In physics, in particular special and general relativity, mass–energy equivalence is the concept that the mass of a body is a measure of its energy content. In this concept, mass is a property of all energy; energy is a property of all mass; and the two properties are connected by a constant.
This means (for example) that the total internal energy E of a body at rest is equal to the product of its rest mass m and a suitable conversion factor to transform from units of mass to units of energy. Albert Einstein proposed mass–energy equivalence in 1905 in one of his Annus Mirabilis papers entitled "Does the inertia of a body depend upon its energy-content?" The equivalence is described by the famous equation:
E = mc2
where E is energy, m is mass, and c is the speed of light. The formula is dimensionally consistent and does not depend on any specific system of measurement units. The equation E = mc2 indicates that energy always exhibits relativistic mass in whatever form the energy takes.
Mass–energy equivalence does not imply that mass may be "converted" to energy, but it allows for matter to be converted to energy. Through all such conversions, however mass remains conserved (i.e., the quantity of mass remains constant), since mass is a property of matter and also any type of energy. Energy is also conserved.
In physics, mass must be differentiated from matter. Matter, when seen as certain types of particles, can be created and destroyed (as in particle annihilation or creation), but a closed system of precursors and products of such reactions, as a whole, retain both the original mass and energy thoughout the reaction.
When the system is not closed, and energy is removed from a system (for example in nuclear fission or nuclear fusion), some mass is always removed along with the energy, according to their equivalence where one always accompanies the other. This energy thus is associated with the missing mass, and this mass will be added to any other system which absorbs the removed energy. In this situation E = mc2 can be used to calculate how much mass goes along with the removed energy. It also tells how much mass will be added to any system which later absorbs this energy. This was the original use of the equation when derived by Einstein.
Any time energy is generated, the process can be evaluated from an E = mc2 perspective. For instance, the "Gadget"-style bomb used in the Trinity test and the bombing of Nagasaki had an explosive yield equivalent to 21 kt of TNT. About 1 kg of the approximately 6.15 kg of plutonium in each of these bombs fissioned into lighter elements totaling almost exactly one gram less, after cooling. The electromagnetic radiation and kinetic energy (thermal and blast energy) released in this explosion carried the missing one gram of mass. This occurs because nuclear binding energy is released whenever elements with more than 62 nucleons fission.
So the energy equivalent of one gram (1/1000 of a kilogram) of mass is equivalent to:
This means (for example) that the total internal energy E of a body at rest is equal to the product of its rest mass m and a suitable conversion factor to transform from units of mass to units of energy. Albert Einstein proposed mass–energy equivalence in 1905 in one of his Annus Mirabilis papers entitled "Does the inertia of a body depend upon its energy-content?" The equivalence is described by the famous equation:
E = mc2
where E is energy, m is mass, and c is the speed of light. The formula is dimensionally consistent and does not depend on any specific system of measurement units. The equation E = mc2 indicates that energy always exhibits relativistic mass in whatever form the energy takes.
Mass–energy equivalence does not imply that mass may be "converted" to energy, but it allows for matter to be converted to energy. Through all such conversions, however mass remains conserved (i.e., the quantity of mass remains constant), since mass is a property of matter and also any type of energy. Energy is also conserved.
In physics, mass must be differentiated from matter. Matter, when seen as certain types of particles, can be created and destroyed (as in particle annihilation or creation), but a closed system of precursors and products of such reactions, as a whole, retain both the original mass and energy thoughout the reaction.
When the system is not closed, and energy is removed from a system (for example in nuclear fission or nuclear fusion), some mass is always removed along with the energy, according to their equivalence where one always accompanies the other. This energy thus is associated with the missing mass, and this mass will be added to any other system which absorbs the removed energy. In this situation E = mc2 can be used to calculate how much mass goes along with the removed energy. It also tells how much mass will be added to any system which later absorbs this energy. This was the original use of the equation when derived by Einstein.
Any time energy is generated, the process can be evaluated from an E = mc2 perspective. For instance, the "Gadget"-style bomb used in the Trinity test and the bombing of Nagasaki had an explosive yield equivalent to 21 kt of TNT. About 1 kg of the approximately 6.15 kg of plutonium in each of these bombs fissioned into lighter elements totaling almost exactly one gram less, after cooling. The electromagnetic radiation and kinetic energy (thermal and blast energy) released in this explosion carried the missing one gram of mass. This occurs because nuclear binding energy is released whenever elements with more than 62 nucleons fission.
So the energy equivalent of one gram (1/1000 of a kilogram) of mass is equivalent to:
- 89.9 terajoules
- 25.0 million kilowatt-hours (≈25 GW·h)
- 21.5 billion kilocalories (≈21 Tcal) [21]
- 85.2 billion BTUs[21]