# Mass and Energy

Would the mass of burnt firewood be equal to the mass of firewood before burning?

Then where does that heat come from?

According to Einstein's equation, $E=mc^2$ Shouldn't there be some mass going out of the Earth which contradicts the law of mass conservaton?

• When you say "mass of burnt firewood," does the mass of the smoke that went away count? Or do you mean just the mass of the ashes? Nov 3 '14 at 8:11
• mass of smoke also...i mean every byproducts. Nov 3 '14 at 10:44
• en.wikipedia.org/wiki/Conservation_of_mass Nov 3 '14 at 13:07

Would the mass of burnt firewood be equal to the mass of firewood before burning?

You won't get a good answer by simply looking at the "burnt firewood". The combustion is using oxygen from the air, and it is creating carbon dioxide and many volatilized materials that will disperse in the air. But we can imagine combustion happening in a box that is sealed to retain any materials (such as smoke and gases), but which allows energy (perhaps in the form of heat and light) to leave. If done to a very high precision, there would be a tiny difference found in the measured mass. The difference would be equal to the energy liberated during the combustion.

A generous value for the amount of energy liberated due to combustion would be $20MJ/kg$. If we were to combust a $1kg$ log in the presence of sufficient oxygen, then the mass deficit would be on the order of $$m = \frac{E}{c^2}$$ $$m = \frac{2\times 10^7 J}{9.0\times 10^{16}\frac{m^2}{s^2}}$$ $$m = 2.2\times10^{-10}kg$$ This difference in a $1kg$ mass is not measurable.

With such small differences, we can assume that mass is conserved during chemical reactions. When nuclear reactions are considered, the amount of mass converted becomes large enough to be measured and the law of mass conservation has to be modified.

• So to make the earth's mass a constant. The energy coming from external sources should make up the mass to compensate the mass lost. Is it really happening ? Nov 3 '14 at 11:21
• The earth's mass is not constant. By far the largest change is the fact that hundreds of tons of material fall to earth each day (dust and meteorites). The interior of the earth is losing heat to space, and that is not being replaced. Nov 3 '14 at 17:18
• Ok, there's some reconciling to be done among the various answers here. Some say that energy stored in the form of chemical bonds or potential energy is not the kind of energy that becomes/subtracts mass when it's gained/lost. This answer clearly says otherwise. So, for the sake of coherence (and my own curiosity), which is right? Nov 3 '14 at 19:35
• @BowlOfRed If so how can the earth be held in position ? Due to changes in mass, wouldnt there be an imbalance in the centripetal force etc. Nov 4 '14 at 15:44
• If the material arrives with a net momentum, it will modify the earth's momentum. But the net momentum is likely small, also the scale makes the change almost insignificant. Hundreds of tons is about $1\times10^{-19}$ the mass of the earth. Perturbations due to this addition of mass would not be detectable. Nov 4 '14 at 16:06

The law of the conservation of mass was superceded by the more general law of conservation of energy when it was realized that mass and energy were equivalent. Anyway, you are correct. The mass of the combustion products will always be less than the mass of the original materials. The difference being equivalent to the energy produced.

• Would the downvoters care to explain? Perhaps it's not strictly correct to say mass and energy are equivalent? OK, then state that so Dirk can make a more precise statement, but many people think in Planck units so that $c=1$. The answer IMO is succinct, clear and directly answers the OP's question. Nov 3 '14 at 8:54
• The more precise statement is the equivalence E=Mc^2
– user56903
Nov 3 '14 at 9:02
• I really think that voting someone down on your statement in 2014 is waaaay too pedantic and even bespeaks a lack of understanding for the central ideas here. In 1914, maybe your statement might have been questionable. Nowadays, especially from a relativity standpoint, unless you need to specify exactly what the particular "stuff" in question is (i.e. photon, muon, quark, ....) then for these kinds of questions, if it makes the same contribution to $T_{0\,0}$ then its all the same. Nov 3 '14 at 11:20
• @WetSavannaAnimalakaRodVance i think some people downvote (esp with no comments or clarification) to make their own answers stand on top :) (but maybe i'm wrong) Nov 3 '14 at 13:10
• @Lord_Gestalter, well 1st if you downvotyed for these reasons you could as well explain them and even better make the answer better. 2nd i would take the answer "The law of the conservation of mass was superceded by the more general law of conservation of energy" to mean "has been superceded by the energy-mass conservation", which is correct and does not need to refer to relativitic effects Nov 3 '14 at 15:49

I think this solves everything, it is slightly adapted from the wikipedia.

"The closely related concept of matter conservation was found to hold good in chemistry to such high approximation that it failed only for the high energies treated by the later refinements of relativity theory, but otherwise remains useful and sufficiently accurate for most chemical calculations, even in modern practice."

And Einstein had some other perceptions and meanings for this equation.

If we add the energy and mass we will find that it adds to the total mass of the original wood. The total energy of the system is conserved, this will always be true.

If you only look at the weird and burnt wood you will find a discrepancy. This is because some of the mass was lost in smoke. If you measured the mass of the smoke and the wood you will be in almost exact agreement to the original mass, as the energy/mass lost to heat is negligible compared to these values.

Wood does not spontaneously combust. We couldn't have forests if it did. Extra energy is required to ignite wood. So no, the law of conservation of energy/mass is not violated. We need to consider the system as a whole to actually gather everything. But if we do, we find no violation.

• Your 3rd paragraph is not correct. The heat comes from an en.wikipedia.org/wiki/Exothermic_reaction. What you need from extern is the activation energy Nov 4 '14 at 6:39
• I meant that the energy required to start the combustion needs to come from an external force. I'll fix that. Thanks. Nov 4 '14 at 6:40

The mass of the original material equals the mass of the combustion product. You have to take the carbondioxide and the oxygen into account, not just wood and ash.

The energy is stored chemicaly before released. Not every time energy is stored it is in form of additional mass. For the subject of mass loss have a look at weak interaction, Einstein is off topic for burning wood

• Mass of combustion object plus mass of remaining product. All the wood won't burn. Plus you have to consider the oxidation (though this will be small in comparison) Nov 3 '14 at 8:20
• @StevenWalton I did: "You have to take the carbondioxide and the oxygen into account, not just wood and ash." Nov 3 '14 at 13:40