming in the summer.)  Even in Southern California, people use heat in the winter.  And in most of the U.S., people heat their houses with fossil fuels!  An overall heating trend will tend to lead to an electrification of HVAC systems, since winter heating loads, which are generally handled by burning fossil fuels, are shifted towards summer cooling loads, which are almost always handled by electric air conditioners, which are relatively easy to run off solar power especially since the demand for air conditioning is the highest on the sunniest days!

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I have an Emporia Energy monitor for independent monitoring of each electrical circuit in the breaker panel. Here are actual figures from my home condenser units from today in Dallas with outside temp: low 77, and high 98.

AC system info: 2 units (ducted, 9 tons combined cooling capacity - not a typo) set to 74F upstairs and 73F downstairs throughout the day. Highest efficiency inverter units (Carrier Greenspeed), house built in 2005 with standard builder grade insulation.

Combined kWh consumed by the condenser units in the highest and lowest hour of the day:

low (6am hour): 1.04 kWh

high (4pm hour): 4.6kWh

Considering that the delta T is 4F at the min and 25F at the max, the square relationship opined isn't reflected in the empirical measurements. The daily difference measured here also maps well to monthly electrical bills in the area where roughly a 4x increase in bill cost is seen in the summer months.

It is true that compressor BTU capacity drop is non-linear with the increase in outside temp. However, as long as you operate in the more linear lower section of the asymptotic performance fall off curve, then you're not going to get killed by it. I chose my units specifically because their performance roll off was at a higher temp than other manufacturers. Their better performance is undoubtedly a function of the absurdly large condenser surface area they have in comparison to other units.

Graph from manufacturer's data sheet: https://imgur.com/a/carrier-ac-consumption-capacity-s5yHheu

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Australia has 8 million homes built before there were efficiency standards like basic insulation, sensible siting of windows etc. Decent building standards would make the need to run aircon way cheaper and less frequent for people.

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It should he mentioned that the temperatures in the formulae presented are in terms of an *absolute* temperature scale, either Kelvin (degrees Celsius + 273) or degrees Rankine (Fahrenheit + 460).

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One other item: Thermodynamicists also refer to a Carnot Cycle heat engine as a thermodynamically-reversible heat engine and to its opposite as a thermodynamically-reversible heat pump.

These are the "perfect" cases in theory only; the Second Law requires that there is no such thing as perfect. Thermodynamic irreversibilities, which can be quantified, include as sources the additional delta-T associated with heat transfer to and from the refrigerant (the "working fluid".

For example, the compressor needs to bring the working fluid to a temperature that is at least several degrees greater than that of the outside air, and the expansion valve needs to bring the working fluid to a temperature that is at least several degrees colder than the inside air. Thus, the total delta-T required for operating the real (non-reversible) heat pump has to sum all three delta-Ts, which makes the overall temperature lift higher, and therefore requires still greater compressor work.

Finally, the compressor also operates with irreversibilities associated with the electric motor as well as with the mechanical compressor, so still more electricity is needed to produce the required actual compressor work. As a result, the actual heat pump has a working COP that is substantially less than the perfect, thermodynamically-reversible, heat pump, sometimes less than half that of the theoretical, reversible heat pump.

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As an alternative to converting to Kelvin, you could convert from Fahrenheit to Rankine, by adding 460. That is, 600 F = 1060 R. The critical requirement is to work in absolute temperature units.

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Ummm the inside of my house would be the hot reservoir wouldn't it, not the cold one?

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Your question got me thinking; I imagine that the reservoir is the relatively stable source/sink that one relies on for the effect desired. If I draw heat from outside that’s the reservoir, if I dump heat to the outside then it’s still the reservoir. I’m sure someone else can clarify.

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