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We know petrol is a fuel and water is not. But how come 1 kg of water and 1 kg of petrol have the same energy content? The total energy is given by $E=mc^2$, it says nothing about the chemical composition of the material.

PM 2Ring
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Shafeek
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    $E = mc^{2}$ (for a particle at rest) refers to the equivalent energy that you get if you were to ``destroy'' the mass (put simply). Burning of fuel is a chemical reaction where mass is conserved. The energy released is the difference of the binding energies of the products and the reactants, a completely different process. – r_phys Aug 25 '23 at 04:23
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    Actually, it is always at least two compounds that participate to release the energy. Petrol + oxygen works as source of energy, without oxygen or other oxidizer, petrol would be as useful as a fuel as water usually is (does not react with oxygen). Water can behave as fuel too if we make it react with proper chemical, e.g. fluorine. It is not easy to say where the energy actually comes from, the petrol, or the oxygen, or the water, or the fluorine. – Ján Lalinský Aug 25 '23 at 04:31
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    @PM2Ring right, not always, but when we say fuel, usually at least two chemicals reacting are implied, so it is not clear how much of the released energy comes from each component, they are both instrumental. – Ján Lalinský Aug 25 '23 at 05:52
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    @r_phys $E=mc^2$ also applies to chemical reactions, but the mass equivalence of the chemical energy change is extremely tiny. See https://physics.stackexchange.com/q/16351/123208 & https://physics.stackexchange.com/q/11449/123208 – PM 2Ring Aug 25 '23 at 06:07
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    This is essentially a fancy version of "which weighs more, 1lb of feathers or 1 lb of lead" – By Symmetry Aug 25 '23 at 08:09

3 Answers3

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The mass-energy content of a kilogram of anything is 89.9 x 10^9 megajoules. This means the mass-energy content of 1 kilogram of matter is equal to the chemical potential energy of 21.9 x 10^9 kilograms of TNT.

So, saying that the total energy content of a kilogram of TNT is the same as the energy content of a kilogram of water is just another way of saying (a truly huge number) + (a tiny number) is just about equal to (a truly huge number).

niels nielsen
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    Good answer, but I'm not happy with "just about equal". The total energies are exactly equal. – PM 2Ring Aug 25 '23 at 06:12
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    I am even less happy than @PM2Ring with "just about equal". A kilogram of anything already includes the tiny chemical binding energy (as well as the less tiny nuclear binding energy). Therefore, if 1 kg of matter is converted into photons (just to have a common exchange rate), the total energy of those photons is always the same, regardless if the matter is water, TNT, uranium, or neutron matter. – GiorgioP-DoomsdayClockIsAt-90 Aug 25 '23 at 07:15
  • @GiorgioP-DoomsdayClockIsAt-90 then why don't we use garbage to power nuclear reactors instead of uranium? – Juan Perez Aug 25 '23 at 10:14
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    @Juan Most atoms in typical garbage cannot undergo fission in a standard nuclear reactor. And even atoms like uranium, plutonium, and thorium only liberate a small proportion of their rest mass when they fission. Even an ideal deuterium cycle engine converts around 260 kg of fuel to 259 kg of exhaust and 1 kg * c² energy. – PM 2Ring Aug 25 '23 at 11:18
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    To get the full 89.8755... petajoules from 1 kg, you need to do an annihilation reaction, eg 0.5 kg of water + 0.5 kg of antimatter water. Building such a reactor, ensuing that the reaction proceeds to completion, and capturing the energy in a useful form are left as an exercise for the reader. ;) – PM 2Ring Aug 25 '23 at 11:19
  • @JuanPerez Theoretical energy limit which shows what maximum amount of energy you can extract from a given mass, does not say anything about how easy/viable some specific energy conversion scheme is. – Agnius Vasiliauskas Aug 25 '23 at 11:27
  • @JuanPerez For the same reason we do not have nuclear fusion reactors yet. Between the possibility of using some energy source and its practical and controlled use, there is a huge technological gap. – GiorgioP-DoomsdayClockIsAt-90 Aug 25 '23 at 14:19
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1kg of petrol and 1kg of water indeed have the same amount of energy. Howeever, the amount of thermal energy that can be extracted from them under certain reactions, is different for both depending on the reaction, because of their different chemical structures.

You can extract energy from petrol by burning it because of petrol's specific chemical structure due to which the chemical energy gets converted into thermal energy. But you can't extract much thermal energy from water like this because water is not much reactive here.

Hypothetically, if you annihilate both 1kg of water and 1kg of petrol with 1kg of anti-matter water and 1kg of anti-matter petrol, they would both get converted into photons and release the same amount of energy.

Ryder Rude
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The total energy has several components. The far biggest is the mass-energy due to the matter itself. But there is also nuclear and chemical binding energy.

In the case of TNT, one can release some of the chemical energy by allowing it to explode, which leaves you with slightly more tightly bound molecules and a fair bit of mechanical energy. Water is already at its lowest chemical energy state, so it cannot be burned or explode.

Considering the atoms themselves, they could be fused to iron in theory, again releasing energy and leaving a more tightly bound mass. This is a significantly larger amount than the chemical energy but not readily released.

When you weigh matter and find that it weighs exactly 1 kg, it might hence be that some of that mass is actually stored and releasable energy. Normally this is microscopic (the fusion energy is at most 0.7% of the mass energy). The $E=mc^2$ formula talks about the mass as measured, not the mass you would get by taking one kilogram of matter leaving out the various energy components.

Anders Sandberg
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