- #1
Elu314
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I just read this passage, which is really all I've read about relativity so excuse me if this is basic. I don't understand how rest-energy is defined. I thought it was the energy content of the mass only, not including the energy due to motion (hence, rest, right?). But this passage says it is the sum of both. So why is it called rest-energy, then?
(Here, S refers to the system consisting of a contained ideal gas)
"Einstein's equation also says, of course, that if there is a change to the inertial mass of S, then there is a concurrent change to the rest-energy of S. Thus, if we remove one molecule from the gas sample, the rest-energy of the gas sample will diminish by an amount equal to the sum of the molecule's kinetic energy and the mass of the molecule times c2. We can modify our example to make it a bit more telling if we consider the gas sample to be at a temperature of absolute zero, i.e., if we consider the gas sample when all of its molecules are in a state of relative rest. In this case, the rest-energy of S is simply the sum of the masses of the molecules times c2. Let us suppose for simplicity that there are n molecules each of rest-mass m. The rest-energy of S is then simply E = n·mc2. If we remove one of the molecules from the gas, then the rest-energy decreases by an amount ΔE=mc2 and the new rest-energy of S becomes E′ = (n − 1)mc2."
(Here, S refers to the system consisting of a contained ideal gas)
"Einstein's equation also says, of course, that if there is a change to the inertial mass of S, then there is a concurrent change to the rest-energy of S. Thus, if we remove one molecule from the gas sample, the rest-energy of the gas sample will diminish by an amount equal to the sum of the molecule's kinetic energy and the mass of the molecule times c2. We can modify our example to make it a bit more telling if we consider the gas sample to be at a temperature of absolute zero, i.e., if we consider the gas sample when all of its molecules are in a state of relative rest. In this case, the rest-energy of S is simply the sum of the masses of the molecules times c2. Let us suppose for simplicity that there are n molecules each of rest-mass m. The rest-energy of S is then simply E = n·mc2. If we remove one of the molecules from the gas, then the rest-energy decreases by an amount ΔE=mc2 and the new rest-energy of S becomes E′ = (n − 1)mc2."