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If I were to burn a pile of wood weighing a hundred kilograms and I would have a big sack hanging over the burning pile. In this sack I would catch all the smoke that came from the burning pile, if all the wood turned to ashes and I'd put this in the sack with smoke. Would the sack weigh a hundred kilograms or would it weigh less?

Is it the case that all the mass of the burning pile is converted in to ash and smoke and therefore weigh the same as the unburnt pile of wood? Or is it the case that because of $E=mc^2$ the burning pile emits energy and the mass of the pile is converted into the heat that a burning pile of wood gives and therefore takes away most of the mass?

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    $\begingroup$ If you just capture the smoke you loose some weight. A significant fraction of initial mass goes into carbon dioxide and other oxidation products. Water vapor too. If you capture all the gases you end up with more mass due to added oxygen. $\endgroup$ – nasu Feb 15 at 17:18
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    $\begingroup$ Note: Mass is not the same as weight. @nasu said, "if you capture all the gasses you end up with more mass..." But if you put all of that captured gas into a thin envelope, it would seem to weigh almost nothing because it would be buoyed upward by the weight of the surrounding atmosphere. $\endgroup$ – Solomon Slow Feb 15 at 18:33
  • $\begingroup$ I'm unclear about whether you're most interested in relativistic mass loss (in which case you need to much more aggressive "sealed environment" to counteract loss or gain of gasses) or whether you're most interested in the chemical reaction of burning wood? Which of those did you have in mind? $\endgroup$ – Brondahl Feb 16 at 7:48
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    $\begingroup$ Would changing the environment of the test to a completely sealed room, with standard air, at standard pressure at the tester's location (i.e. a room with a door that has closed and sealed to be molecularly impervious) and is large enough to have enough oxygen to burn the wood? (taking any consternation of a "big sack" out of the question) $\endgroup$ – CGCampbell Feb 16 at 16:05
  • $\begingroup$ Specifically, calculating on the back of that thin envelope, the 207 kg of product 180 kg of glucose produces would weigh between 21 kg and -165 kg once temperature and pressure is equalised, depending on how much of the water vapour condenses (water vapour is less dense than air) Pure carbon would weigh pretty much the same as it had before combustion though. $\endgroup$ – timuzhti Feb 16 at 16:25
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You would have much more mass than 100 kg after the wood was burned. As it turns out, wood is made of cellulose and lignin. Both are cross-linked glucose polymers, so a good approximation of what you would get is given by the chemical reaction of burning glucose:

$$\rm C_6H_{12}O_6 + 6O_2 \to 6CO_2 + 6 H_2O$$

This means that 6 oxygen molecules combine with one glucose molecule when it is burned. The molar mass of the glucose molecule is 180 and the molar mass of the six oxygen molecules is 192. This means that when you burn 180 kg of glucose, 192 kg of oxygen take part in the chemical reaction, producing an equal mass of carbon dioxide and water vapor. At these ratios, when you burn the 100 kg of wood, you would collect 207 kg of carbon dioxide and water vapor.

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    $\begingroup$ I'm not sure what kind of sack you're imagining, but every sack I've ever seen wouldn't catch Carbon Dioxide! You might just about be able to capture the Water, but there's no way it's capturing a gas. $\endgroup$ – Brondahl Feb 16 at 7:45
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    $\begingroup$ Sure, there is a way to capture a gas in a sack. That's how hot air baloons work. $\endgroup$ – fraxinus Feb 16 at 8:42
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    $\begingroup$ @Brondahl imagine a plastic rubbish sack instead of hessian $\endgroup$ – Chris H Feb 16 at 16:14
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    $\begingroup$ So wait...are we counting the mass of the gas/vapor after the reaction but not before? And that’s why we have more mass afterward? $\endgroup$ – Gilbert Feb 17 at 0:14
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    $\begingroup$ @Brondahl You're being rather pedantic - I read sack to mean Magical container that traps all products without loss, like a weightless rod or a frictionless surface. Much of the early work on chemical composition was done by weighing reactants and products before and after combustion. The "sack" was a glass gas jar. $\endgroup$ – Oscar Bravo Feb 17 at 15:00
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Depends on what your sack manages to capture

This was a thing that finally helped kill the phlogiston theory of fire (that burning something means releasing the phlogiston enclosed in it): most things got lighter by burning them, but some got heavier! This could only be explained by having some materials contain negative-mass phlogiston, which pretty much everyone agreed was silly.

Reaction products

So what does everything burn to?

Metals

When you burn a metal, you get a metal oxide. Most metal oxides are not volatile, and they're the white ash you're left with when you fully burn wood. Metal oxides are heavier than the metals or metal ions you started with, because you've added oxygen.

These ashes can actually be a good source of metal oxides for making things such as lye.

Carbon

When you (fully) burn hydrocarbons, you get carbon oxides: Carbon dioxide and/or carbon monoxide. Both of these are gases, though you can capture them with an airtight bag. If your fire isn't enclosed, your wood smoke will also contain various volatile hydrocarbons (due to pyrolysis) that still have various other elements attached to the carbon.

If your fire doesn't quite fully burn, you'll also be left with "black ash", which is actually just charcoal, or mostly pure carbon.

Again, if everything is fully burned, the resulting products will be heavier than the starting materials, but can you capture them?

Volatiles

Wood also contains hydrogen, oxygen, nitrogen and (in smaller quantities) various other (non-metal) elements. When burned this turns into water (vapor), free nitrogen and various other gases. The water is fairly easy to capture. The other gases will be harder. All of these are heavier or the same weight as their starting material.

Results

If you can capture everything, you can certainly measure that the contents of the bag are now heavier than the wood you burned. This is only logical, as the bag now contains the wood plus all the oxygen from the air that you used to burn the wood.

If you cannot capture all the gases, the answer will depend on what it is you burnt. For most materials (such as wood), the contents of your bag will be lighter than the starting material. For metals it will be the opposite. The answer for any material in particular will depend on the ratio of capturable and non-capturable materials, along with how much oxygen the capturable materials will bind to them by weight.

Fun fact: for wood, this is called the "ash content". For wood, this is typically 0.1% to 0.2%.

As $E=mc^2$, the energy involved in chemical reactions is far too small to be measured outside of a laboratory setting. You will lose a tiny bit of mass-energy due to energy being released, but it will be less than a speck of dust that you didn't quite manage to get onto the scale, or a fingerprint you left on the bag. (I mean that last bit literally. A fingerprint is about 50 μg, which has a mass-energy of about 4.5 GJ. That's about a quarter ton of dry wood worth of energy)

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  • $\begingroup$ TL;DR: If you burned the wood in a fireproof, airtight box that also contained enough O2 for the wood to completely burn, the mass of the box's contents would be the same before and after burning; however the weight would be heavier because some of the combustion products would have the formerly gaseous oxygen bound into heavier-than-air solids (unless you were weighing the entire system in a vacuum). $\endgroup$ – Doktor J Feb 17 at 18:02
  • $\begingroup$ How would that increase the weight? $\endgroup$ – AI0867 Feb 18 at 9:13
  • $\begingroup$ @DoktorJ, hmm, how would that work? I may have forgotten about all this stuff, but wouldn't the volume of the box determine the lifting force it experiences in the atmosphere? And the volume of such a fireproof, all-tight box would probably be unchanged by the burning inside. (Hmm, what if were a balloon that could expand and contract to do changes in pressure inside?) $\endgroup$ – ilkkachu Feb 18 at 13:37
  • $\begingroup$ Sorry, I was thinking of an elastic container (like a balloon, but of course fire in a balloon is a bad idea 😆) where gaseous O2 would expand the volume of the container and thus have buoyancy in a non-vacuum environment. Assuming the container was rigid (which most fireproof containers would be) it would occupy a fixed volume and thus its weight wouldn't change either. $\endgroup$ – Doktor J Feb 18 at 17:32
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Relativistic loss of mass is unmeasurable here, but in principle, you’d lose some tiny fraction of the mass by heat transfer to the surroundings.

Whether the smoke would weigh more or less than the wood depends on your definition. Oxygen from the air is combining with carbon in the wood to form carbon dioxide. If this counts as smoke, then the smoke weighs more than the wood because it includes the weight of the oxygen. If smoke is just the particulate stuff you can see, then it weighs much less.

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    $\begingroup$ FWIW, using David's example, you'd have to burn over 5,772 tons of glucose to liberate 1 gram's worth of energy. Google Calculator says (1g)*c^2*(180.156 g/mol)/(2805 kJ/mol) equals 5,772,411.34 kg $\endgroup$ – PM 2Ring Feb 16 at 10:34
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Other answers have focused on the combustion products mass, and the mass of oxygen. I want to cover the other part not in those answers. I'm also keeping it very simple, so.bear in mind this isn't how a Chemistry or Physics graduate would describe it. I'm ignoring truly tiny effects that only get noticed at degree level and higher, and being a bit simplistic. I think from the question, simpler is what is wanted. Please bear that in mind when you read.....

E = mc2 is an equation showing matter-energy equivalence. In the situation you describe, you're trying to use it as an equation concerning matter converted to energy, and therefore presumably how some mass could be "lost" from your "bag" of combustion products.

In general, and in simple terms, chemical processes such as reactions, and combustion (burning), and physical changes of state (boiling/evaporation), do not involve matter-energy conversion. What is happening in simple terms is, that chemical bonds are being reconfigured due to the presence of other chemicals, or physical conditions. The chemical bonds usually involve the outer electron/s of atoms, and their bonds to other atoms.

If a different layout (configuration/bond) is energetically favoured, and achievable, then the existing configuration will change to it. The resulting bonds may need less energy, in which case the reaction gives off heat (such as combustion processes, or more generally exothermic processes - ones that give off heat).

But that heat isn't obtained by converting matter to energy. It was energy already, stored in the form of higher energy chemical bonds (a type of "potential energy"), that became changed to lower energy chemical bonds, and the "spare" energy was released as heat (a type of "kinetic energy").

If it helps, also imagine a tall stack of bricks. When it topples, the books were stationary but now move quickly (kinetic energy). But that speed didn't come out of nowhere, or by converting matter to energy. It was originally energy at the start - the bricks were higher up in the Earths gravitational field, and this was also a form of potential energy. What has happened to the bricks is, the potential energy of their higher position is now a lower.energy position so they have lost potential energy, and the potential energy they lost, was converted to kinetic energy - speed. Likewise with your combustion - the burning processes involve chemical bonds moving from higher states to lower states of potential energy. The potential energy they lost, was converted to kinetic energy in the form of heat, this time.

(We can follow this in the books example a bit further - when the books land on the ground, their kinetic energy is dissipated as friction and vibration (of the ground and air), which both ultimately end up as very low grade heat. Ultimately the room becomes an undetectably tiiiiiiiiny bit warmer! But still its energy changing form, not matter changing to energy)

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    $\begingroup$ What's the connection between the bricks and the books? $\endgroup$ – PM 2Ring Feb 16 at 2:46
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    $\begingroup$ Your answer is factually not correct. Mass-Energy equivalence does also apply to chemical reactions. Although "appearently" no mass is destroyed in creating energy, a water molecule WILL weigh a bit less than it's constitutes (2 hydrogen atoms and one oxygen atom). The weight difference will only a little bit (as you say), but not even mentioning it explicitly, especially for the given reason (matter - energy conversion as a special type of reaction) is wrong. $\endgroup$ – Quantumwhisp Feb 16 at 9:50
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    $\begingroup$ OP asked about matter energy equivalence. The right answer would have been "it's a very tiny effect, but it's there". Saying "I ignore very tiny effects. ... there is no mass to energy conversion" is at least misleading. What's more is that you give general explanations on why there isn't an effect, and they are plain wrong. Regarding mass energy equivalence, there is no conceptual difference between a planet orbiting a star, two atoms bonding, an electron bonding to a proton, or serveral protons bonding to an atoms core. Your answer implies that this is the case here. $\endgroup$ – Quantumwhisp Feb 16 at 21:27
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    $\begingroup$ I feel like this answer misses the very point: that mass and energy are simply equivalent. You can't have energy released without mass being reduced, even if it is "truly tiny". "Tiny" is a very subjective amount. The amount of mass lost in a nuclear explosion is also very "tiny" and qualitatively no different from the mass lost in a chemical reaction..... $\endgroup$ – Joel Keene Feb 17 at 1:01
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    $\begingroup$ I second the above objections. This answer seems to state exactly the opposite of what is true: the rearranging of the chemical bonds to store less potential energy is precisely the reason that the molecule has less mass after the rearrangement. The energy stored in the chemical bonds actually made the molecule heavier, and discussing this would be the entire point of bringing up this topic. The "truly tiny effects" you're ignoring are literally the entire conversation to be had about mass-energy equivalence in this context. $\endgroup$ – jawheele Feb 17 at 22:55
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Greetings from Mikhail Lomonosov from 18th century.

In chemistry (and burning is pretty much a chemistry) mass is considered a conserved property.

(It is a conserved property outside of the chemistry as well, but chemists have the luxury not to deal with the heat energy used or produced, because it has a negligible mass in chemical reactions.)

If you have a closed (and heat resistant) container with the wood and all the air (or oxygen) needed to burn it down, the mass of the container will not change by burning the wood.

What most people skip in these considerations is that gases have mass. A cubic meter of air in normal conditions is like 1.2kg - not much, compared to a 1 cubic meter of piled wood (like 600kg), but still important.

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  • $\begingroup$ (And as other answers show, it takes a large mass of oxygen to burn that much wood, and Earth's air is only about 1/4 oxygen, so your sack would need to be huge to burn that much wood.) $\endgroup$ – Peter Cordes Feb 16 at 14:34
  • $\begingroup$ @Peter 100kg dry wood use ~100kg oxygen or ~400 cubic meters of air. A mid-range single family house contains that much air. $\endgroup$ – fraxinus Feb 16 at 22:10
  • $\begingroup$ Yeah, a 6-house-sized bag / balloon is pretty huge compared to a 1m^3 wood pile (somewhat larger than a standard plastic garbage bag.) Mentioning the volumes is IMO useful for doing this experiment in your head, thanks for running the numbers. (Although of course in practice, the fire would go out as O2 partial pressure dropped. If you trapped the heat, oxidation would continue more and more slowly as oxygen became rarer, and would look like smouldering embers. So you'd need an even bigger bag or higher O2 concentration and/or pressure for it to fully burn normally.) $\endgroup$ – Peter Cordes Feb 16 at 22:44
  • $\begingroup$ 1 cubic meter of wood is like 500-700kg depending on wood type and ordering. As for the full burning - not sure about wood, but modern internal combustion engines burn the gasoline down to like 0.5% using the exact amount of air (the catalyst makes this like 0.05%). Diesels are even better because they use excess amount of air. $\endgroup$ – fraxinus Feb 17 at 7:15
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From The Evolution of Physics:

... all energy resists change of motion; all energy behaves like matter; a piece of iron weighs more when red-hot than when cool ...

In answer to your main question, energy from the chemical bonds is converted to energy in the form of heat, so there won't be a change in the mass of the products of combustion and the result unless you allow the gases to cool.

The process is more complicated though but to create a simple example let's take David White's answer. 100kg of wood at room temperature will combine with 107kg of oxygen at room temperature and create 207kg of hot gases. In an isolated system, there is no net change of mass since the energy of the chemical bonds is converted to heat energy.

If you allow those gases to cool back to room temperature, they will have less mass because that heat energy resists change of motion like matter. Looking at wikipedia, red oak has an energy content of about 14.9 megajoules per kilogram. 100kg would then be 1.49E9 joules. Also according to wikipedia the conversion rate is about 8.99E16 joules per kilogram. Dividing that out I get 1.657E-8 kilograms or 1.647E-5 grams in the form of heat.

So cooling that 207 kg of hot gases back to room temperature would make it lose about the same mass as 1/2000th a grain of rice. That energy (mass) isn't 'lost' however, for example some will be emitted in the form of black-body radiation

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