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I've got a post-climate change world where summer temperatures make most of the planet uninhabitable, and the vast majority of the population lives in tightly-packed apartments either in buildings or underground, without direct access to the outside world to dump heat.

The rich have large estates in isolated parts of the world that are still inhabitable, while the poor majority can't afford to move, and are stuck trying to make do. On the bright side, they've got a few decades of technological development into tech needed to survive the new world.

How do you cool an apartment without a window to dump the heat? I've considered finding other places to dump the heat, like into the earth for underground dwellings, but insulation isn't quite good enough to make that process efficient. A more interesting option is chemical methods of cooling, or methods that do something with ambient heat beyond pumping it somewhere.

Is there a good solution for this?

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  • $\begingroup$ Comments are not for extended discussion; this conversation has been moved to chat. $\endgroup$ – L.Dutch - Reinstate Monica Jun 10 at 13:19
  • $\begingroup$ If you want to relax the science-based a bit, I would recommend using cold spots (generated by ghosts) as your heat sinks. $\endgroup$ – Michael Jun 11 at 0:42
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    $\begingroup$ Rather than break thermodynamics, you could launch a lot of Mylar shades into the Earth-Sun liberation point to dim the sun. It's not hard either--we could do it today if we felt like it was worth doing. Launching enough would take a couple of decades probably, and buying that many rockets would be really expensive, but it's far cheaper than the cost of allowing "most of the planet [to become] uninhabitable". $\endgroup$ – neph Jun 11 at 0:44
  • $\begingroup$ Plus, you'd get a burgeoning heavy-lift space market now, and the associated economy of scale would make it far cheaper to lift heavy things into Earth orbit, like big space stations & telescopes & rides to the moon. You'd want to keep launching a few every year even after you have "enough" up there--they'll run out of maneuvering propellant to stay at the Lagrange point, or even if you use solar sails to maneuver, eventually some will break and need replacement. $\endgroup$ – neph Jun 11 at 0:45

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On the bright side, they've got a few decades of technological development into tech needed to survive the new world

Thermodynamics is a harsh mistress and doesn't care about your technological development. If you want to dump heat, you need a place at lower temperature where you can dump the heat, because thermodynamic laws state that heat flows naturally from higher temperature to lower temperature.

That said, windows are a really poor way to dump heat in hot places, because they actually are the places where the heat leaks into the place. If you live in a hot place you keep your windows closed during the day to lessen the amount of sunlight and energy that enters the place.

If the outside is hot, your only choices are insulation to lessen the energy flow in the place and heat pumping to get rid of the excess energy which reached it:

  • build underground
  • pump the heat away, underground will be surely cooler than the surface, unless you are living on a lava pool, in which cases you have other worries than keeping your room cool.
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compressors

You can always dump heat. With a compressor, you can transport the heat from a cool to a hot environment in oder to keep the cool environment cool.

But the cost is high. Living underground lessens the cost, good insulation, too.

heat dumps

You can also dump your heat underground just by boring a deep hole for your compressor's pipes. It's done today and is actually considered a environmentally friendly way of heating or cooling your house, if combined with good insulation.

radiate it

Within sci-fi maybe you can find a way to radiate the heat away from earth, too. There are some metals which, when heated, light up in certain frequencies where our atmosphere is as transparent as for yellow light, but outside the visual spectrum deep inside the IR.

This is a supreme way to just dump the excess heat into space: let your compressor move the heat into those radiators on the roof. A downside may be that you need this space for your solar cells, or more generally speaking, surface space is a premium on earth.

long term solution

Better, build lots of superstructures from materials which are designed with this radiation behaviour in mind. You can artificially design colours to radiate exactly where you want them to radiate.

What if the road network starts to cool down the planet instead of heating it? But ok that would go against the will of your rich people I guess. I mean. It costs money and it helps the poor. :-)

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    $\begingroup$ We already have materials that are highly reflective in visible light, while being highly emissive in IR. They stay colder than their surroundings even in direct sunlight! It's something that will probably be a common part of solar panels in the near future, since high temperatures considerably decrease the efficiency of photovoltaics. There's many things you can do with sufficiently advanced materials that seem to be almost magical. $\endgroup$ – Luaan Jun 9 at 13:49
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    $\begingroup$ @Luaan curious if you could provide an example of such a material or terminology that would assist me in searching for such... $\endgroup$ – Kaya Jun 9 at 18:07
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    $\begingroup$ Radiating heat into space is actually not fiction technologyreview.com/2017/09/12/149205/… $\endgroup$ – asm Jun 9 at 20:10
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    $\begingroup$ @Kevin: It's not a black body, that's the trick. It has color. This material has a color spike in the IR spectrum which is fitting with the atmosphere's IR transparency slot. $\endgroup$ – Anderas Jun 10 at 5:31
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    $\begingroup$ @Kevin another major factor is that the sun is a small area in the sky, while the radiator can see a much larger area. Combined with emitting in an ideal spectral region you can passively cool even in direct sunlight. The conference where I heard about this was probably the only time I've been awestruck in a keynote $\endgroup$ – Chris H Jun 11 at 7:46
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All cooling involves dumping energy somewhere

The laws of thermodynamics essentially mandate this. There ain't no such thing as a free lunch. As such, you can shift the thermal energy around but you can't just make it go away.

Air conditioners blow hot air out one end and cold air out the other. The basic principle is adiabatic expansion and this is why an air conditioner is called a compressor. You compress air, it heats up. That hot air then naturally cools down to room temperature. (This is the part that blows hot air.) Then, when you decompress the air, it cools down again and voila, cold air.

You don't want to use this for whatever reason. There are two other techniques that I know of:

Radiative Cooling

Here, you cool an object down by literally radiating the heat away from it, in the form of actual radiation. Specifically, infrared radiation, which any hot object radiates and this is what heat sensing cameras use to see. It would in theory be possible to create an infrared emitter ("heat laser") that would have a net negative effect on the surrounding temperature. Shoot the beam into space. How, exactly, to build one of these so the net effect is cooling? I have no idea.

Endothermic Cooling

Fire is an example of an exothermic chemical reaction: as things burn, heat is generated. The reverse also exists; there are chemical reactions that absorb heat from the surroundings as they proceed. This is how those single-use chill packs work.

Entropy still wins, though. Entropy always wins. If A -> B is endothermic, B -> A is exothermic. You will also never find a chain of reactions, A -> B -> C -> A, where every step is endothermic. Likewise, the total energy involved in running chemical plants to manufacture the reactants will always wind up working out such that the net heat released is positive.

But you can manufacture the ingredients somewhere else, then transport them to where you need them.

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    $\begingroup$ Sympathetic about the chemical coolant is that it would fuel an entire industry on the cost of ever more destroying the planet. It's a typical thing a rich would do in order to become even more rich. $\endgroup$ – Anderas Jun 9 at 8:18
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    $\begingroup$ "Heat is a form of entropy" - Isn't it cold ? I agree and like most of your answer appart from that. Max entropy is absolute zero, not the other way around. And at the end of your message you explain that you can't end up with positive heat release, isn't it the point ? You want to have less energy, so any reaction that consume that heat into something else is good to go, you don't care that you consume more heat that "necessary" ! $\endgroup$ – Echox Jun 9 at 12:14
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    $\begingroup$ @Echox you can't extract work from heat, you can extract work from heat differences. The efficiency of an internal combustion engine or a coal power plant is determined by the temperature difference of the hot (burning) stuff and the cooling(outside) temperature. You can use work to pump the heat from a room to warm a boiler. Though the net effect is that the boiler will be heated more than the room was cooled, since in the process of pumping heat you also created new heat by doing that work; just as a refrigerator heats your room more than it cools its inside. $\endgroup$ – Peteris Jun 9 at 21:49
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    $\begingroup$ Melting and evaporation can also absorb a fair bit, if you have the mass to evaporate or melt. $\endgroup$ – Ben Barden Jun 10 at 19:20
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    $\begingroup$ @EricDuminil Done. $\endgroup$ – Ton Day Jun 10 at 19:21
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As long as just your summer temperatures are that high, building mostly underground is the best solution for your problem.

At a small depth (from 12 to 40 feet) below the surface of the earth the temperature is constant throughout the year, and this constant temperature of the soil differs little from the mean annual temperature of the air. (Johann Koenigsberger - 'the temperature of Earth's interior')

This constant temperatures were the reason, caves were the first habitations for early men and we use cellars nowadays still to keep food and other stuff save from temperature changes. So by building your homes completly undergrund with a layer of earth over the tops (do not cover the entrances of course ^^) would give you temperated shelters for the poor. Air conditioners pumping air trough pipes in the earth outside the shelters could help for cooling down, if it gets to cold just pump hot air from above the surface down. Another problem could be feeding those people, but that was not part of the question (and as they are more developed then we are could be solved by bioengineered plants growing in intense heat).

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  • $\begingroup$ "without the entrances of course" - and who would be servicing the air ducts and surface installations? $\endgroup$ – Alexander Jun 9 at 16:37
  • $\begingroup$ @alexander: I wanted to say: no layer of earth over the entrances because else you can't leave anymore. $\endgroup$ – Charisturcear Jun 9 at 16:45
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    $\begingroup$ Bear in mind that this isn't a long term solution: eventually the rock itself warms up. This is a problem for old Metro systems which have put a century of heat into the rock, and this cooling is now far less efficient. "[The Underground] was advertised as a place to keep cool on hot days. ...[T]he temperature has slowly risen as the heat sink formed by the clay has filled up. When the tunnels were built the clay temperature was around 14ºC; this has now risen to 19–26ºC and temperatures in the tunnels now reach as high as 30ºC." en.wikipedia.org/wiki/London_Underground_cooling $\endgroup$ – Dragon Jun 10 at 2:33
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Evaporative Cooling

Evaporative cooling is used to lower the temperature and increase the humidity of air by using latent heat of evaporation, changing liquid water to water vapor. In this process, the energy in the air does not change. Warm dry air is changed to cool moist air.

Use evaporative cooling during the day. Refresh the moist air with dry air during the night, where the temperature outside would be lower.

Wiki

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  • $\begingroup$ This would work. There is plenty of liquid water in the deep earth. Letting it turn into gas will absorb heat and you can release the water vapor topside. This is a swamp cooler. home.howstuffworks.com/home-improvement/heating-and-cooling/… $\endgroup$ – Willk Jun 9 at 13:03
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    $\begingroup$ @Willk will it work when the ambient temperature "make(s) most of the planet uninhabitable"? $\endgroup$ – RonJohn Jun 9 at 14:31
  • $\begingroup$ @RonJohn - as long as there is liquid water you can use evaporative cooling to cool things. $\endgroup$ – Willk Jun 9 at 15:19
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    $\begingroup$ @Willk when the temperature is that high, and people are living in caves or tightly packed into apartments, I'm dubious that there will be much easily available liquid water that's not tightly regulated and already used. $\endgroup$ – RonJohn Jun 9 at 15:56
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    $\begingroup$ @Willk getting to that groundwater is the trick, though, and using ocean water requires that you be near the ocean. $\endgroup$ – RonJohn Jun 9 at 17:53
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Same problem as power plants

(including nuclear and focused-beam solar).

They need an ultimate heat sink as cool as possible, to get the most out of their thermal cycle.

Now, their ultimate heat sink is a continuous source of cool water - water is wonderful because it's a) plentiful and b) the densest carrier of heat available. They want it as cool as possible. However often they are forbidden to suck up cool river water and dump that water back in piping hot.

Use cooling towers, just like they do.

So in that case they use spargers (think: sprinkler heads), and if necessary, cooling towers. The spargers spray the water into the air in a fine mist. This heats the air and some of the water vaporizes; most of the rest falls down into the cooling pond below the spargers.

If needed, they put a cooling tower on top of the spargers to force air through them. The iconic curved tower you associate with nuclear plants, works by convection (there are air inlets at the bottom of the tower). They also make much more ordinary-looking ones that use powered fans/blowers. Instead of spargers, they may use a "wet filter material", but it's the same concept - force water to evaporate to cool it.

Even if the relative humidity of the air is already 100%, cooling the hot water has the side-effect of warming the air. Warmer air can hold more water, so warming air reduces its relative humidity and makes room for more water.

Of course as soon as the air cools off, its relative humidity exceeds 100% and the water condenses. And that's why power plant towers make white billowy smoke on humid days! That's not exhaust.

In our case, we are trying to dump heat from an air conditioner, so we place the air conditioner's condenser (the hot thing) in the stream of cooling water. This is nothing new; boats do this. **

Or just boil the water

Your last resort is to add a second "stage" of air conditioning whose job is to raise the refrigerant temperature to well over 100C.* You then place its refrigerant condenser in the bottom of a tank of water. This forces the water in the tank to boil, and the tank vents steam.

Our friend, latent heat of vaporization

This works so well because of a concept called the "Latent heat of vaporization". Say you put a pot of 62F (17C) water to boil. In 150 seconds, it reaches 212F (100C) starts to boil. But after it boils, it stays at 212F/100C. Yet it takes over 1000 more seconds for the water to boil away. The water remains at 212F/100C. This is a lot of energy; where is it going?

It's going into the latent heat of vaporization - the real energy required to convert water from a liquid to a gas.

Water has a rather large latent heat of vaporization, so it works really well for this if the machine is never subject to freezing conditions.

So by boiling - or simply by evaporating water - we are exploiting the latent heat of vaporization to get rid of heat.



* This could be two different types of refrigerant with a freon-freon heat exchanger between them.

** We just saw a question from a student who hacked a fridge and put the outside coil in a pan of water. The student couldn't understand why the pan of water wasn't turning to ice. Not a thermodynamics student, clearly.

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  • $\begingroup$ Or opening the fridge door to cool the room. $\endgroup$ – Justin Thyme the Second Jun 9 at 15:22
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Use air conditioners. Just like today. All you need is a condenser that's not inside the flat you're trying to cool, and piping that connects a unit in the flat with the condenser. No magic needed, although of course ACs get less efficient the hotter or more moist that the outside air is. https://en.wikipedia.org/wiki/Air_conditioning#Installation_types

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  • $\begingroup$ The missing bit here is the "condenser that's not inside the flat you're trying to cool." You've got neighbors to all sides, including up and down, unless you're planning on dumping the heat in the hallway $\endgroup$ – Tal Jun 10 at 4:40
  • $\begingroup$ @Tal That's fine. Have you ever been inside an enclosed room in a large building with central air? It's cooled the same way. I think you using the phrase "dumping heat" is confusing you in terms of how cooling normally works. Normally you just bring cool air in, and the heat is "dumped" in the room you're in! $\endgroup$ – spacetyper Jun 10 at 4:43
  • $\begingroup$ It seems therein lies the problem. There's no central air, and with dozens to hundreds of dwellings lying between you and the outside world, there's no easy way to get access to cool air, or any place to move the heat filling the dwelling $\endgroup$ – Tal Jun 10 at 4:54
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    $\begingroup$ The air conditioners can dump their waste heat onto a heatpipe, operated at possibly hundreds of degrees celcius. The heatpipe would be a basic utility just like flowing water, waste water and electricity. It could be a huge piece of copper or it could actually consist of hot water or hot steam that is pumped around (probably cheaper). Outside of the dwelling there would be a massive cooler that would dissipate the far-above-environment-temperature heat from the heatpipe to the environment. The hotter the heatpipe, the smaller the cooler (but the higher the AC power draw). $\endgroup$ – mic_e Jun 10 at 14:41
  • $\begingroup$ For large buildings, the airconditioning itself would be provided by the building. And they can be powered by solar panels as conveniently the need for cooling matches with when the sun is shining. If individual apartments want their own aircos, the building could just provide a cooling loop for the aircos to dump their heat into, consisting of pipes of water that are cooled by outside radiators. No need for expensive heatpipes when regular plumbing will do. $\endgroup$ – JanKanis Jun 12 at 8:39
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Use A Heat Sink

A heat sink is a large block of heavy internal material that has a lot of thermal mass. It must be insulated from the outside air temperature.

Most air temperatures throughout the world are hot during the day, but cooler at night.

So the method is to dump heat during the day into your Heat Sink keeping the air of the room cool. Then, at nighttime, it radiates out this heat and cools itself down, but warms the air in the room. Essentially what you are doing is 'spreading' the heat of the day over that of the night, and the cool of the night into the heat of the day, resulting in a smooth comfortable temperature throughout both day and night.

This technique is regularly used in Architectural design now to prevent the need for Air Conditioning, even in hot climates (works exceptionally well in deserts, where there is a large difference between daytime and nighttime temperatures).

The heat sink could simply be:

  • Heavy masonry internal walls (liked rammed earth) that are insulated from the outside air temperature
  • A water tank that is internal, again insulated from outside
  • A thick concrete floor slab that is insulated from the outside air temperature

In fact, you don't even need to pump heat in or out, it happens naturally by radiation and convection if the heat sinks are ideally placed.

EDIT: I should add, that if a window is placed on the northern side of the Heat Sink (in Southern Hemisphere) or southern side (in Northern Hemisphere) the winter sun will enter the room and heat the Heat Sink. This is a passive heating device for winter, and works exceptionally well.

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  • $\begingroup$ Is that why the modern kitchen has dual sinks - one is the 'hot' sink and the other is the 'cold' sink? $\endgroup$ – Justin Thyme the Second Jun 9 at 15:34
  • $\begingroup$ @JustinThymetheSecond No - that is just for convenience and the term 'sink' here means 'mass' (not kitchen sink). To answer though: For many decades, single sinks were used, until a double sink was invented so you could drain waste water while still washing dishes. It is simply a symptom of our age of convenience. $\endgroup$ – flox Jun 9 at 15:37
  • $\begingroup$ It was a pun. I love puns and word play. And the additional pun on 'hot' and 'cold' sinks was irresistible. $\endgroup$ – Justin Thyme the Second Jun 9 at 16:41
  • $\begingroup$ This works as long as the average temperature is below the temperature you would like to live in. In the post climate-change world the OP is describing I'm not sure if that would hold. $\endgroup$ – JanKanis Jun 12 at 8:54
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I like the idea of using existing waste streams to transfer waste heat. I.e. graywater and blackwater could serve as the heat sink for waste heat as these wastes are already being removed from area. As an added bonus, the heat may assist in the treatment and decomposition of these wastes.

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'Heat' is such an over-rated but poorly understood concept.

In the final analysis, there is no such thing as 'heat' and 'temperature'. Look up the definitions, and they form a tautology - 'heat' is what is measured by 'temperature', and 'temperature' is a measure of 'heat'. If you remove 'heat', you lower the 'temperature'. But to remove 'heat', you do so by lowering the 'temperature'. Really, there is no such thing as 'heat' and 'temperature' outside of the human experience.

Humans THINK there is such a concept, only because we are warm-blooded, and we have evolved particular biological sensors that send signals to the brain which are interpreted as 'hot' and 'cold'. These in turn have lead us to believe there really is such a thing as 'temperature', that can 'measure' this thing called 'heat', into degrees of 'hotness' or 'coldness'. In truth, what 'temperature sensors' are detecting is 'high energy, high vibration, high expansion, high radiation' as 'hot' and 'low energy, low vibration, low expansion, low radiation' as 'cold'. When we measure 'temperature', we are actually measuring artifacts of the energy state - expansion, vibration leading to state change, emitted energy levels, and so forth. But 'hot' and 'cold' are purely constructs of our minds.

So what you are after, is how to move energy from one place to another, or to convert energy from one form into another. The cause of 'global warming', once we strip it of the psychological concept 'temperature', is that the earth is retaining more solar energy than it is radiating back into space. It is the energy levels of earth that are going up, not this particular physiological artifact that we refer to as 'temperature', and it is this increasing energy levels and the physical changes resulting from high energy levels that is causing the problems, not that things are getting 'hotter'.

So unless you have some mechanism of removing this excess energy from the earth, everything you do will amount to 'robbing Peter to pay Paul'. You might deplete the available energy in one place (lowering the vibrations, movement, radiated energy, and so forth), but only at the expense of building it up in another place. Eventually, that energy will flow back, equalizing the energy distribution.

In fact, that is exactly what is happening today. The excess energy produced by the sun, and absorbed by the earth, has been stored over billions of years in what we are now using as sources of energy - fossil fuels. All of the energy in oil and gas originally came from the excess energy of the sun, was biologically chemically converted into long-chain carbon molecules by biological processes, and stored in the earth. We are now releasing that energy back into the earth's atmosphere, and that increased energy is being perceived by us as 'getting hotter'. No, it is not 'getting hotter', the air molecules are just vibrating more. Winds and storms have more energy. Electrons and electrical charge is building up in the atmosphere, and being released in lightning discharges. Rocks and such are radiating more of this energy through the EM spectrum. Water, rocks, and the earth's crust are expanding.

So, your solution is to mimic biological evolution.

Use huge masses of plants and biology to take all of this excess radiated EM energy and convert it to long-chain carbon-based molecules. Store it as oil. The humans must vacate the earth's surface completely. Live underground, that is a start. No roads, buildings, parking lots. Let vegetation, of any form, completely over-grow every bit of earth's surface, then continuously cut the vegetation down and store it in huge 'compost bins'. The only products and manufacturing processes we can use, are the ones directly related to plants, not resources from the earth that have to be processed through the expenditure of energy. Basically, everything must be made from wood, hemp, and plant fiber, not concrete, steel, and refined minerals. As the vegetation continues to regrow, it will continue to do what vegetation has always done on the earth - convert energy to long-chain carbon-based molecules, and store it.

In this way, your underground apartments and living units will be 'cooled' (energy levels reduced) by the vegetation covering them, and you will let the plants do the manufacturing, not the materials fabrication industries.

But minimal electronic communications. That requires processed copper, aluminum, or other such metals. Can plants manufacture fiber optic cables?

Fun fact - the earth just may be the only place in the entire universe that has oil and gas, if in fact earth is the only place that has life.

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    $\begingroup$ -1, physics nonsense. Temperature is real; heat energy flows from hot (high temperature) to cold (low temperature). And global warming is not caused by the release of chemical energy as heat, but by the IR blocking caused by CO2. And vegetation cannot use this IR because it's too low a frequency. They need visible sunlight (red and blue; plants of course reflect green). $\endgroup$ – MSalters Jun 12 at 10:58
  • $\begingroup$ @MSalters ENERGY flows, not 'heat'. It has been proven that a substantial component of global warming has been the energy released into the atmosphere and oceans by industrial processes, using the air and water as a heat sink. Every single BTU released by any heating process goes directly to warming the earth. The greenhouse effect is only part of the problem. If the IR was blocked, then it would not be a global warming problem. You seem to be confusing the ozone layer depletion from hydroflourocarbons and other chemicals NOT blocking the IR spectrum with the problem of CO2. $\endgroup$ – Justin Thyme the Second Jun 12 at 13:50
  • $\begingroup$ @MSalters If 'bright light' were treated as humans treat 'heat', caused severe pain with intense brightness and dimness, meant 'life or death' depending on intensity, and it had the same equivalent physiological avoidance effect, then we would all say 'light travels from high brightness to low brightness', we would treat 'bright' and 'dark' the same way we treat 'hot' and 'cold', and we would be obsessed with measuring it on some scale the way we report 'temperature'. But in the physics world, there is no difference between 'light' and 'heat' as energy on some measurement scale. $\endgroup$ – Justin Thyme the Second Jun 12 at 14:01
  • $\begingroup$ Ozone depletion is an UV problem, which causes skin cancer, and the problem is a lack of ozone. CO2 blocks emissions in the IR, and the problem is an abundance of CO2. That's why it's a greenhouse effect; it traps the radiative heat transfer to space. As for "light" and "heat" being the same, no - you can't convert heat back to other energy forms except in the presence of a temperature difference, and the Carnot efficiency furthermore limits how much of the heat can be converted back. $\endgroup$ – MSalters Jun 12 at 14:23
  • $\begingroup$ @MSalters You can[t convert heat back to anything because there is no such thing as heat. There is only energy. Maxwell did his studies in an atmosphere, where 'heat' is synonymous with the motion of atmospheric molecules. His ideas depend on atmospheric conduction, and essentially described how energy is transferred from molecule to molecule through conduction. His 'closed system' meant a system in which external conduction was not possible. In pure space, where there is no conduction of heat possible, his ideas had to be generalized to radiation of energy. $\endgroup$ – Justin Thyme the Second Jun 12 at 21:37
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Assuming unlimited technological development, it's reasonable to suppose they've figured out how to pump water around to wherever it's needed. The ocean is an effectively unlimited supply of liquid water, and if it's that hot in summer we can assume there's plenty of solar power, one way or another.

Then you can simply use a heat pump (similar to the one in your existing air conditioner and/or refrigerator) to move heat out of your living space, into a supply of water. Assuming arbitrarily good insulation of the living space from the outside world (easier if you build underground, but you can do this in apartment blocks too with good planning), you'll only need to deal with perhaps 100W per resident on average. Windows should be small, or absent entirely.

Water is capable of absorbing a fantastic amount of heat. Assuming tropical ocean water starts at 25°C, it takes more than 300 MJ to heat one metric tonne to 100°C, and a further 2.25 MJ to convert that water at boiling point into steam at condensing point. At 100W power input, that would take 3 million seconds (more than a month) to achieve - and a metric tonne of water occupies only one cubic metre. I think you can pump a tonne of water per person per month out of the ocean without great difficulty; after all, people need water to drink too, and we can assume you've solved that problem.

You could even simplify the problem by cooling the surface of the building by simply pumping a steady flow of water through it. This would greatly reduce the need for cooling individual living spaces. A closed coolant circuit dedicated to this purpose could have a heat pump moving surplus heat into a municipal coolant system. The latter could simply involve a steady flow of pumped ocean water.

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Building underground using insulation would be the obvious initial choice, but this could be augmented by refrigeration. The higher the temperature the less efficient and more complex a refrigeration plant needs to be but it is certainly possible. It is possible to make cryogenic liquids in hot climates therefore it must be possible to cool an apartment building by refrigeration technology.

Whether this can be achieved cheaply enough for your purposes is another matter but some form of refrigeration is certainly possible even if it uses a lot of power and multistage compressor loops.

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The problem is that temperature increases as you go deeper. The deeper you dig, the warmer it gets. If you have resources, you'd want to live on higher ground, where the air was thinner, or on the coasts, to take advantage of cooler temperatures from the water. The air conditioning they are trying to do is effectively cooling the core of the planet, and even that is going to dump heat into their surroundings. They should move to the surface. Save the caverns for winter, when that same heat from below can warm the cold winter air, which sinks during that season. Less energy needed to warm themselves, as well as cutting their carbon footprint, which over time addresses the warming of the climate. Why not work with the heat gradient, as opposed to against it?

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    $\begingroup$ this very much depends on how deep you go and where & when you are. Away from geological activity, temperature increase with depth only happens at quite large scales. The insulation from the surface is generally more significant and results in quite complicated relationships between depth and temperature for the first tens of metres. $\endgroup$ – Tristan Jun 9 at 13:40
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    $\begingroup$ Here is a chart of the temperature profile for depths of up to 30m is malaysia, you can see how at all dates, there's at least some depths where going deeper results in lower temperatures, andfoor the majority of dates, the temperature at 30m is lower than the surface temperature researchgate.net/profile/A_B_M_Kaish/publication/256838899/… $\endgroup$ – Tristan Jun 9 at 13:41
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Convert the heat into electricity

If you are discussing a futuristic society, they could have invented a technology that converts heat directly into electricity. this would allow for no cooling issues, as well as unlimited electricity to power air filters or other machines required.

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    $\begingroup$ This is thermodynamically impossible, as it is otherwise known as a perpetual motion machine. Heat is a product of doing any kind of work, but you can't just turn that excess heat back into more work. The efficiency of an engine is based upon the difference between the sources of heat and cold, so it won't work without some reservoir of cold to give a balance between. Most engines work fine with air as their cooling source, but that would not work in this situation because the ambient temperature is too high. $\endgroup$ – Adam Reynolds Jun 9 at 22:47
  • $\begingroup$ @AdamReynolds - I'm not sure this is the best answer to the question, but your comment is definitely incorrect. Turning heat into electricity isn't perpetual motion, and the technology has existed for over 150 years: en.wikipedia.org/wiki/Thermoelectric_generator Perpetual motion would be turning heat -> electricity -> heat again and expecting to get more heat out than you started with, $\endgroup$ – David258 Jun 10 at 11:39
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    $\begingroup$ @David258 as written, the answer states it would provide "unlimited electricity." Sounds like perpetual motion to me. Thermoelectric generators certainly have their uses, but they don't fill the requirements for the question as asked. They're not good for removing ambient heat from the environment because they depend on a high temperature differential. $\endgroup$ – barbecue Jun 10 at 12:42
  • $\begingroup$ @barbecue - fair point. I guess I was reading "unlimited energy" as being able to extract unlimited energy given the environment was constantly hot, but I suppose that's a weird interpretation too! $\endgroup$ – David258 Jun 10 at 14:00
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    $\begingroup$ You cannot turn heat into electricity. However, if you have a hot place and a cool place between which heat would naturally flow (a heat differential), you can block its path with a variety of machines, such as thermoelectric generators (very inefficient), steam turbines, stirling engines etc. which get work or electricity out of it at the cost of slowing down heat flow. $\endgroup$ – mic_e Jun 10 at 14:33
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Solar Chimney

There are both home-scale and industrial scale chimneys which feature essentially "free convection" (air movement is driven by thermal differences, and thus requires no powered fans). The industrial-size chimneys are very large indeed, and would supply a decent number of buildings with cold air, if configured appropriately.

Now, industrial scale solar chimneys are intended to operate as a kind of solar power plant. But if your bigger problem was heat removal, then consider the top of the chimney. It works because air temperature decreases with elevation (it's more complicated than that, but let's ignore inversions, etc.). So the air at the top is relatively cold compared to the air coming in at the bottom. Instead of using turbines to power generators, the chimney could instead be engineered to dump hot air at the high elevation and simultaneously pull cooler air down for distribution to residential buildings. There are usually winds aloft which help you with moving the warm air out of the way and providing more cool air so that you don't poison your intake with the hot air you are trying to get rid of.

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Energy Efficiency

Really, pumping your heat into the ground is probably the most efficient way to get rid of it. The amount of heat that you will add to the ground is relatively tiny compared to its thermal mass, and the earth's crust will eventually radiate away the excess heat all over its surface. This is why the crust near the surface is a pretty darned uniform 50 degrees F or so. That's essentially the thermal equilibrium between the primordial heat in earth's core, the solar flux earth receives, and the blackbody radiation of the planet dumping excess heat.

Any building can be insulated sufficiently to make this work. It's just a question of cost and materials. From an energy efficiency perspective, the solar chimney is strictly worse, both in capital costs and operating costs, because dumping heat into the ground can be done easily via liquid refrigerants that have high heat capacity. Whereas, gases have far lower heat capacity, so getting rid of heat via air and bringing in cold air results in far lower heat exchange for the amount of work you're doing.

However, the chimneys are cool from a story-telling perspective because they are unusual and a potential weak spot if you want to drive conflict. It makes the landscape seem all that more different from what we are used to.

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I immediately thought of taking advantage of the Infrared window of the atmosphere. On Earth, our atmosphere is basically transparent to certain wavelengths of infrared light, which means that something that creates those wavelengths, facing the sky, is basically throwing energy into space.

Perhaps you could imagine a field of IR lasers pointing at the sky, dumping excess energy from heat exchangers routed to each underground apartment. Could be an interesting dynamic if things happen to block or disable the laser array.

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  • $\begingroup$ lasers themselves require energy (in a usable form, not waste heat) to run and produce more waste heat themselves so that wouldn't work. But radiators made from a material that emits a lot in those infrared windows while being reflective at visible light frequencies does work, but you need a lot more area than with the lasers idea. $\endgroup$ – JanKanis Jun 12 at 9:27
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Since there's apparently backlash against regular ol' ACs (which answer the question), here's a zanier idea which is a little science based:

Use Maxwell's Demon to selectively trap the hot air and move it somewhere.

You could invent a futuristic smart nano-mesh box which is fed in information about the incoming air particles and selective allows only the highest energy ones to enter, while keeping the lower energy ones out. Of course, computation generates heat, so the computation can't be done on site--the box has to have a fiber-optic cable connecting it to some computer in the outside world, where it can feed in information about the room and receive information about which slits it should open to trap the hot air particles.

Of course, I think this won't really work that well unless you invent some more crazy less-science based things, because I think the air in the room will be pretty uniform in energy overall, and you're still going to have to be receiving some cooler air from somewhere. And you're going to have to empty the box and keep it from radiating heat if it gets too hot. But I'll leave that up to you.

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  • $\begingroup$ The laws of thermodynamics forbid Maxwell's demon from existing, it would trivially allow for perpetual motion. $\endgroup$ – mic_e Jun 10 at 14:53
  • $\begingroup$ @mic_e Maxwell's demon isn't forbidden if you account for the computation needed for the demon, which is what I elaborate on in my answer. The only reason it's a "paradox" normally is because Maxwell's positing doesn't quantify the information required by the demon. $\endgroup$ – spacetyper Jun 11 at 2:02
  • $\begingroup$ @mic_e Maxwell's Demon exists - efficiency is poor. Names used include "Wirbelrohr". , "Vortex Tube", Ranque Hilsch Vortex Tube. | Gas is admitted to a tube tangentially orthogonal to the long axis adjacent to a wall with a partial diameter hole in the middle. . The spiral current drives the entering gas along the wall edge. Lower energy particles (colder) migrate to the centre and higher energy (hotter) to the outer wall . An exit end conical section reflects the inner core of cold gas and allows the hot gas to escape via an annular orifice. ... $\endgroup$ – Russell McMahon Jun 11 at 7:02
  • $\begingroup$ The cold gas stream returns past the entrance and passes through the centre hole so that there is a hot and a cold end [!!!!]. || It has been stated that these cannot be "staged" but I've established how " :-). this can be done "with a little magic . || Many images here $\endgroup$ – Russell McMahon Jun 11 at 7:02
  • $\begingroup$ Vortex tube & Wirbelrohr & Text search & DIY Wirbelrohr - 1958 Scientific American ! :-) - here || Origins here -> Link that has a "possible adult page" warning is 100% safe. $\endgroup$ – Russell McMahon Jun 11 at 7:12
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By using a heat pump, you can dump heat somewhere hotter and make it even hotter, hotter than its environment. As a result, it will lose heat to that environment. For example: a large pit excavated near the underground complex. You can pump 700 °C air along the walls of the pit so that it forms a sort of a scorching cyclone, and at the same time pump cooler air from outside to feed the heat exchanger.

Or you can dump the heat into the water table (even with the Earth made mostly uninhabitable, by digging deep enough you will find a water table).

Or (which is probably best) you can set up heat exchangers on the surface, connected with a large heatpipe or a closed circuit water pipe.

Another way still (much more expensive) is to use lasers to disperse the heat outside ("refrigerator lasers"). The concept was set forth by David Brin in Sundiver, and while implausible, it appears to be achievable.

All this costs energy, but to live underground you must have energy.

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  • $\begingroup$ Why was this voted down? $\endgroup$ – mic_e Jun 10 at 14:43
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What if you were okay with dumping heat into a contained location in your environment?

Consider this - with some form of powerful cooling and "super" insulation, you could have a cooling system that takes heat energy and dumps it into a compressed space that is inside the system and insulated. The waste heat from the carnot cycle could also be dumped into that system. So you end up with a "heat closet" that eventually becomes millions of degrees, and be damned the future consequences! Or else at high cost people can ship these heat closets out to be vented into the atmosphere and/or space?

This is not violating the carnot cycle and this is not Maxwell's Demon. Waste heat is also generated and contained.

Imagine putting a window air conditioner where the "outside" is actually a closet. You'll start to cool off the room while you heat up the closet (with both pumped heat + waste heat). The system fails when either the insulation is leaking heat faster than you can pump heat in, or when your heat pump can't push any more heat into an already hot "closet".

That happens pretty quick with today's technology, but a future insulation solution and a future heat pump solution would push those limits higher and higher.

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  • $\begingroup$ The question is tagged science-based. What mechanism are you going to use to extract low grade heat from the environment and transfer it into this closet that's a million degrees? $\endgroup$ – barbecue Jun 10 at 12:34
  • $\begingroup$ @barbecue: Not going into the details, what you're looking for is a heat pump. Some of the simplest heat pumps (which clearly wouldn't be able to pump heat to a million degrees celcius) are refrigerators and air conditioners. Heat pumps that could handle such a giant differential can certainly be imagined and constructed, but I doubt that they'll be cheap (I'm thinking of particle accelerators). And they'll draw a lot of power. I like the idea of super-high-energy waste heat containers that would need to be swapped out regularly though :) $\endgroup$ – mic_e Jun 10 at 14:51
  • $\begingroup$ @mic_e I'm familiar with heat pumps. The problem is they don't support this scenario. For a science-based question, you need to explain how you are able to continue transferring more heat into an already extremely hot container without producing even more waste heat in the process. That's basically Maxwell's Demon. $\endgroup$ – barbecue Jun 10 at 15:36
  • $\begingroup$ This is not Maxwell's Demon. From my post: "The waste heat from the carnot cycle could also be dumped into that system." $\endgroup$ – David Ljung Madison Stellar Jun 10 at 18:46
  • $\begingroup$ I've clarified my answer to show that it considers waste heat as well. $\endgroup$ – David Ljung Madison Stellar Jun 17 at 22:17
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I use reflective resources to help keep things cool around my domain. The color white reflects a lot of light and prevents it from being converted to heat and the resulting shade is considerably cooler. It's probably not going to solve everybody's comfort issues, but when used in combination with evaporation it could theoretically create cool areas that could be used to dump heat using conventional refrigeration methods.

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Unfortunately, the laws of thermodynamics prevent you from cooling (removing heat from) a room unless that heat has somewhere to go. Regardless of any technological advancement and post-apocalyptic MacGyver-ism, you simply cannot reduce the temperature without placing the heat somewhere.

Heat Transfer is Required

Your tech-savvy lower-class needs to engineer some way to move the heat outside the apartment. If they are living in a co-op type manner this could involve a communal heat transfer source built into the apartment/underground complex which each home then connects to.

Each home could have a compressor, that feeds the coolant liquid through the central system and disperses it outside the home, working like a refrigerator.

Chemical-reaction based cooling mechanisms are interesting. There are currently heat exchange systems that work based on the principle of phase-change. Electricity is required to power fans—the method of which depends on how electricity is generated in your world—which move the hot air towards a solid substance. The solid substance is melted, which removes heat from the air, and the cooler air is cycled back into the home.

Chemical Reaction

A 100% chemical-based solution you would require an endothermic reaction which pulls heat from the surroundings in order to power the reaction. One such example (that would have to be scaled up) is ammonium thiocyanate and barium hydroxide octahydrate.

https://www.youtube.com/watch?v=MyAzjSdc3Fc

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There are chemical process that absorb heat - collectively known as endothermic reactions Few of the examples would be reasonable in a domestic environment, but one stands out: Photosynthesis

I can't find a figure for how much heat is absorbed by Earth plants, but there's a precedent, and you control your world so have some native plant that does this particularly well and more in the IR range than the UV or visible range.

Bonus, the plants absorb CO2 and release Oxygen, which will help make your underground living areas more breathable without requiring as much surface ventilation.

In short - use that energy, rather than dumping it.

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You don't dumps "heat" to outside. You extract "cold" from inside.

A very small vacuum pump could freeze water very fast. A lot of water, if you like. Simply run a fan in front a reservoir of water with a vacuum pump attached to it, and voalá.

"Cold from tap" is a registered mark from Very Rich People, patent pending. Taxes will apply.

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  • $\begingroup$ You need then to find a place to dump the water vapour created by the vacuum pump; if you let it condense, it will release the accumulated heat. $\endgroup$ – LSerni Jun 9 at 23:09
  • $\begingroup$ The output of this configuration is about 10 l of water vapor per hour. This can be ventilated with the same air needed to breath. $\endgroup$ – André LFS Bacci Jun 10 at 14:54
  • $\begingroup$ Yes, but you are still dumping heat, no more and no less than if you expelled warm water or hot air. It may be latent heat, but it's heat nonetheless. Using a vacuum pump and ambient temperature water, or using a heat pump (compressor) and boiling water, boils down to more or less the same thing. $\endgroup$ – LSerni Jun 10 at 16:41
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I'm going to suggest the same thing as others but still differently, radiate the heat away.

I simply base my assumptions on this video, a shorter version typed by me below if you don't want to watch it.

In warm countries centuries ago the people used radiative cooling to get ice. They would use a kind of pool that they filled with water during the evening, and by morning it would be frozen even if the surrounding air was warmer.

Every warm thing radiates heat, usually this radiation will hit something nearby, heat that up and it will radiate a portion back. But this type of night time cooling used a "gap" in the atmosphere where radiation would be able to reach space and leave the planet. This allowed the water to lose more heat and get colder than the air surrounding it. During the day however the sun would shine into that atmospheric gap as well and heat it up more than it lost heat.

Using a particular composite material you can simultaneously reflect the heat of the sun and still radiate heat from the object away. This can make the prototypes they had during the filming up to 42 degrees Celsius colder than the surroundings. This material can be mass-produced even today, so your future civilization could use this en-masse on top and the sides of their buildings.

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