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I was reading this link.

Just above the paragraph titled "OTHER CONSERVATION LAWS", it says that

"This conversion of mass to energy happens well below the speed of light, in a very small way, when a stick of dynamite explodes. A portion of that stick becomes energy, and the fact that this portion is equal to just 6 parts out of 100 billion indicates the vast proportions of energy available from converted mass."

I think this is incorrect. The chemical energy in the dynamite is converted to heat, light and sound. There is no nuclear reaction taking place to convert mass into energy. Am I wrong?

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    $\begingroup$ Nuclear reactions are not needed to "convert" mass into energy. Any form of energy release will do the same, just not in an easily measurable quantity. In terms of physics the mass/energy conversion is sloppy speak, anyway. Most of the "mass" in your body can be directly attributed to kinetic energy of relativistic quarks that are bound in your nuclei, the rest is potential binding energy plus a small Higgs contribution which one can think of as a self-binding energy. $\endgroup$ – CuriousOne Jan 6 '15 at 3:07
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    $\begingroup$ Please see this post regarding how to write good question titles. $\endgroup$ – DanielSank Jan 6 '15 at 3:17
  • $\begingroup$ Thanks everyone who has answered. I question arose from something that I learnt 25 years ago. Having learnt something new I'll be happily sleeping today :) $\endgroup$ – user2225138 Jan 6 '15 at 13:35
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As a matter of fact, chemical reactions can reduce mass just like nuclear reactions. I find it hard to accept, but it's true.

When the molecules in the dynamite explode, bonds between atoms are broken and reformed in different configurations. The result of this is that the net electrical potential energy in the resulting molecules is less than the electrical potential energy of the original stick. Now here's the cool part – that means it has less mass. Like, literally, less mass. Like, if you let the heat, light, and sound dissipate, and ultracarefully collect and weigh all the reaction products (impossible in practice, of course), it would weigh a tiny bit less than the original stick.

I find it helpful to think of a simpler example. Take two hydrogen atoms, and an oxygen atom. Allow them to run into each other. Their electron orbitals merge and hybridize. As their electrons settle into their new, shared, lower-energy state, they release photons. These photons carry away energy, and therefore mass, from the atoms. The resulting $\mathrm{H_2O}$ molecule literally weighs less than the two hydrogen and one oxygen beforehand.

Weird!

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The chemical energy in the dynamite is converted to heat, light and sound.

That chemical energy is bound energy. The heat, light, and sound that are created when that chemical energy is unleashed are unbound energy. Another name for bound energy in physics is mass. You've certainly read that nuclear reactions convert mass into energy. An alternate view: Mass isn't converted into energy because mass already is energy. Mass is just another form of energy, just as heat, light, and sound are forms of energy.

Developments in quantum mechanics made physicists revisit the distinct notions of conservation of mass and conservation of energy. Mass most definitely is not conserved when a proton and antiproton annihilate one another, nor is energy in the older notions of what constitutes energy. The new notion (actually not so new anymore) is that conservation of energy includes mass as a form of energy.

I mentioned annihilation above. Mass also isn't conserved when four protons combine via a series of reactions to form helium (but energy, or mass+energy is conserved). What about chemical reactions such as a stick of dynamite exploding? The same applies. The only difference between that stick of dynamite versus an annihilation event is the amount of energy released. Unbound energy is released by both reactions, so bound energy ("mass") must necessarily decrease.

Mass appears to be conserved in chemical reactions because dividing the amounts of energy released in a chemical reaction by the speed of light squared results in a immeasurably small amount of mass. The difference is one of "in practice" versus "in principle". In practice, the changes in mass in chemical systems is too small to measure. In principle, the mass does change.

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The chemical energy makes up a small portion of the mass of the stick of dynamite. $E=mc^2$ does not apply for just nuclear reactions! Nuclear reactions are the archetypical way of "verifying" the equation though in a popular physics sense. (Only about <0.7% of the mass can be turned into energy in a nuclear process. I know 0.7% is the value for fusion, fission should be less.) (Actually, Einstein proposed massing radium salts before and after some nuclear decay in 1905, long before fission.) There are lots of other ways to see $E=mc^2$ in action. Here are a few (including your example):

1) Chemical bonds. What we usually think of chemical energy is contained in the chemical bonds between molecules, etc. This is energy, and by $E=mc^2$ can be realized as a part of the mass of the chemical system. So when the bonds are broken and formed in a dynamite explosion, some of that mass is lost as radiant energy (infra-red radiation, i.e. heat).

2) Gluons. This is really interesting, at least to me. I'm sure you've heard of the Higgs boson and the Higgs mechanism. In popular literature it is said to give all things mass. But the interesting thing is that if you look at the mass of a proton (~938MeV) and masses of the constituent 2 up-quarks and the one down-quark (each ~4MeV), we see a HUGE disparity! Where is the extra mass? Here $E=mc^2$ and quantum mechanics come together to tell us that in the proton there is actually a sea of virtual quark-antiquark pairs and gluons. (This is called the dynamical model of the nucleon). The energy contained in all the gluons and virtual quarks makes up 99% of the mass of the proton.

3) Gravitational radiation. This requires some understanding of general relativity. In a binary system, the quadrupole moment is nonzero. Therefore, the system emits gravitational waves. Those waves have energy, so the mass of the system should decrease. This corresponds to an increase in the rotation frequency of the system. This effect has been measured to a very high degree of accuracy (no numbers off the top of my head).

4) Accretion tori. We can use accretion tori around black holes to convert mass into energy by exploiting the gravitational binding energy. This effect gives about 6% for a nonrotating black hole and 42% for a rotating one.

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During the nuclear fusion of four Hydrogen atoms to a single Helium atom .7% of the mass is converted into energy. Burning a ton of coal ~ 910 KG releases 22 gigajoules (22 E9) of energy. From E=mC^2, the mass converted into energy is 2.44 x 10^-7 Kg. Dividing by 910 Kg the per cent of mass converted to energy is 2.7 x 10^-10 or 0.000000027%. This so small that chemists use 0 for the value.

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    $\begingroup$ Welcome to SE. Unfortunately, this is an old question. If you write an answer, the question is transferred to the main page. Please only do so, if you consider your contribution to be significant. Furthermore, please use Mathjax to format formulas.Finally, I don't think you are answering the question. You talk about fusion, while the question is about chemical reactions. $\endgroup$ – Semoi Mar 17 at 22:34

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