# Is $E=mc^2$ reserved to nuclear physics?

I was wondering, while putting a log in my fireplace, how much energy the piece of wood would give. The most famous formula poped into my head: $E=m \cdot c ^ 2$!

Is this formula applicable to a burning object or is in only applicable to a nuclear reaction?

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The identity $E=mc^2$ is a universal law of physics. It says that the mass – that can be interpreted as the conserved mass; inertial mass determining the resistance to acceleration; or gravitational mass determining the strength of the gravitational field – is equivalent to the energy, a conserved quantity that was originally defined as the sum of the kinetic and potential energy and that was extended to many other forms of energy later. The identity $E=mc^2$ also says that each kilogram in mass $m$ carries a latent energy $9\times 10^{16}$ joules that may be extracted from the mass under some circumstances (annihilation; collapse into a black hole that later evaporates, and so on).

We usually talk about $E=mc^2$ in nuclear physics where the kinetic energy is often comparable (or even much greater) than the latent energy associated with the rest mass (for the LHC, the kinetic energy is 4,000 times greater than the latent energy stored in the rest mass). However, the energy-mass conversion is potentially important in all other situations.

In annihilation, one converts 100% of $E=mc^2$ to pure energy – thermal energy, mostly usable as work. In thermonuclear fusion, one gets about 1% of $E=mc^2$. In nuclear fission, one gets about 0.1% of $E=mc^2$. Chemical reactions only convert one millionth of a percent of the mass to pure energy; they're one million times less "efficient" than nuclear reactions. For example, a typical reaction involving two atoms or two molecules produces (or consumes) 1 electronvolt of energy. That's equal to $1.602\times 10^{-19}$ joules which is about $1.8\times 10^{-36}$ kilograms. It looks like a little but if the number of atomic or molecular pairs is $10^{26}$, comparable to Avogadro's constant, one already gets $10^{-10}$ kilograms which may be in principle measured.

If you could measure the mass of the coal plus ashes plus gases with the precision of 8 significant figures – which is on the edge of the current technological abilities – you could see that the burned coal (plus the gases, ashes) is lighter than the original coal (plus oxygen) by about one millionth of a percent. This tiny portion of the original mass was converted to heat, radiation, or related forms of energy. In a similar way, if you heat an object, it becomes a bit heavier; the energy added to the object also increases its mass according to $E=mc^2$.

Roughly speaking, one could say that the energy-mass conversion becomes large and important if we deal with massive particles that move by speeds comparable to the speed of light. But the general law applies to all phenomena in Nature although the mass equivalent to the converted energy is usually small.

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+1: This prevents me from writing an answer. I love it :-) – Waffle's Crazy Peanut Dec 13 '12 at 11:26
Wow… thanks. Amazing answer! – SteeveDroz Dec 13 '12 at 16:48