How is the energy content in 1 kg of water and petrol the same?

Question

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.

Answer 1

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).

Answer 2

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.

Answer 3

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.