In response to the Eating Food on an Airplane question (Does an airplane weigh less after the passengers have eaten their meals? - The Straight Dope), the loss of matter due to digestion is brought up, and the E=mc^2 equation is brought up and Cecil has us believe that it applies to all releases of energy. This is not the case. The simplest equation of combustion is:
CH4 + 2x O2 => C02 + 2x H2O + energy
This equation has no loss in mass (there are still 1 carbon, 4 hydrogen and 4 oxygen atoms on each side of the equation), yet, energy is released.
The energy is stored in the bonds of the molecules, and breaking the bonds and recreating them releases and uses energy. See the following near the end:
(The site won’t allow me to edit a message more than 5 minutes after posting…)
Cecil would have us believe that matter is converted directly to energy during digestion via the E=mc^2 equation. This is not the case. That equation only applies to nuclear reactions.
The URL I gave describes the amount of energy in the chemical bonds and the energy levels in the above formula.
Since E=mc2 is such a basic fact about space and time, it shouldn’t surprise you that it is carried out physically in almost everything we do. The frustrating thing is that the enormous size of c-squared makes us completely unaware of it! Even when the amount of energy (E) released in a chemical or nuclear reaction is large, the staggering size of c-squared (c2) means that the change in the mass of the material in the reaction (m) will be incredibly small. As an example, the energy released in chemical reactions when an average person shovels snow for one hour amounts to a mass loss (by E=mc2) of only 10 billionths of a gram! Link.
tshort, you’re right that the energy comes from the molecular bonds. However, Cecil is correct that E=mc[sup]2[/sup] still applies. The molecular bonds themselves contribute to the mass, however slightly. In the context of relativity, one generally speaks of inertial mass, which is the energy content of the system in the frame of reference where it has zero total momentum.
This might seem like a counterintuitive definition of mass, since a system’s total mass (as defined in this way) is not just the sum of the masses of the system’s constituents. But the advantage of this way of defining mass is that mass is always conserved.
I should add that when we’re talking about atoms and molecules the total mass of the system will very nearly be equal to the sum of the mass of its constituents. So it’s understandable that a chemist would treat mass in that way. But it’s not at all true at the level of protons, which have something like a hundred times more mass than their constituent quarks would have individually.
This shouldn’t really be surprising. After all, most of the energy in nuclear reactions (fission or fusion) comes from a process that preserves the number of protons, neutrons, and electrons (some energy comes from free neutron decay, but this is relatively small). This is fairly analogous to chemical reactions where each element must have the same count before and after. So even in the case of nuclear reactions, the mass difference is largely from the bond energy.
Exactly. The only difference is that of degree, in that the mass difference (i.e. “mass defect”) in nuclear reactions is measurable, whereas the mass difference in chemical reactions is not. However, this is not because mass-energy equivalence does not apply in chemical reactions, but simply because the amount of energy involved in chemical reactions is orders of magnitude less than that of nuclear reactions.
