Conservation of mass

The law of conservation of mass, also known as the principle of mass/matter conservation, states that the mass of an isolated system (closed to all matter and energy) will remain constant over time. This principle is equivalent to the conservation of energy, in the sense when energy or mass is enclosed in a system and none is allowed in or out, its quantity cannot otherwise change (hence, its quantity is "conserved"). The mass of an isolated system cannot be changed as a result of processes acting inside the system. The law implies that mass cannot be created or destroyed, although it may be rearranged in space and changed into different types of particles; and that for any chemical process in a closed system, the mass of the reactants must equal the mass of the products.

The concepts of both matter and mass conservation is widely used in many fields such as chemistry, mechanics, and fluid dynamics. Historically, the principle of mass conservation, discovered by Antoine Lavoisier in the late 18th century, was of crucial importance in changing alchemy into the modern natural science of chemistry.

In special relativity, the mass-energy equivalence theorem states that mass conservation is equivalent to energy conservation, which is the first law of thermodynamics. In special relativity, mass cannot be converted to energy, since energy always retains its equivalent amount of mass within any isolated system. However, certain types of matter may be converted to energy, so long as the mass of the system is unchanged in the process. When this energy is removed from systems (they are opened), they lose mass.

In general relativity, mass (and energy) conservation in expanding volumes of space becomes a complicated concept, subject to different definitions, and neither mass nor energy is as strictly and simply conserved as is the case in special relativity and in Minkowski space. For a discussion, see mass in general relativity.

Historical development and importance

An important idea in ancient Greek philosophy is that "Nothing comes from nothing", so that what exists now has always existed, since no new matter can come into existence where there was none before. An explicit statement of this, along with the further principle that nothing can pass away into nothing, is found in Empedocles (ca. 490–430 BCE): "For it is impossible for anything to come to be from what is not, and it cannot be brought about or heard of that what is should be utterly destroyed".^[1] A further principle of conservation was stated by Epicurus (341–270 BCE) who, describing the nature of the universe, wrote that "the totality of things was always such as it is now, and always will be".^[2] Jain philosophy, which is a non-creationist philosophy and based on teachings of Mahavira (6th century BCE),^[3] states that universe and its constituents like matter cannot be destroyed or created. The Jain text Tattvarthasutra (2nd century) states that a substance is permanent, but its modes are characterised by creation and destruction.^[4] A principle of the conservation of matter was also stated by Nasīr al-Dīn al-Tūsī (1201–1274) during the 13th century. He wrote that "A body of matter cannot disappear completely. It only changes its form, condition, composition, color and other properties and turns into a different complex or elementary matter".^[5]

The principle of conservation of mass was first outlined clearly by Antoine Lavoisier (1743–1794). It has been claimed that Mikhail Lomonosov (1711–1765) had expressed similar ideas during 1748—and proven them by experiments—but this has been challenged.^[6] Others who anticipated the work of Lavoisier include Joseph Black (1728–1799), Henry Cavendish (1731–1810), and Jean Rey (1583–1645).^[7]

Historically, the conservation of mass and weight was obscure for millennia because of the buoyant effect of the Earth's atmosphere on the weight of gases. For example, since a piece of wood weighs less after burning, this seemed to suggest that some of its mass disappears, or is transformed or lost. These effects were not understood until careful experiments in which chemical reactions such as rusting were performed in sealed glass ampules, whereby it was found that the chemical reaction did not change the weight of the sealed container. The vacuum pump also helped to allow the effective weighing of gases using scales.

Once understood, the conservation of mass was of great importance in changing alchemy to modern chemistry.

When chemists realized that substances never disappeared from measurement with the scales (once buoyancy effects were held constant, or had otherwise been accounted for), they could for the first time embark on quantitative studies of the transformations of substances. This in turn produced ideas of chemical elements, as well as the idea that all chemical processes and transformations (including both fire and metabolism) are simple reactions between invariant amounts or weights of these elements.

Generalization

Main article: Conservation of mass in special relativity

Main article: Conservation of energy

In special relativity, the conservation of mass does not apply if the system is open and energy escapes. However, it does continue to apply to totally closed (isolated) systems. If energy cannot escape a system, its mass cannot decrease. While any type of energy is retained in a system in relativity, this energy exhibits mass.

The mass associated with chemical amounts of energy is too small to measure

The change in mass of certain kinds of open systems where atoms or massive particles are not allowed to escape, but other types of energy (such as light or heat) were allowed to enter or escape, went unnoticed during the 19th century, because the mass-change associated with addition or loss of the fractional amounts of heat and light associated with chemical reactions, was very small. (In theory, mass would not change at all for experiments conducted in closed systems).

In relativity, the theoretical association of all energy with mass was made by Albert Einstein in 1905. However, Max Planck first pointed out that the change in mass of systems for which the chemical amounts of energy were allowed in or out of systems, as predicted by Einstein's theory, was so small that it could not be measured with available instruments, even if it was sought as a test of relativity. Einstein in turn speculated that the energies associated with radioactive phenomena were so large as compared with the mass of systems producing them, that they might be measured as loss of fractional mass in systems, once the energy had been removed. This later indeed proved to be possible, although it was eventually to be the first artificial nuclear transmutation reactions in the 1930s, using cyclotrons, that proved a successful test of Einstein's theory regarding mass-loss with energy-loss.

Mass conservation remains correct if energy is not lost

The conservation of relativistic mass implies the viewpoint of a single observer (or the view from a single inertial frame) since changing inertial frames may result in a change of the total energy (relativistic energy) for systems, and this quantity determines the relativistic mass.

The principle that the mass of a system of particles must be equal to the sum of their rest masses, even though true in classical physics, may be false in special relativity. The reason that rest masses cannot be simply added is that this does not take into account other forms of energy, such as kinetic and potential energy, and massless particles such as photons, all of which may (or may not) affect the mass of systems.

For moving massive particles in a system, examining the rest masses of the various particles also amounts to introducing many different inertial observation frames (which is prohibited if total system system energy and momentum are to be conserved), and also when in the rest frame of one particle, this procedure ignores the momenta of other particles, which affect the system mass if the other particles are in motion in this frame.

For the special type of mass called invariant mass, changing the inertial frame of observation for a whole closed system has no effect on the measure of invariant mass of the system, which remains both conserved and invariant even for different observers who view the entire system. Invariant mass is a system combination of energy and momentum, which is invariant for any observer, because in any inertial frame, the energies and momenta of the various particles always add to the same quantity. The invariant mass is the relativistic mass of the system when viewed in the center of momentum frame. It is the minimum mass which a system may exhibit in all possible inertial frames.

The conservation of both relativistic and invariant mass applies even to systems of particles created by pair production, where energy for new particles may come from kinetic energy of other particles, or from a photon as part of a system. Again, neither the relativistic nor the invariant mass of totally-closed (that is, isolated) systems changes when new particles are created. However, different inertial observers will disagree on the value of this conserved mass, if it is the relativistic mass. However, all observers agree on the value of the conserved mass, if the mass being measured is the invariant mass.

The mass-energy equivalence formula requires isolated systems, since if energy is allowed to escape a system, both relativistic mass and invariant mass will escape also.

The formula implies that bound systems have an invariant mass (rest mass for the system) less than the sum of their parts, if the binding energy has been allowed to escape the system after the system has been bound. This may happen by converting system potential energy into some other kind of active energy, such as kinetic energy or photons, which easily escape a bound system. The difference in system masses, called a mass defect, is a measure of the binding energy in bound systems – in other words, the energy needed to break the system apart. The greater the mass defect, the larger the binding energy. The binding energy (which itself has mass) must be released (as light or heat) when the parts combine to form the bound system, and this is the reason the mass of the bound system decreases when the energy leaves the system.^[8] The total invariant mass is actually conserved, when the mass of the binding energy that has escaped, is taken into account.

Exceptions

The principle of matter conservation may be considered as an approximate physical law that is true only in the classical sense, without consideration of special relativity and quantum mechanics. Another difficulty with the idea of conservation of "matter" is that "matter" is not a well-defined word scientifically, and when particles that are considered to be "matter" (such as electrons and positrons) are annihilated to make photons (which are often not considered matter) then conservation of matter does not take place, even in isolated systems.

Mass is also not generally conserved in open systems (even if only open to heat and work), when various forms of energy are allowed into, or out of, the system (see for example, binding energy). However, the law of mass conservation for isolated systems (totally closed to all mass and energy), as viewed over time from any single inertial frame, continues to be true in modern physics. The reason for this is that relativistic equations show that even "massless" particles such as photons still add mass and energy to isolated systems, allowing mass (though not matter) to be conserved in all processes where energy does not escape the system. In relativity, different observers may disagree as to the particular value of the mass of a given system, but each observer will agree that this value does not change over time as long as the system is isolated (totally closed to everything).

In general relativity, the total invariant mass of photons in an expanding volume of space will decrease, due to the red shift of such and expansion (see mass in general relativity). The conservation of both mass and energy then depends on corrections made to energy in the theory, due to the changing gravitational potential energy of such systems.

See also

• Antoine Lavoisier
• Albert Einstein
• Conservation law
• Continuity equation in fluid dynamics
• Groundwater energy balance
• Mass balance
• Law of identity
• Second law of thermodynamics

References

1. ^ Fr. 12; see pp.291–2 of Kirk, G. S.; J. E. Raven, Malcolm Schofield (1983). The Presocratic Philosophers (2 ed.). Cambridge: Cambridge University Press. ISBN 9-780-521-27455-5. 
2. ^ Long, A. A.; D. N. Sedley (1987). "Epicureanism: The principals of conservation". The Hellenistic Philosophers. Vol 1: Translations of the principal sources with philosophical commentary. Cambridge: Cambridge University Press. pp. 25–26. ISBN 0-521-27556-3. 
3. ^ Mahavira is dated 599 BCE - 527 BCE. See. Dundas, Paul; John Hinnels ed. (2002). The Jains. London: Routledge. ISBN 0-415-26606-8.  p. 24
4. ^ Devendra (Muni.), T. G. Kalghatgi, T. S. Devadoss (1983) A source-book in Jaina philosophy Udaipur:Sri Tarak Guru Jain Gran. p.57. Also see Tattvarthasutra verses 5.29 and 5.37
5. ^ Farid Alakbarov (Summer 2001). A 13th-Century Darwin? Tusi's Views on Evolution, Azerbaijan International 9 (2).
6. ^ *Pomper, Philip (October 1962). "Lomonosov and the Discovery of the Law of the Conservation of Matter in Chemical Transformations". Ambix 10 (3): 119–127. 
   Lomonosov, Mikhail Vasil’evich (1970). Mikhail Vasil’evich Lomonosov on the Corpuscular Theory. Henry M. Leicester (trans.). Cambridge, Mass.: Harvard University Press. Introduction, p. 25. 
7. ^ An Historical Note on the Conservation of Mass, Robert D. Whitaker, Journal of Chemical Education, 52, 10, 658-659, Oct 75
8. ^ Kenneth R. Lang, Astrophysical Formulae, Springer (1999), ISBN 3540296921