Category: Heat Transfer & Thermodynamics

A fundraiser called TeamTrees was recently started by a group of YouTube content creators with the goal of raising $20 million by the end of the year, which will go towards planting 20 million trees. While trees provide lots of environmental benefits besides sucking carbon dioxide out of the air, the ostensible reason for planting these trees is to fight climate change. When I heard about this fundraiser, it made me curious: how much will planting 20 million trees help? None of the folks that are part of the fundraiser seemed to address this question in their announcement videos, so I figured I’d do some rough estimates myself.

A note up front: just because I’m taking a critical look at how much the fundraiser will help doesn’t mean I think it’s not worth donating to or that it’s a waste of time/money/energy. I donated to TeamTrees, and I make monthly donations to a few different environmental organizations. Please read through the full post before making assumptions about what I think of the efficacy of the fundraiser.

One way to approach this question is to look at how many trees there are in the world. According to a research paper in Nature, there are about 3 trillion trees on Earth, and there were roughly 6 trillion trees at the beginning of human civilization. Thus, humans could be considered responsible for cutting down or otherwise killing roughly 3 trillion trees. From this perspective, 20 million trees seems like barely a drop in the bucket: we’d be restoring about 7% of 1% of 1% of all the trees we’ve cut down.

We can also take a more direct look at the effect of planting trees on the amount of carbon dioxide (CO2) in Earth’s atmosphere right now. Atmospheric CO2 is the main reason we’re experiencing global warming – I won’t go into the details in this post, but essentially to stop climate change we’ll need to stop putting more carbon dioxide in the atmosphere. Atmospheric CO2 is measured in parts per million, or ppm. Currently, Earth’s atmosphere has about 410 ppm, which means that for 1 million air molecules, about 410 are carbon dioxide. Prior to human civilization, atmospheric carbon dioxide was at around 280 ppm. So we’ve been responsible for an increase in CO2 of roughly 130 ppm. A 1 ppm increase in CO2 corresponds to roughly 7 trillion kilograms of carbon dioxide.

So the question then becomes, how much CO2 does a tree take out of the atmosphere? Some rough estimates are that a tree can absorb about 20 kg of CO2 per year while it’s growing and about 1000 kg of CO2 over the course of its life. Assuming that each of the 20 million trees absorbs 1000 kg of CO2, all the trees combined would absorb 20 billion kg of CO2 – far short of the 7 trillion kg required to reduce atmospheric CO2 by just 1 ppm.

These calculations might seem discouraging, and they explain why none of the TeamTrees participants made a video about them. It will take a lot of work to stop global warming – so much so that planting 20 million trees would be a rounding error within a plan that could actually reduce atmospheric CO2 by the ~100 ppm required to return us to pre-industrial revolution levels.

Does that mean that TeamTrees is bogus and shouldn’t be bothered with? Definitely not. For one, trees provide benefits beyond just absorbing carbon dioxide. But beyond that, planting 20 million trees will ideally be viewed as a first step. If you donate to TeamTrees and then go back to living a high carbon footprint lifestyle guilt free, then TeamTrees isn’t doing much good. On the other hand, if you donate to TeamTrees and continue to think about your carbon footprint in the future, reducing your consumption over time and contributing to environmental efforts long after the 20 million trees have already been planted, then TeamTrees can really be viewed as a positive force against climate change. There will be a lot more work required after the 20 million trees get planted, but that doesn’t mean they’re not worth planting.

A few months ago, a video was forwarded to me about an air-conditioning unit being developed for developing countries which didn’t require electricity, dubbed the “Eco-Cooler.” It’s not clear to me exactly who or what is behind the idea: the “official” website gives little confidence that it is a serious project, and the videos, while well-produced, seem to be posted through third party accounts and get taken down after a while (this is the original link that was shared with me). In any case, you should be able to search for “eco cooler” on Google or YouTube to find the information I’m talking about, even if these links become defunct.

The science used to explain how the Eco-Cooler works in the video is wrong, and there are others who have already explained this elsewhere (1,2), although unfortunately it seems there’s a lot of noise – incorrect explanations are given along with the correct ones, and skeptics still aren’t sure what to believe. While I’ll take some time to explain why the explanation is wrong, I’m more interested (impressed really) in the experiment the video suggests you try in order to explain the working principle of the Eco-Cooler.

So how does the Eco-Cooler work, according to the video? Air is forced through a nozzle into the house, which pressurizes the air, therefore cooling it. This is bogus. First, pressurizing air heats it, while lowering pressure will lead to a lower temperature. For a real life example of this, you can look at what happens when you use a can of compressed air (or an air horn, or spray paint): as you spray, the can gets cold. When you release air from the can, you’re reducing the pressure inside, and that expansion of gas (not compression/pressurizing) is associated with lowering temperature. Second, the increase in pressure from air flowing through a water bottle nozzle would lead to a negligible change in temperature. If you want to calculate the magnitude of the change yourself, you can use the Joule-Thomson effect, the Bernoulli equation, and conservation of mass – with a back of the envelope calculation I get that air squeezed through the bottle nozzle should heat up by about 0.0001 °C. Finally, even if the air changes temperature as it is squeezed through the nozzle, it will expand as it flows into the room, so the temperature will return to its original value.

So if the scientific explanation they give doesn’t make any sense, why did the video go viral? I think the video’s success is due to the extremely convincing (albeit misleading) “try this yourself” experiment. In the video, the viewer is invited to breathe onto their open palm, first slowly with an open mouth, then quickly with pursed lips. Blowing with pursed lips feels cooler, and they (falsely) claim that this is the same principle which the Eco-Cooler runs on. So what’s actually going on? The air in our bodies is typically warmer than the ambient environment, so if you breathe that air onto your skin, you’ll feel warm (this is step 1 of the video’s experiment). When you purse your lips and blow, the air comes out of your mouth at higher velocity. This leads to more entrained air, that is, the air from your mouth drags along air from the environment with it (this is also how Dyson fans work). As the ambient air is entrained, it mixes with the air from your mouth, lowering its temperature. Overall, the air hitting your hand will be at a higher temperature than the environment (since it’s a mix of high temperature air from your body and ambient air), but it still feels cool since moving air can pull heat out of your body more effectively than still air (this is why sitting in front of a fan feels cool even though the fan doesn’t cool the air at all). To experience this first hand, you can try holding your palm at different distances as you blow with pursed lips. Holding your palm further away should feel cooler, since the hot air from your mouth will have longer to mix with colder ambient air.

So how does the Eco-Cooler actually work? First, I’m not convinced that it does. The video claims the Eco-Cooler can lower the temperature inside a house by 5 °C, but the other content in the video is full of falsehoods, so there’s no reason they couldn’t have just lied about that point as well. That being said, it’s possible that Eco-Cooler could lead to a lower temperature. Air flow through a house will keep the temperature closer to the outside temperature (the house can be hotter than outside because of absorbed sunlight – the same way a car sitting in the sun can get much hotter than its surroundings), and the Eco-Cooler might be more effective than a window because the white panel will reflect sunlight away. However “possible” does not mean “true,” and without much stronger evidence, I am not convinced that the Eco-Cooler is an idea worth pursuing.

Seeing something related to your field of study out in the “real world” can be a mixed experience. On one hand, it’s nice to have evidence that the topics you think about more than 99.9% of people (it would probably still be accurate with more 9s, but I’ll be conservative here) are important in contexts other than academia, and that non-academics do indeed sometimes think about them. On the other hand, it can be frustrating to see poorly reasoned/incorrect explanations about something related to your area of expertise.

I’ve encountered a few examples of frustrating heat transfer explanations out in the real world, and in this post I’ll look at one of them: Salt Cases. Salt Cases are cases designed for iPhones that are advertised as protecting the phone from both hot and cold. The basic premise alone is already suspicious, as being able to passively (i.e., without an external power source) maintain an intermediate temperature in both hot and cold environments is not easy to do (at least, not in steady state).

For cold protection, the explanation given is that the case is thermally insulating, and since the phone is dissipating a bit of power as heat (while it’s on, at least) it traps the heat in the phone and maintains it at a higher temperature than without the case. This explanation is completely reasonable – it’s the same reason why you get warmer when you put on more layers of clothes. You generate heat, and by adding the insulation of additional clothing layers, you trap that heat in your body, leading to a higher temperature.

The heat protection explanation isn’t very different: they say that the case is insulating (although with more of a focus on radiative heat transfer, which might be important if the case is in the sun, for example). At first blush, this might seem reasonable: the case is insulating, so if it’s hot outside you want to insulate the phone from that heat. However, when you consider this in combination with their cold protection explanation, things start to seem a little wonky. The phone is still dissipating power as heat when it’s hot out, and the same principle as before applies. So their explanation is akin to claiming that you’re going to wear a thick winter jacket in the middle of summer because you want it to insulate you from the hot weather outside.

Basically, it’s easy for something to be higher temperature than its ambient environment, you just need heat generation and insulation. It’s hard for something to be lower temperature than its ambient environment – with the exception of some exotic techniques, you need a refrigerant cycle and a decent amount of power.

That being said, they show a video where their case clearly leads to a lower temperature when two phones are left sitting in a car on a sunny day. There are a few explanations for why this could be:

1. The cynical explanation is that they didn’t really leave the Salt Case phone in the car, they kept it somewhere else cooler and moved it into the car to take the video. As easy as this would be to do, I don’t think this is the correct explanation.
2. They advertise their case as reflecting (and therefore not emitting) infrared light, and the thermometer they use is an infrared thermometer. When this type of thermometer is used to measure the temperature of something that doesn’t emit infrared, it’s doesn’t accurately measure the temperature of that object. I don’t think this is correct explanation either, because in the video they open the case, and it would be weird if the screen protector also reflected infrared.
3. The case offers heat protection for a limited amount of time. Since phones don’t dissipate that much heat (if they did, you’d often notice that they felt hot in your hand), even if they were perfectly insulated the temperature would rise slowly. A back of the envelope calculation suggests a temperature rise on the order of 1 degree Fahrenheit per minute, so a well insulated phone might not start overheating in 30 minutes, but would after a few hours. I think this is the correct explanation.

Presumably the product’s claimed heat protection works to some degree, or Salt Cases would have many unhappy customers. But as best I can guess, they only provide passive heat protection over short periods of time. In any case, regardless of the effectiveness of their product, the explanation doesn’t really make sense – hopefully some day they’ll update their “technology” page to give an explanation more consistent with my understanding of heat transfer.

Note: this post is based off a recitation problem I wrote when I was TAing graduate heat transfer last semester. At some point I hope to upload some of the problems I wrote, including this one, which should provide a more structural/mathematical approach to answering the question (rather than just the conceptual approach provided here).

In high school, I read the science fiction novel Red Mars by Kim Stanley Robinson, which chronicles the efforts of a colony of astronauts to terraform Mars (that is, make it more Earth-like, and therefore habitable to humans). Red Mars is fairly far towards the “hard” end of science fiction, meaning that the story is fueled, as much as possible, by actual science that we currently have a strong understanding of. To give recent Hollywood examples, The Martian is representative of hard science fiction, while Interstellar is representative of soft science fiction. This distinction is important because when something doesn’t click as being realistic (in terms of the science) in soft sci-fi, you’re expected to continue suspending disbelief, while if something doesn’t click as being realistic in hard sci-fi, it means the author messed up.

I read Red Mars many years ago, and in the intervening time I’ve forgotten most of the book. However, there is one plot point I still remember, because I disagreed with my high school science teacher about its scientific accuracy. At one point in the story, the colonists distribute windmills all over the surface of Mars which power heaters, with the intention of raising the average temperature of Mars. This post is concerned with the question of whether or not such a scheme could actually raise the surface temperature of Mars. Later in the story we find (spoiler alert) that the proponent of the windmill distribution plan didn’t care about their ability to raise the planet’s temperature, he wanted to use them to distribute plant life (algae? I don’t remember exactly) around Mars. That’s all fine and good, except that 1. some scientists in the story later find that the temperature of Mars has risen by some small (but apparently measurable) amount that they attribute to the windmills, and 2. the plan should be thermodynamically sound if we’re to believe that the other colonists could be convinced to go along with it, regardless of the plan’s true goals.

My science teacher argued that the plan is unsound, because wind is kinetic energy that will eventually be viscously dissipated and converted to heat anyways, so the windmills are pointless. My argument was that a Mars with windmills will be less windy on average (and therefore have less kinetic energy in its atmosphere) and because of conservation of energy its reasonable that the drop in kinetic energy would be accounted for by a rise in thermal energy (i.e., Mars would be at a higher temperature). For a long time I couldn’t reconcile these two viewpoints, however with some simplifying assumptions, we can capture the physics of the situation in a way that is compatible with both arguments.

Our Mars model has two forms of energy: kinetic energy (how windy it is on Mars) and thermal energy (how hot Mars is). The other important piece to know is that the only way Mars can exchange energy with the universe is by radiation: it absorbs energy radiated from the sun, and radiates out infrared radiation to the universe. The energy it receives from the sun should be constant, but the energy it radiates away is a function of its temperature (the hotter Mars gets, the more it radiates away). That means that Mars has some equilibrium temperature, at which the rate it loses energy to the universe is equal to the rate it absorbs energy from the sun. This system is self-balancing (or has negative feedback, to use control theory terminology): if Mars’ temperature rises above the equilibrium, it radiates away more than it absorbs, so the temperature lowers back to the equilibrium value. And vice-versa if Mars’ temperature drops below the equilibrium value. What is not defined by our simple model is how fast this happens, we just know that given enough time, Mars will reach its equilibrium temperature. From this perspective, my science teacher’s argument is correct, and even if you convert kinetic energy to thermal energy, in the long run the Martian temperature remains unchanged. However, this is only the long term behavior. When the windmills are deployed on Mars, they act to convert some of the kinetic energy in the wind to thermal energy. They will continue this conversion process until the wind on Mars reaches a new, lower, “post-windmill” value. Immediately after the windmills have converted the kinetic energy to thermal energy, they will have temporarily increased the average temperature of Mars.

So the full picture of this simple model for Mars is that with the windmills, the average temperature of Mars could be changed temporarily by converting kinetic energy to thermal energy, but in the long run the equilibrium temperature of Mars is determined by radiative exchange with the universe, which the windmills can’t (directly) address. In terms of how this fits into how realistic Red Mars is, I would say that on the first point, there could be a tiny (temporary) increase in temperature due to the windmills, but on the second point, at least one of the colonists should’ve had a strong enough understanding of thermodynamics to explain that this plan would ultimately be futile, and resources should be diverted to a different endeavor. So unfortunately, for this small corner of the story, it seems that Kim Stanley Robinson messed up.