Mass-energy equivalence:
Einstein's equation, E = mc2 represents one of those amazing qualities about nature that one would never imagine without a whole lot of work on some background stuff. This equation is saying that energy is mass or mass is energy. Or you could say energy has mass. It is a matter of semantics. The constant c is the speed of light, c=3x108 m/s. Where this equation comes from is a long story. If you have had a course in electricity and magnetism, and you know about the Poynting vector, you could look into a way to derive it.
CONSERVATION OF ENERGY
We need to modify this law now. Mass and energy are not each conserved independently; they are both forms of one entity which we call mass-energy. It is mass-energy that is conserved. We can use either mass units or energy units.
Example: consider a simple chemical reaction C + O2 --> CO2 + E. We ordinarily do not bother with E/c2 as a mass on the right, because it is so small, but the truth is that CO2 has a mass that is slightly less than the sum of the masses of C and O2. If you ask a chemistry person about this (s)he might think that you are crazy (unless you go into it in depth and make it clear that the amount of mass difference is too small to be detected). The total mass on the left equals that on the right exactly if we include E/c2. An alternative approach is to multiply each mass by c2, then m1c2 + m2c2 = m3c2 + E, where m1, m2, and m3 are the masses of the three substances. Mass-energy is conserved.
Example: consider two deuterium nuclei fusing to form a helium nucleus. D +
D --> He + E (D consists of a proton and a neutron; He consists of two of
each.) Each D has mass 2.01410 and He has mass 4.00260 atomic mass units (1 amu = 1.660566 x 10-27 kg). This time the E is
significant. Calculate E.
(Ans. 3.8 x 10-12 J. Not much, but to get a GJ of energy, we would
only need a couple of milligrams of D.)
People often cite nuclear energy as THE example of converting mass into energy. I hope that what they mean by this is that the change of "regular" mass is significant enough to give us a practical means of calculating the energy. I hope they do not think that there is anything else to it.
Example: A stick of wood is burned, and it releases 1000 joules of heat energy. How much mass was "converted into energy?" (Ans. 1.1 x 10-14 kg)
If you have studied the theory of relativity and a year of calculus, you may wish to look into the relationship between momentum and kinetic energy in relativity. Or you may go to the energy page or the main physics page, where you can find other stuff on special and general relativity.
My main pages:
mechanics
fluids, heat, electricity and magnetism
vibrations and waves
quantum
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