Where does a candle go when it burns? | Hacker News Reader

Where does a candle go when it burns?

nytimes.com

194 pointslxm145 comments

There's a hell of a lot more.

Michael Faraday's "Chemical History of a Candle" is a very readable masterpiece on the subject, despite its age.

The Engineering Guy has done much to revive Faraday's work: http://www.engineerguy.com/faraday/

One of my favourite books, especially for his demonstration of how they know what's going on at each point of the chemical reaction.

Also, he explains clearly what fire is, which is something that many people puzzle about for all their lives.

He also did a full video series. "Chemical History of a Candle" was originally a series of lectures given by Faraday; he recreated the lectures and the demonstrations. Definitely worth a watch, especially if you don't have a conceptual understanding of fire

Awesome, thank you! "a series of six lectures on the chemistry and physics of flames given by Michael Faraday at the Royal Institution in 1848, as part of the series of Christmas lectures for young people founded by Faraday in 1825 and still given there every year."

First video: https://www.youtube.com/watch?v=6W0MHZ4jb4A

And indeed the Royal Institution seems to be still pumping out popular lectures, now available on youtube:

https://www.youtube.com/user/TheRoyalInstitution/videos

This is interesting, but why does he speak archaically? I understand it fine, but I'll have to stop the video every 5 seconds to translate for my kid. Is it part of his style in general?

He's reciting directly from Michael Faraday's manuscript

Ah gotcha, thanks!

Thanks for linking that. I did not know the Engineer Guy had a website. His youtube videos are superb. I need more of them, and more often. I was going to comment that I think he is the Carl Sagan of engineering because he explains things with such clarity, and then I noticed on his website that he actually recently received the Carl Sagan award.

I highly recommend that everyone checkout his videos.

Fun thing about the carbon cycle, much of the candles mass goes into the air and much the mass of a tree comes from the air.

My mind was blown a little bit when I realized that when you lose fat, you do so by breathing it out. Some of which will also go on to make trees as well.

But there’s also water generated when buying (edit:burning) carbo hydrates.

I assume you mean burning, but if you drive or even walk to the store to buy the carbs that also generates water.

The final bit that locked it in for me (and someone please correct me if this is wrong) is that going to the bathroom (which what many people assume is where weight leaves the body) is actually the last stage of "energy input" to the body and doesn't really play a role in "energy output".

Well, your body does not utilize all the energy it could from the food and drink you ingest. Say if you get a condition where your digestive efficiency goes down - tapeworm, inflammation, whatever - all else equal, you're going to start losing weight fast. This is why gastric bypass surgery works.

I don't understand what you are saying here. The physical weight of the feces does leave your body. How is that an input?

It's the end of the input. Think about it another way... say you chew on a slice of orange, swallow the juice, and spit out the pith. The pith isn't output of your body. It's just the end of the intake process.

Feaces isn't produced by your metabolic system. It's just the byproduct of intake. The stuff that your body didn't absorb.

Feces may not be produced by your metabolic system, but it is certainly not just a byproduct of intake. It includes red blood cells that have failed quality assurance and been filtered out of the bloodstream by the spleen; that is why it's brown.

Not long ago I googled why shit and piss are two things and not one. It just suddenly seemed odd to me one day. The answer seemed to be that the stuff we poo out never goes 'inside' our body. Imagining our bodies being like a tube or doughnut, what goes in our mouths just goes through the hole, staying in a sense on the outside. What comes out is just what we couldn't use as it passed along the conveyor belt. Piss, on the other hand, is the waste from (truly) inside us.

Hmm seems there are (at least) two levels of 'inside' here. It's quite a weird, topological subject hehe. It seems odd that we don't intuitively think of those as different degrees of insideness.

Therefore, trees are fat.

;)

Cheekily, this also means that if you're losing weight, you are a net emitter of CO2, thus hastening global warming. On the other hand, if you gain weight, you are a net sink.

Of course the carbon cost of food production does… complicate this a little bit :)

The balance evens out pretty quickly on the other end though. Does anyone know if crematoriums do carbon capture?

IIRC, you urinate a decent chunk of it out too.

Hey snap! I just posted the same thing before I read your post!

> much the mass of a tree comes from the air

A fun pastime of mine is asking people where they think the mass of a tree comes from and trying to guide them to the right answer (CO2) via the socratic method (i.e. trying to only ask questions)

I was wondering how much of a tree's mass is not Carbon or Oxygen. Turns out it's somewhere around 10%; half of that is light weight hydrogen. So water probably provides a decent chunk of a tree's oxygen content also.

Page 4 https://www.urban-forestry.com/assets/documents/Coder_Tree%2...

I also love the idea that when you exercise more and lose weight, you shed the body mass by breathing out co2.

"Where do trees get their mass?" - https://www.youtube.com/watch?v=2KZb2_vcNTg

This was highly enlightening the first time I watched it :)

Paywall bypass: https://archive.is/9IOgm

If the products of incomplete combustion make up just 0.1%, how come if you pass your fingertip through the flame, too quickly to feel any pain, you get a solid black swath of soot on your skin in just that split second? The stuff is just spewing out.

The yellow part is glowing soot particles. Where it stops being yellow, it has mostly burned up (turned into carbon dioxide). No surprise that there's a lot of soot in the flame.

Where it stops being yellow, the particles have just cooled down so they don't glow. At that point, you see a black trail of smoke wafting upward. You won't see easily that by the light of the candle alone, though.

Hold a spoon above the flame, it takes a long time to become black, if at all. Hold it into the flame, it becomes black instantly. You need to explain why that is so to convince me.

The spoon causes more soot to be created by interfering with the combustion process.

Putting something relatively cold and with high thermal mass (like anything solid) to a flame drastically increases how much incomplete combustion happens near it. Basically you take the heat away before it can finish burning the fuel.

That's why a clean flame will still soot anything you put over it.

If you interfere with the flame, by taking away heat or limiting airflow so it can't get enough oxygen, you will get partial combustion, where you have incomplete combustion byproducts and vaporized fuel in the mix as well. Same reason why a can of gasoline on fire will produce huge billows of black smoke (insufficient oxygen) while when burned under precise conditions in an engine it's much cleaner, even without exhaust filtering.

One thing that always amazed me is how the wick burns at just the right speed, how it keeps pace with the wax. Neither does it burn away too quickly leaving nothing to keep the flame going, nor does it burn too slowly leaving decimeters of wick when the candle is burnt out.

I guess there must be some feedback process going on, which makes a long wick burn faster than a short one.

The wick is in a local negative feedback cycle with its fuel. If it were to burn “too fast” then its fuel input rate will be reduced, and it would burn more slowly.

If the negative feedback mechanism didn’t exist, the candle combustion reaction would runaway and the whole thing would explode.

As GOOP discovered...

https://www.theguardian.com/lifeandstyle/2021/mar/19/experie...

There probably are some feedback loops like this, but there's also just a careful balance between the wick size, the size of the jar, the formulation of the wax, the preparation of the candle, and the use of it.

Some examples of things that can go wrong: https://www.candlescience.com/wax/soy-wax-trouble-shooting-g...

This is in some sense the conclusion of a conversation that has been going on for months on TikTok.

People ask Hank Green (of Crash Course/Youtube/etc. fame) questions. Sometime last year, someone asked where the wax went in a candle when you burn it (https://www.tiktok.com/@hankgreen1/video/6890298762032368898). Since then, hank has been in a bit of a feud with the collective of TikTok, who seem to be unwilling to understand that the wax is what burns (https://www.tiktok.com/@hankgreen1/video/6955202282313059590), despite his many attempts to explain (https://www.tiktok.com/@hankgreen1/video/6945244159187897605).

I'm partial to this explanation by another user (https://www.tiktok.com/@tomlumperson/video/69554934350171210...), who also has a great tiktok about bees: https://www.tiktok.com/@tomlumperson/video/69508366516858585....

Now, nearly 6 months later, the same question has made it to the mainstream and is getting asked of Randall Munroe in the NYT.

Reading another article in this series, "Can You Boil an Egg Too Long?" [1] really made me smile. Apparently no one knows exactly what happens if you boil an egg for multiple months or years. This seems such a trivial thing compared to all the other stuff humans have discovered. On the other hand this also means almost anyone can expand the limits of human knowledge: you just need an egg, a reliable source of heat and water, and lots of patience. Granted, the knowledge gained may not change the world, but you will still be the first who is in possession of that knowledge!

[1]: https://www.nytimes.com/2020/06/09/science/randall-munroe-qu...

> but you will still be the first who is in possession of that knowledge!

Are you sure about that? How do you know that no one has done that experiment. Expanding the limits of human knowledge is not just about learning something new, but also sharing it in such a way that makes it part of humanities general knowledge base (even if still restricted to a relativly small group of people). Most people do not have the means to establish human knowledge in this way; and those that do are generally limited to a scope that does not contain hard-boiling eggs.

You'd probably have to make do with a blog post rather than a journal publication.

Okay, I got way more of a kick than necessary from the image of a map which depicts 'you' traversing from 'the land of normal eggs' to '?'.

Also - and more relevant to HN - this is the first time I noticed Randall Munroe of xkcd fame has written for the New York Times. Good job on him for landing that gig! :D

Julia Child's tip on cooking a poached egg:

1. Poke a small hole with a pin in one side of egg.

2. Put the whole egg in boiling water for 10 seconds.

3. Remove egg, and run under cold water. (So you can handle it.)

4. Crack the egg back into the boiling water, and cook.

5. The poached egg comes out more uniform, and whole.

Does it though? I found a video of Julia using this method, but there is also step 4.5 where you crack the egg into an egg poacher, which is designed to help keep the egg nicely shaped. Maybe it's just the egg poacher doing its job?

https://www.youtube.com/watch?v=KvSnUmU509k

Also, publishing the result will almost certainly win you an Egg Noble prize (https://en.wikipedia.org/wiki/Ig_Nobel_Prize)

The experiment might not be that simple, though. You would no want to boil away all the water.

That means using a closed system (might go BOOM), starting with lots of water (expensive), or finding a way to add water while keeping the water at boiling temperature (you don’t have to add cold water, so that is probably not that hard, but not trivial, either)

I don’t think it’s that big of an explosion risk; it’s just a matter of finding the right pressure to hold water at 212F permanently. Pressure cookers already exceed this IIRC, so off the shelf equipment should suffice.

"Iron eggs", eggs boiled multiple times across multiple days, is a delicacy in Taiwan. In case anyone is curious to see what an egg boiled for longer than usual (with soy sauce and spices) looks like.

They seem to harden more and more upon boiling, so I'm not sure I subscribe to the idea that _eventually_ a super-boiled egg would disintegrate into soup...

https://en.wikipedia.org/wiki/Iron_egg

Fun fact, this is also where fat goes when your body burns it: Into the air.

A good demonstration of this by Ruben Meerman: https://www.youtube.com/watch?v=vuIlsN32WaE

Except the fat goes out of your body and the candle is going into your body.

I saw a study showing correlation between cognitive impairment and sub-micron particles in the air. They used candles for the study but coal factories are the large scale concern.

Related to this, I've seen research showing that by the time a room feels stuffy there is enough CO2 to measurably affect cognitive performance. Now I'm much better about remembering to open a window when I'm coding and starting to drag.

Highly recommend getting a cheap CO2 meter. We have a couple around the house. It’s amazing how fast a room fills with CO2 when cooking or having people over (pre-COVID). You can become more attuned to it — I have a pretty good idea what 800PPM feels like compared to 500PPM compared to 1000PPM. Weird party trick too.

What do they feel like for you? I’ve had a CO2 sensor in my office for a long time, and don’t think I can tell the difference between 500 and 1500ppm.

It honestly doesn’t feel like anything. I just ask my body what the number is and it’s always within a hundred ppm. it feels like a guess, but like a guess when you’ve been counting cards so long you know roughly what the count is without consciously keeping track of it? If that makes sense.

A couple of years ago, I started getting headaches. Everything in my noggin appeared normal, and one day I worked with the window open. No headache. So I got my first one, it wasn’t very expensive (€50-100 IIRC) and did some experiments. Sure enough, it would get up to 1800ppm in my tiny office and I’d get a headache.

I’d say the biggest thing it seems to affect is coding. If I can keep it below 600ppm in my office, I can code all day and late into the evening without feeling too exhausted. At about 1k, I start to feel kinda sleepy and tired after awhile.

My wife and kid had fun doing the observations and asking the questions during the experiment. Good times. We used it as a way to teach our son how to do experiments and ethics.

A quick search shows a ton of choices, Are there any models or brands you like, or dislike?

I wasn’t too picky, I ended up with tfa dostmann‘s which seemed reasonable in price point vs accuracy.

Do you have a recommendation for one? I heard it's quite hard to get accurate ones without paying a lot.

Yet another advantage of remote work! How many offices have windows you can open? (I used to work in one that did, because it was in an old mill building. It was great.)

You can breath in your burned fat too, if you wish.

Related study, which I found interesting, that confirms the weight you “lose” is excreted primarily through your breath:

https://www.medicalnewstoday.com/articles/287046#Tracking-th...

What I find most interesting is that so many people, including those with supposed expert knowledge of physiology, get this totally wrong.

On the flip, that tree in your backyard isn't growing out of the ground outside of the moisture that falls from the sky -- if it did the ground would sink -- it is growing out of the air.

I 'discovered' this as a teenager because my weight in the morning would be lower than my weight at night and I had done nothing but lie in bed comfy all night. There was only one place it could reasonably go - now that I wasn't wetting my bed that is.

how did you weigh yourself so precisely?

Its pretty common to weigh 1lb less in the morning than night, don't need a fancy scale for that. But decimal level accuracy scales are also common.

This takes surprisingly little precision, you really exhale quite a lot of mass over 8 hours.

I suppose you could also lose weight via the moisture in your breath, or sweat of operation. But yes, it’s pretty cool.

You do lose weight via the moisture, typically around 200g if this article[1] is to be trusted (doesn't cite its sources). More if you are sweating heavily for one reason or another. Much bigger effect than calories burnt in the same duration.

[1] https://washingtoncitypaper.com/article/221338/straight-dope...

The amount of mass exhaled as CO2 at night is nowhere near as much as the loss through perspiration and evaporation. Water loss happens pretty much constantly and is why one dies of dehydration after a couple days.

I was curious about this. I'm on a diet now and I often weight like 0.5-0.8 kg less in the morning.

And when I go on a 20km walk on the weekend I lose about 1kg in 5 hours. Is it mostly water? Cause I drink a lot during the walk and I don't go fast enough to get sweaty.

It pretty much has to be. 1kg would be 1L of water, which is not that much to lose over 5 hours.

But 1kg of fat is 7700 kcal, which would be a massive amount of energy to expend in 5 hours. Unless your "walks" involve running uphill with a 25kg pack or something like that. :)

Short-term energy consumption on a 5 hour hike would be from stored glucose, fat breakdown IMHO would happen slower. A 20km hike can consume 1000-2000kcal depending on how hard it is (climb, terrain, weight of hiker, weight of pack matter) so that would be 0.25-0.5kg of carbs - so potentially that loss could be 50/50 carbs and water.

But hydration definitely is a big aspect of mass simply because of how much you add and lose. I once did a ~90km hike in 24 hours or so, and I believe I drank something like 15+ litres of liquids during that.

Depends on what you’ve eaten recently. It’s pretty easy to burn fat on a hike if you go while fasting.

Yes. A lot of fad diets and supplements work on this principle; dehydrating you appears to lose weight really quickly initially. It's not sustainable.

The human body is darn efficient.

You would probably have to run 50-70km to lose 1kg fat.

It's easier to not eat calories than to burn them after eating.

Humans lose moisture for a variety of reasons normally, you don’t need to be sweating in order to lose it, although that obviously drives the loss rate up. You lose a ton of water through just breathing.

On your walks you’re probably burning glycogen, the carbohydrate we store in our liver and muscles for easy access energy, and exhaling a lot of water. We store about half a kilo of glycogen which is then bound up with 3-4x as much water still. While you’re not likely to consume all your glycogen in a 20km walk (you need a marathon to do it), burning a decent chunk of it on top of normal water loss isn’t an unreasonable hypothesis.

Yep! When you lose weight you slightly increase the mass of the atmosphere by roughly the amount you lost. Whatever doesn't go into the atmosphere goes into the toilet (mostly water).

I had no idea Randall Munroe of XKCD has had a column at NYT since 2019. His illustration style is so distinct.

For a while, he was dabbling with long form (rather than pure comic) writing.

https://what-if.xkcd.com

Its more than a dabble - there are 157 of them, but that's the type of thing that a paper looking for original content and writing would like.

The last what-if was published in May of 2018.

There have been occasional grumblings for a couple of years now that the humour of the XKCD webcomic has declined, Munroe just doesn’t seem to have his mind on the job now that he is doing these other projects. However, the what-if and pop-science explanatory stuff is generally of very good quality, so on balance one can’t really complain.

Well, he certainly has already contributed his fair share, and most of it totally free, not even banner ads.

Those were compiled into a physical book. The online content stopped shortly after; pity.

The book was published in '14 ( https://en.wikipedia.org/wiki/What_If%3F_(book) ) . The what if long form continued on for another four years.

After watching the first illustration went up and confirmed that was Randall Munroe the one that wrote it. I've been missing for too long his what-if posts.

Still, would be nice to have his typical mouseover messages.

I was wondering what happened to those I figured he was just writting book of them now so he wasn't going to post them for free.

My favourite part of the book xkcd: volume 0 is the beginning of the introduction:

Hi!

This book is a collection of strips from xkcd, a free webcomic. I want to get that out of the way so you don't feel betrayed later when you realize you paid for a book of things that you could get for free on the Internet. I like books a lot, so I've put this one together from my webcomic (and added some annotations and other tidbits), but that's really no excuse for poor economic sense on your part. Still, if you've purchased this book, I suppose it's too late for regrets. Let's gloss over this incident and move on to the story of xkcd.

Same here. I was intrigued by both writing style and then the way the diagram was drawn. Scrolled up and sure enough i found it's from Randall Munroe, as expected :)

> Wax is made of hydrogen and carbon.

Too bad he doesn't explain where the energy in the wax came from like Feynman does when explaining fire:

https://youtu.be/N1pIYI5JQLE

Paraffin wax is derived from petroleum, so like the wood in Feynman's explanation, the energy is from the sun via ancient photosynthesis.

All fossil fuels are solar power in that sense?

Only in the most pendantic of senses - a bit like arguing that my car is fusion powered because it runs on gas that was originally given energy from the sun. I suppose in a sense everything in the universe is powered by whatever triggered the Big Bang.

Most of them. There are also the nuclear reactions in the earth's core.

I know that there are organisms that thrive in geotermally heated environments, but do they really produce fossil fuels?

Or more recent photosynthesis. You can make candle wax out of soy, beeswax, crisco, etc.

Also from animal fat.

I just skimmed the article but it seems to not talk about the fact that (what I feel like is) a majority of candles is not made from bee wax any more, but rather paraffine.

The intermediate image of globe with particles dispersed only through the northern hemisphere is because of the Coriolis force?

> After about a year, atoms from your candle will have spread completely around the globe.

How on earth is this provable?

Probably based on data from radiation leaks.

It seems plausible.

Earth has a radius of about 6400 km. That makes half of the circumference about 20100 km.

For something you release to spread all the way around the world in a year requires it to spread out from you at about 20100 km/year. That is about 2.3 km/hr, or about 0.6 m/s or about 25 inches/second.

I've never tried to measure it, but my recollection of about how long it has taken after something nearby emits a strong odor for that odor to reach my nose is that the speed is in that ballpark.

Woah, particle dispersion is fucking crazy. I had no bloody idea it spreads all around the world in a year. I wonder what the minimum size of radioactive explosion would be to send a particle from say India (on the other side of the world) to me here on the West Coast and provide appreciable harm.

A few months after the Fukushima Daiichi disaster, the background radiation where I lived in Anaheim, CA went from like 0.08 - 0.12usv to 0.40 - 0.70usv depending on the day.

I had a radiation detector because I lived in a historic home and was a little paranoid about things like lead, radiation, etc.

It's of course anecdotal.

Fascinating. Thanks for that anecdote.

I remember a story where some European nuclear plant operators all evacuated when their badges reported high radiation and on stepping out they realized the count was higher outside. Chernobyl had just failed. Might be apocryphal but I enjoyed the picture so I'm not even going to verify.

It's true, the Chernobyl disaster was first detected and announced from the Forsmark plant in Sweden, while USSR was still hoping no one would notice.

Over a day after, radiation was detected on a shoe of an employee about to enter. It was concluded there was no radiation inside the plant, and that it wasn't the plant leaking outside. That left winds from east as the source and that's how the world got to know.

You're welcome! I decided to look it up, and found this:

"Canopy-Forming Kelps as California’s Coastal Dosimeter: 131I from Damaged Japanese Reactor Measured in Macrocystis pyrifera"

https://pubs.acs.org/doi/abs/10.1021/es203598r?journalCode=e...

Wow, the New York times has truly hired or acquired everyone.

I guess that's where the What If blog went, it hasn't been updated for a while now. No timestamps on the last post but wiki says he started writing this column for NYT late 2019, which feels about right.

https://what-if.xkcd.com/

I had no idea Randall started writing for the nytimes. Seems like a great continuation to his what if series. I've missed it dearly. Hope he writes more!

Wouldn't also some mass be converted into energy? Probably not much though

How? What do you mean by that?

Trace amounts of radioisotopes found in the candle will be subject to decay while the candle is burned (much as they would be while the candle isn't burning), so there would presumably be some negligible amount of alpha, beta and/or gamma radiation.

very very very little

None, actually.

It’s a chemical reaction which means all mass is preserved.

No, actually, very very little, not zero. The candle (summed with its gas emissions) loses mass equal to the relativistic mass of the photons emitted. For something like a candle it's an undetectably small amount but it's not zero.

Good catch, thanks.

Is heat basically a bunch of photons?

For normal non-nuclear candles the energy obtained through breaking chemical bonds and creating outputs with less energy contained in the connections between atoms. The matter is not destroyed.

Well, sure, but energy=mass; just as an atom's mass is not equal to the sum of the protons, neutrons and electrons masses but depends also on their binding energy, in the same manner, a compound with highly energetic chemical bounds has a (very, very slightly) different inertia and gravity than the separate components. The difference of this effect between atomic and chemical bounds [spelling? English isn't my main language] is quantitative, not qualitative; chemical bounds have much less energy, so the effect is much smaller, so for most purposes it can be considered as insignificantly small, but it's still there and not zero.

Any system that loses energy (e.g. releases an energetic photon - no matter if it's because of a nuclear or chemical reaction) also loses mass, though E=mc^2 means that losing reasonable amounts of energy mean losing very, very small amounts of mass.

energy != mass; e=mc^2 declares there is a proportional relationship between energy and mass while the speed of light, c, squared is the constant of proportionality.

You can set c to 1 if you want, then energy == mass.

As a matter of fact this is pretty common in particle physics where all masses are given in electronvolts.

https://en.wikipedia.org/wiki/Geometrized_unit_system

"there is a proportional relationship between energy and mass" -> exactly. the mass of the system is strictly proportional to its total energy, and changes in the energy of a system will have a corresponding proportional effect on its mass.

If you split the system into two components and release X energy, then the two components will weigh X/c^2 less than the whole system did; if splitting the system consumed X energy, then the separate components will weigh X/c^2 more than the original thing.

Thank you for the explanation, that makes perfect sense.

So... the energy content in wax is about 45MJ/kg. An 8 in ch taper candle weights about 40g. This means it contains about 1.8 MJ of energy.

Of that 40g about 20 nanograms turned into energy! That is about 0.5 parts per billion.

https://physics.stackexchange.com/questions/195696/do-chemic...

Seems the unanimous answer is 'yes', which surprised me. I considered that chemical bonds are actually changes in electromagnetic potential (i.e. similar to the leaves in a Leyden jar repelling, converting electrical potential to gravitational potential). With no change in mass, I expected that the relativity equation would zero.

That's the whole point - the inertial and gravitational mass of the system is proportional to the total energy of the system; changes in electromagnetic potential affect the energy within and thus also the mass as far as inertia or gravity is concerned. The same applies for electrostatic potential and gravitational potential. "Rest mass" is just a form of energy - after all, the rest mass of e.g. a block of lead consists mostly of the rest mass of protons and neutrons inside, but the rest mass of those protons and neutrons does not consist of the rest mass of their components, but mostly of the binding energy between their quarks - so the block of lead weighs as much as (and because of) the stored binding energy.

>Any system that loses energy (e.g. releases an energetic photon - no matter if it's because of a nuclear or chemical reaction) also loses mass

Lol sorry my friend but this is just plain false. Photons can carry away energy in the form of momentum but they're massless. Remember, it's E^2 = (pc)^2 + (mc^2)^2. Nuclear reactions can involve the conversion of mass into energy because they involve the strong force, but that's not how chemical reactions work.

Think about it like this: you have two H atoms bump each other perfectly and come to rest, and in the process an electron gets excited to a higher energy state. Eventually it spontaneously pops back down, emitting a photon that escapes. The mass of the two H atoms is unchanged, but a photon took energy away. It carried away momentum, not mass.

"The mass of the two H atoms is unchanged" -> No, if an electron on an H atom is excited to a higher energy state, the mass of the atom increases (although with the relatively low energies involved, that mass increase is extremely tiny). The mass of nucleus isn't equal to the mass of neutrons and protons, the binding energy matters, and the mass of an atom isn't equal to the mass of the nucleus plus the mass of the electrons, the energy states matter.

Not an authoritative reference, but perhaps a sufficient explanation is here - https://physics.stackexchange.com/questions/149744/does-the-...

You ignored the part where the electron decays back to the lower energy state. The ending states are the exact same as the initial states, since the electron decays back to the lower (initial) state by emitting a photon. The photon carries away momentum, but the mass of the two particles is unchanged.

> bounds [spelling? English isn't my main language]

"Bonds" is the spelling. I don't normally correct spelling here, but you did ask.

think about the energy in a candle released via burning vs the energy of that same mass viewed through E=mc^2. that's the ratio

No this is a chemical reaction, not a nuclear reaction.

Yes. Back of envelope, took physics in college many years ago[1] analysis:

E=mc^2, or energy = mass * (speed of light)^2. According to Wikipedia a candle can produce 77 watts of energy "combined." I guess that means 77 joules (1 watt = 1 J/s). So we have:

77 = m * (299792458)^2

Solving for m via Wolfram Alpha:

m = 11 / 12839369696240252

Which is in grams. That's a _very_ small amount, but it's not zero.

edit:

[1] If I'm being honest, I got E=mc^2 from watching the Twilight Zone as a kid, not college physics.

Kind of pedantic but I've never understood why it's E=mc^2 and not E=Δmc^2. In Einsteins original paper he derives the equation with a delta m: a change of mass corresponds to some amount of energy. To me that is different than to say that a whole mass corresponds to a some amount of energy. I've never seen a justification why the delta can be omitted and why the equation still would hold true.

The delta is implied. If you're being rigorous yea you'd include it. But you never see it used rigorously.

Physics is usually pretty rigorous. In the context of science for a general audience, or printing pretty T-shirts, I get why it's omitted. I just find it funny that when it comes to E=mc^2 physics suddenly lack some rigour even in the college physics classes I've taken. It's probably OK to skip it I'm just curious as to why. I don't think I've ever seen the delta mentioned except in Einstein's original paper.

usually the momentum is really low so it's fine, you could read this wikipedia article about it, share questions if that doesn't clear things up

https://en.wikipedia.org/wiki/Energy%E2%80%93momentum_relati...

I'll give it a read-through this weekend, thanks!

I would assume it has to do with relativistic mass, which used to be somewhat commonly used (m used for relativistic mass, m_0 for rest or invariant mass), but which is now disfavoured. For m as relativistic mass, E = mc^2 holds.

There isn't a delta because E=mc^2 isn't just describing a reaction, or a conversion. It is describing the fundamental equivalence between mass and energy. It is true even in situations where ΔE and Δm aren't defined.

"It is describing the fundamental equivalence between mass and energy" I agree that this is widely agreed upon when referring to E=mc^2. It's almost a dogma by this point. But the derivation Einstein used to come up with his equation doesn't actually support said dogma. I'd really like to understand how this "fundamental equivalence" came about and the proof behind it, or if it's just dogma. E=mc^2 is a lot more profound than E=delta m * c^2. IIRC Einstein in the final sentence of his paper tries to generalize his result and jumps on the E=mc^2 train without backing it up.

I think you could say Einstein proposed the fundamental equivalence between mass and energy as a hypothesis and there has been much evidence since. Apparently it was based partly on a proposed symmetry between space and time. Einstein being Einstein probably had some deep reasoning behind it which was not necessarily all put down in that paper.

> According to Wikipedia a candle can produce 77 watts of energy "combined." I guess that means 77 joules (1 watt = 1 J/s).

Watts is energy/time. 77 watts for a candle sounds about right. That means it is producing 77 joules per second. The amount of energy released by burning such a candle is therefore proportional to how long it burns, which is proportional to its mass. The thing you are looking for is the specific energy, listed as 45 MJ/kg upthread. See https://news.ycombinator.com/item?id=26973765 for the rest of the calculation.

Isn't that energy what we call "heat?"

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