Mass Energy Conversion

10 Key excerpts on "Mass Energy Conversion"

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  Introduction to Mass in Physics

  • (Author)
  • 2014(Publication Date)
  • Learning Press

    (Publisher)

  Mass–energy equivalence does not imply that mass may be converted to energy, and indeed implies the opposite. Modern theory holds that neither mass nor energy may be destroyed, but only moved from one location to another. Mass and energy are both conserved separately in special relativity, and neither may be created or destroyed. In physics, mass must be differentiated from matter, a more poorly defined idea in the physical sciences. Matter, when seen as certain types of particles, can be created and destroyed (as in particle annihilation or creation), but the precursors and products of such reactions retain both the original mass and energy, each of which remains unchanged (conserve d) throughout the process. Letting the m in E = mc 2 stand for a quantity of matter (rather than mass) may lead to incorrect results, depending on which of several varying definitions of matter are chosen. E = mc 2 has sometimes been used as an explanation for the origin of energy in nuclear processes, but mass–energy equivalence does not explain the origin of such energies. Instead, this relationship merely indicates that the large amounts of energy released in such reactions may exhibit enough mass that the mass-loss may be measured, when the released energy (and its mass) have been removed from the system. Einstein was not the first to propose a mass–energy relationship. However, Einstein was the first scientist to propose the E = mc 2 formula and the first to interpret mass–energy equivalence as a fundamental principle that follows from the relativistic symmetries of space and time. Conservation of mass and energy The concept of mass–energy equivalence connects the concepts of conservation of mass and conservation of energy, which continue to hold separately. The theory of relativity allows particles which have rest mass to be converted to other forms of mass which require motion, such as kinetic energy, heat, or light.

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  Comprehensive Introduction to Special Relativity, A

  • (Author)
  • 2014(Publication Date)
  • Library Press

    (Publisher)

  Mass–energy equivalence does not imply that mass may be ″converted″ to energy, and indeed implies the opposite. Modern theory holds that neither mass nor energy may be destroyed, but only moved from one location to another. In physics, mass must be differentiated from matter, a more poorly defined idea in the physical sciences. Matter, when seen as certain types of particles, can be created and destroyed, but the precursors and products of such reactions retain both the original mass and energy, both of which remain unchanged (conserved) throughout the process. Letting the m in E = mc 2 stand for a quantity of matter may lead to incorrect results, depending on which of several varying definitions of matter are chosen. E = mc 2 has sometimes been used as an explanation for the origin of energy in nuclear processes, but mass–energy equivalence does not explain the origin of such energies. Instead, this relationship merely indicates that the large amounts of energy released in such reactions may exhibit enough mass that the mass-loss may be measured, when the released energy (and its mass) have been removed from the system. Einstein was not the first to propose a mass–energy relationship. However, Einstein was the first scientist to propose the E = mc 2 formula and the first to interpret mass–energy equivalence as a fundamental principle that follows from the relativistic symmetries of space and time. Conservation of mass and energy The concept of mass–energy equivalence connects the concepts of conservation of mass and conservation of energy, which continue to hold separately. The theory of relativity allows particles which have rest mass to be converted to other forms of mass which require motion, such as kinetic energy, heat, or light. However, the mass remains. Kinetic energy or light can also be converted to new kinds of particles which have rest mass, but again the energy remains.

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  Conservation Laws in Physics

  • (Author)
  • 2014(Publication Date)
  • White Word Publications

    (Publisher)

  Mass–energy equivalence does not imply that mass may be converted to energy, and indeed implies the opposite. Modern theory holds that neither mass nor energy may be destroyed, but only moved from one location to another. Mass and energy are both conserved separately in special relativity, and neither may be created or destroyed. In physics, mass must be differentiated from matter, a more poorly defined idea in the physical sciences. Matter, when seen as certain types of particles, can be created and destroyed (as in particle annihilation or creation), but the precursors and products of such reactions retain both the original mass and energy, each of which remains unchanged (conserved) throughout the process. Letting the m in E = mc 2 stand for a quantity of matter (rather than mass) may lead to incorrect results, depending on which of several varying definitions of matter are chosen. E = mc 2 has sometimes been used as an explanation for the origin of energy in nuclear processes, but mass–energy equivalence does not explain the origin of such energies. Instead, this relationship merely indicates that the large amounts of energy released in such reactions may exhibit enough mass that the mass-loss may be measured, when the released energy (and its mass) have been removed from the system. Einstein was not the first to propose a mass–energy relationship. However, Einstein was the first scientist to propose the E = mc 2 formula and the first to interpret mass–energy equivalence as a fundamental principle that follows from the relativistic symmetries of space and time. Conservation of mass and energy The concept of mass–energy equivalence connects the concepts of conservation of mass and conservation of energy, which continue to hold separately. The theory of relativity allows particles which have rest mass to be converted to other forms of mass which require motion, such as kinetic energy, heat, or light.

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  Spacetime and Special Relativity (Concepts and Applications)

  • (Author)
  • 2014(Publication Date)
  • Academic Studio

    (Publisher)

  Mass– energy equivalence does not imply that mass may be ″converted″ to energy, and indeed implies the opposite. Modern theory holds that neither mass nor energy may be destroyed, but only moved from one location to another. In physics, mass must be differentiated from matter, a more poorly defined idea in the physical sciences. Matter, when seen as certain types of particles, can be created and destroyed, but the precursors and products of such reactions retain both the original mass and energy, both of which remain unchanged (conserved) throughout the process. Letting the m in E = mc 2 stand for a quantity of matter may lead to incorrect results, depending on which of several varying definitions of matter are chosen. E = mc 2 has sometimes been used as an explanation for the origin of energy in nuclear processes, but mass–energy equivalence does not explain the origin of such energies. Instead, this relationship merely indicates that the large amounts of energy released in such reactions may exhibit enough mass that the mass-loss may be measured, when the released energy (and its mass) have been removed from the system. Einstein was not the first to propose a mass–energy relationship. However, Einstein was the first scientist to propose the E = mc 2 formula and the first to interpret mass–energy equivalence as a fundamental principle that follows from the relativistic symmetries of space and time. Conservation of mass and energy The concept of mass–energy equivalence connects the concepts of conservation of mass and conservation of energy, which continue to hold separately. The theory of relativity allows particles which have rest mass to be converted to other forms of mass which require motion, such as kinetic energy, heat, or light. However, the mass remains. Kinetic energy or light can also be converted to new kinds of particles which have rest mass, but again the energy remains.

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  Chemistry

  The Molecular Nature of Matter

  • Neil D. Jespersen, Alison Hyslop(Authors)
  • 2021(Publication Date)
  • Wiley

    (Publisher)

  What emerged was a single law now called the law of conservation of mass–energy . Law of Conservation of Mass–Energy The sum of all of the energy in the universe and of all of the mass (expressed as an equivalent in energy) is a constant. NOTE c = 2.99792458 × 10 8 m s −1 , the speed of light. Albert Einstein (1879–1955) won the Nobel Prize for physics in 1921. MPI/Archive Photos/Getty Images 20.2 Nuclear Binding Energy 997 The Einstein Equation Albert Einstein was able to show that when mass converts to energy, the change in energy, ΔE, is related to the change in rest mass, Δm 0 , by the following equation, now called the Einstein equation: ΔE = Δm 0 c 2 (20.2) Again, c is the velocity of light, 3.00 × 10 8 m s −1 . Because the velocity of light is very large, even if an energy change is enormous, the change in mass, Δm 0 , is extremely small. For example, the combustion of methane releases consider- able heat per mole: CH 4 (g) + 2O 2 (g) ⟶ CO 2 (g) + 2H 2 O(l ) ΔH° = −890 kJ The release of 890 kJ of heat energy corresponds to a loss of mass, which by the Einstein equation equals a loss of 9.89 ng. This is about 1 × 10 −7 % of the total mass of one mol of CH 4 and two mol of O 2 . Such a tiny change in mass is not detectable by laboratory balances, so for all practical purposes, mass is conserved. Although the Einstein equation has no direct applications in chemistry involving the rearrangement of electrons in chemical reactions, its importance became clear when atomic fission (i.e., the breaking apart of heavy atoms to form lighter fragments) was first observed in 1939. 20.2 Nuclear Binding Energy As we will discuss further in Section 20.3, an atomic nucleus is held together by extremely powerful forces of attraction that are able to overcome the repulsions between protons. To break a nucleus into its individual nucleons—that is, protons and neutrons—therefore requires an enormous input of energy.

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  Mass and Density Physics

  • (Author)
  • 2014(Publication Date)
  • Academic Studio

    (Publisher)

  Modern theory holds that neither mass nor energy may be destroyed, but only moved from one location to another. Mass and energy ________________________ WORLD TECHNOLOGIES ________________________ are both conserved separately in special relativity, and neither may be created or des-troyed. In physics, mass must be differentiated from matter, a more poorly defined idea in the physical sciences. Matter, when seen as certain types of particles, can be created and destroyed (as in particle annihilation or creation), but the precursors and products of such reactions retain both the original mass and energy, each of which remains unchanged (cons erved) throughout the process. Letting the m in E = mc 2 stand for a quantity of matter (rather than mass) may lead to incorrect results, depending on which of several varying definitions of matter are chosen. E = mc 2 has sometimes been used as an explanation for the origin of energy in nuclear processes, but mass–energy equivalence does not explain the origin of such energies. Instead, this relationship merely indicates that the large amounts of energy released in such reactions may exhibit enough mass that the mass-loss may be measured, when the released energy (and its mass) have been removed from the system. Einstein was not the first to propose a mass–energy relationship. However, Einstein was the first scientist to propose the E = mc 2 formula and the first to interpret mass–energy equivalence as a fundamental principle that follows from the relativistic symmetries of space and time. Conservation of mass and energy The concept of mass–energy equivalence connects the concepts of conservation of mass and conservation of energy, which continue to hold separately. The theory of relativity allows particles which have rest mass to be converted to other forms of mass which require motion, such as kinetic energy, heat, or light.

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  Discover Physics

  • Benjamin Crowell(Author)
  • 2018(Publication Date)
  • Studium Publishing

    (Publisher)

  You’ve encountered two conservation laws so far: conservation of mass and conservation of energy. If conservation of energy is a consequence of symmetry, is there a deeper reason for conservation of mass? Actually they’re not even separate conservation laws. Albert Einstein found, as a consequence of his theory of relativity, that mass and energy are equivalent, and are not separately conserved — one can be converted into the other. Imagine that a magician waves his wand, and changes a bowl of dirt into a bowl of lettuce. You’d be impressed, because you were expecting that both dirt and lettuce would be conserved quantities. Neither one can be made to vanish, or to appear out of thin air. However, there are processes that can change one into the other. A farmer changes dirt into lettuce, and a compost heap changes lettuce into dirt. At the most fundamental level, lettuce and dirt aren’t really different things at all; they’re just collections of the same kinds of atoms—carbon, hydrogen, and so on.

  We won’t examine relativity in detail until chapter 6, but mass-energy equivalence is an inevitable implication of the theory, and it’s the only part of the theory that most people have heard of, via the famous equation E = mc2 . This equation tells us how much energy is equivalent to how much mass: the conversion factor is the square of the speed of light, c. Since c a big number, you get a really really big number when you multiply it by itself to get c2 . This means that even a small amount of mass is equivalent to a very large amount of energy.

  Gravity bending light 

  example 10 

  Gravity is a universal attraction between things that have mass, and since the energy in a beam of light is equivalent to a some very small amount of mass, we expect that light will be affected by gravity, although the effect should be very small. The first experimental confirmation of relativity came in 1919 when stars next to the sun during a solar eclipse were observed to have shifted a little from their ordinary position. (If there was no eclipse, the glare of the sun would prevent the stars from being observed.) Starlight had been deflected by the sun’s gravity. Figure r

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  Nuclear Energy

  An Introduction to the Concepts, Systems, and Applications of Nuclear Processes

  • Raymond L. Murray(Author)
  • 2013(Publication Date)
  • Pergamon

    (Publisher)

  2 O) molecules are essentially at rest. As we add thermal energy to increase the temperature to 0°C or 32°F, molecular movement increases to the point where the ice melts to become liquid water, which can flow rather freely. To cause a change from the solid state to the liquid state, a definite amount of energy (the heat of fusion) is required. In the case of water, this latent heat is 334 J/g. In the temperature range in which water is liquid, thermal agitation of the molecules permits some evaporation from the surface. At the boiling point, 100°C or 212°F at atmospheric pressure, the liquid turns into the gaseous form as steam. Again, energy is required to cause the change of state, with a heat of vaporization of 2258 J/g. Further heating, using special high temperature equipment, causes dissociation of water into atoms of hydrogen (H) and oxygen (O). By electrical means electrons can be removed from hydrogen and oxygen atoms, leaving a mixture of charged ions and electrons. Through nuclear bombardment, the oxygen nucleus can be broken into smaller nuclei, and in the limit of temperatures in the billions of degrees, the material can be decomposed into an assembly of electrons, protons, and neutrons.

  Fig. 1.1 Effect of added energy.

  1.4 The Equivalence of Matter and Energy

  The connection between energy and matter is provided by Einstein’s theory of special relativity. It predicts that the mass of any object increases with its speed. Letting the mass when the object is at rest be m 0 , the “rest mass,” and letting m be the mass when it is at speed v , and noting that the speed of light in a vacuum is c = 3 × 108 m/sec, then

  For motion at low speed (e.g., 500 m/sec), the mass is almost identical to the rest mass, since v/c and its square are very small. Although the theory has the status of natural law, its rigor is not required except for particle motion at high speed, i.e., when v is at least several percent of c . The relation shows that a material object can have a speed no higher than c .

  The kinetic energy imparted to a particle by the application of force according to Einstein is

  (For low speeds, v c , this is approximately , the classical relation.)

  The implication of Einstein’s formula is that any object has an energy E 0 = m 0 c 2 when at rest (its “rest energy”), and a total energy E = mc 2 , the difference being E k the kinetic energy. Let us compute the rest energy for an electron of mass 9.1 × 10−31 kg.

  or

  For one unit of atomic mass, 1.66 × 10−27 kg, which is close to the mass of a hydrogen atom, the corresponding energy is 931 MeV.

  Thus we see that matter and energy are equivalent, with the factor c 2 relating the amounts of each. This suggests that matter can be converted into energy and that energy can be converted into matter. Although Einstein’s relationship is completely general, it is especially important in calculating the release of energy by nuclear means. We find that the energy yield from a kilogram of nuclear fuel is more than a million times that from chemical fuel . To prove this startling statement, we first find the result of complete transformation of a kilogram of matter into energy, viz., (1 kg) (3.0 × 108 m/sec)2 = 9 × 1016 J. The nuclear fission process, as one method of converting mass into energy, is relatively inefficient, since the “burning” of 1 kg of uranium involves the conversion of only 0.87 g of matter into energy. This corresponds to about 7.8 × 1013 J/kg of the uranium consumed. The enormous magnitude of this energy release can be appreciated only by comparison with the energy of combustion of a familiar fuel such as gasoline, 5 × 107 J/kg. The ratio of these numbers, 1.5 × 106

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  Engineering Science

  • (Author)
  • 2014(Publication Date)
  • White Word Publications

    (Publisher)

  That is, energy is conserved because the laws of physics do not distinguish between different instants of time. Energy in various contexts The concept of energy and its transformations is useful in explaining and predicting most natural phenomena. The direction of transformations in energy (what kind of energy is transformed to what other kind) is often described by entropy (equal energy spread among all available degrees of freedom) considerations, as in practice all energy transformations are permitted on a small scale, but certain larger transformations are not permitted because it is statistically unlikely that energy or matter will randomly move into more concentrated forms or smaller spaces. The concept of energy is widespread in all sciences. • In the context of chemistry, energy is an attribute of a substance as a consequence of its atomic, molecular or aggregate structure. Since a chemical transformation is accompanied by a change in one or more of these kinds of structure, it is invariably accompanied by an increase or decrease of energy of the substances involved. Some energy is transferred between the surroundings and the reactants of the reaction in the form of heat or light; thus the products of a reaction may have more or less energy than the reactants. A reaction is said to be exergonic if the final state is lower on the energy scale than the initial state; in the case of endergonic reactions the situation is the reverse. Chemical reactions are invariably not possible unless the reactants surmount an energy barrier known as the activation energy. The speed of a chemical reaction (at given temperature T ) is related to the activation energy E , by the Boltzmann's population factor e − E / kT – that is the probability of molecule to have energy greater than or equal to E at the given temperature T . This exponential dependence of a reaction rate on temperature is known as the Arrhenius equation.

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  Facts and Mysteries in Elementary Particle Physics

  • Martinus J G Veltman(Author)
  • 2003(Publication Date)
  • WSPC

    (Publisher)

  2 . Indeed it is in particle physics that some very remarkable aspects of the theory of relativity are most clearly demonstrated, not just the energy-mass equation. Another example is the lifetime of unstable particles, in particular the muon. The lifetime of a moving muon appears to be longer in the laboratory, in accordance with the time dilatation predicted by the theory of relativity.

  Thus the mass-energy must be included when considering the relation between energy and momentum. The figure shows the relation between energy and momentum for two different particles, respectively with masses m and M . We have taken M three times as large as m . For zero momentum the energy is simply mc 2 for the particle of mass m and Mc 2 for the particle of mass M .

  This figure is really the all-important thing in this Chapter. Understanding it well is quite essential, since we shall draw a number of conclusions from it. In itself it is simple: the curve shows the relation between momentum and energy for a single particle. Given the momentum of a particle of mass m one can find the corresponding energy by using the curve for mass m . If the momentum is zero then the energy is mc 2 .

  In drawing the figure one must make a choice of units. We have drawn a figure corresponding to a choice of units such that the speed of light is one. For very large positive or negative momenta energy becomes very nearly equal to the magnitude of the momentum. In the figure that we have drawn the diagonal lines represent the relation energy = ± momentum. The curves approach these diagonal lines for large momenta. The diagonal lines define the light cone; the reason for that name shall become obvious soon.

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