Changes

{{Use dmy datesInfobox physical quantity|datebgcolour=February 2015}{default}{{chembox| Verifiedfields name = changedKinetic energy| Watchedfields image= changed| verifiedrevid = 477003420| Name = Calcium carbonate| ImageFileL1 = calcium carbonate.png| ImageFileR1 = Calcium-carbonate-xtal-3D-SF.png| ImageFile2 = Calcium carbonate[[File:Wooden roller coaster txgi.jpg| IUPACName = Calcium carbonate220px]]| OtherNames caption= The cars of a [[calciteroller coaster]]; reach their maximum kinetic energy when at the bottom of the path. When they start rising, the kinetic energy begins to be converted to gravitational [[aragonitepotential energy]]; . The sum of kinetic and potential energy in the system remains constant, ignoring losses to [[chalkfriction]]; .|unit = [[Lime joule]] (materialJ)]]; [[Limestone]]; [[marble]]; [[oyster]]; [[pearl]]; |Section1symbols ={{Chembox Identifiers| UNII_Ref = {{fdacite|correct|FDA}}| UNII = H0G9379FGK| ChEMBL_Ref = {{ebicite|changed|EBI}}| ChEMBL = 1200539| KEGG_Ref = {{keggcite|correct|kegg}}| KEGG = D00932| InChI = 1/CH2O3.CaKE, ''E''<sub>k</c2-1(3)4;/h(H2,2,3sub>,4);/q;+2/p-2or T| ChEBI_Ref derivations = {{ebicite|correct|EBI}}| ChEBI ''E''_k = 3311½''[[mass| SMILES = [Ca+2m]].[O-]C([O-])=O| InChIKey = VTYYLEPIZMXCLO-NUQVWONBASvelocity| SMILES1 = C(=O)([O-v])[O-].[Ca+''^2] <br>| StdInChI_Ref = {{stdinchicite|correct|chemspider}}| StdInChI ''E''_k = 1S/CH2O3.Ca/c2-1(3)4;/h(H2,2,3,4);''E''<sub>t</q;sub>+2''E''<sub>r</p-2| StdInChIKey_Ref = {{stdinchicite|correct|chemspider}}| StdInChIKey = VTYYLEPIZMXCLO-UHFFFAOYSA-L| CASNo = 471-34-1| CASNo_Ref = {{cascite|correct|CAS}}| ChemSpiderID_Ref = {{chemspidercite|correct|chemspider}}| ChemSpiderID = 9708| EINECS = 207-439-9| PubChem = 10112| RTECS = FF9335000sub>

|Section2={{Chembox PropertiesClassical mechanics}}| Formula = CaCO₃| MolarMass = 100.0869 g/mol| Appearance = Fine white powder; chalky taste| Odor = odorless| Density = 2.711 g/cm³ (In [[calcitephysics]])<br />2.83 g/cm³ (, the '''kinetic energy''' of an object is the [[aragoniteenergy]]that it possesses due to its [[motion (physics)| Solubility = 0motion]].013 g/L (25 °C)<ref>{{cite book|title=SI Chemical Data Book Textbook of Engineering Physics (4th ed.Part I) |publisherfirst1=John Wiley & Sons Australia, LtdMahesh C. |author1last1=Aylward, Gordon Jain|author2year=Findlay, Tristan 2009|isbn=978-081-470203-816383862-73|yearpage=2008}}</ref><ref>{{cite book9|titleurl=Calcium Carbonatehttps: From the Cretaceous Period Into the 21st Century|publisher=Springer Science & Business Media|year=2001|url//books.google.com/books?id=wKeDYbTuiPAC}}, [https://books.google.com/books?id=pbkKGa19k5QCwKeDYbTuiPAC&pg=RA1-PR2|authorPA9#v=snippet&q=Rohleder, J. |author2kinetic&f=Krokerfalse Chapter 1, Ep. |isbn=3-7643-6425-4}}9]</ref>It is defined as the [[work (physics)| SolubilityProduct = 3work]] needed to accelerate a body of a given mass from rest to its stated [[velocity]]. Having gained this energy during its [[acceleration]], the body maintains this kinetic energy unless its speed changes. The same amount of work is done by the body when decelerating from its current speed to a state of rest.3 In [[classical mechanics]], the kinetic energy of a non-rotating object of [[mass]] ''m'' traveling at a [[speed]] ''v'' is {{esmallmath|-9f=\frac{1}{2}mv^2}}. In [[Special relativity|relativistic mechanics]], this is a good approximation only when ''v'' is much less than the [[speed of light]]. The standard unit of kinetic energy is the [[joule]]. ==History and etymology==The adjective ''kinetic'' has its roots in the [[Ancient Greek|Greek]] word κίνησις ''[[-kinesis|kinesis]]'', meaning "motion". The dichotomy between kinetic energy and [[potential energy]] can be traced back to [[Aristotle]]'s concepts of [[actuality and potentiality]].<ref>{{cite book|last title=BenjaminLogic in Reality |firstedition=Mark M.illustrated |yearfirst1=2002Joseph |titlelast1=Water Chemistry Brenner |publisher=McGraw-HillSpringer Science & Business Media |year=2008 |isbn =0978-1-074020-2383908375-94 |page=93 |url=https://books.google.com/books?id=67anQgAACAAJJnj5E6C9UwsC}}[https://books.google.com/books?id=Jnj5E6C9UwsC&pg=PA93 Extract of page 93]</ref>| Solvent = dilute acids| SolubleOther = soluble| MeltingPt = 1,339 °C (The principle in [[classical mechanics]] that ''E ∝ mv²'' was first developed by [[Gottfried Leibniz]] and [[Johann Bernoulli]],442 °F; 1who described kinetic energy as the ''living force'',612 K) (calcite) <br> 825 °C (1517 °F; 1''[[vis viva]]''. [[Willem 's Gravesande]] of the Netherlands provided experimental evidence of this relationship. By dropping weights from different heights into a block of clay,098 K) (aragonite) [[Willem 's Gravesande]] determined that their penetration depth was proportional to the square of their impact speed. [[Émilie du Châtelet]] recognized the implications of the experiment and published an explanation.<ref>{{cite webCite book|urlauthor=https://www.cdc.gov/niosh/docs/81-123/pdfs/0090Judith P.pdfZinsser |title=Occupational safety and health guideline for calcium carbonateEmilie du Chatelet: Daring Genius of the Enlightenment|publisher=US Dept. of Health and Human ServicesPenguin|year= 2007|accessdateisbn=31 March 20110-14-311268-6}}</ref>| BoilingPt = decomposesThe terms ''kinetic energy'' and ''work'' in their present scientific meanings date back to the mid-19th century. Early understandings of these ideas can be attributed to [[Gaspard-Gustave Coriolis]], who in 1829 published the paper titled ''Du Calcul de l'Effet des Machines'' outlining the mathematics of kinetic energy. [[William Thomson, 1st Baron Kelvin| RefractIndex = 1William Thomson]], later Lord Kelvin, is given the credit for coining the term "kinetic energy" c. 1849–51.59<ref>{{cite book| pKa author= 9Crosbie Smith, M.0Norton Wise| pKb title=Energy and Empire: A Biographical Study of Lord Kelvin| MagSus publisher= -38.2·10⁻⁶ cm³/mol}}Cambridge University Press|Section3pages={{Chembox Structure866| CrystalStruct isbn= Trigonal| SpaceGroup = <span style="text0-521-26173-decoration: overline">3</span>2/m}}|Section5={{Chembox Thermochemistry| DeltaHf = −1207&nbsp;kJ·mol<sup>−1</supref><ref name=b1>{{cite book| author = Zumdahl, Steven S.John Theodore Merz|title =Chemical Principles 6th Ed.A History of European Thought in the Nineteenth Century| publisher = Houghton Mifflin CompanyBlackwood| year = 20091912|page= 139| isbn = 0-6188446-946902579-X|page=A215}}</ref>| Entropy = 93&nbsp;J·mol⁻¹·K⁻¹<ref name=b1 /> }}|Section6={{Chembox Pharmacology| ATCCode_prefix = A02| ATCCode_suffix Overview= AC01| ATC_Supplemental = {{ATC|A12|AA04}}}}[[Energy]] occurs in many forms, including [[chemical energy]], [[thermal energy]], [[electromagnetic radiation]], [[gravitational energy]], [[electric energy]], [[elastic energy]], [[nuclear binding energy|Section7=nuclear energy]], and [[rest energy]]. These can be categorized in two main classes: [[potential energy]] and kinetic energy. Kinetic energy is the movement energy of an object. Kinetic energy can be transferred between objects and transformed into other kinds of energy.<ref>{{Chembox HazardsCite web| ExternalSDS url= [httphttps://www.inchemkhanacademy.org/documentsscience/icscphysics/icscwork-and-energy/eics1193.htm ICSC 1193]| MainHazards =| NFPAwork-and-energy-H = 0| NFPAtutorial/a/what-F = 0| NFPAis-R = 0| NFPAkinetic-S =energy| RPhrases title=Khan Academy| SPhrases website=Khan Academy| LD50 access-date= 6450 mg/kg (oral, rat)| PEL = TWA 15 mg/m³ (total) TWA 5 mg/m³ (resp)<ref>{{PGCH|00902016-10-09}}</ref>}}Kinetic energy may be best understood by examples that demonstrate how it is transformed to and from other forms of energy. For example, a [[cyclist]] uses [[food energy|Section8={{Chembox Relatedchemical energy provided by food]] to accelerate a [[bicycle]] to a chosen speed. On a level surface, this speed can be maintained without further work, except to overcome [[drag (physics)|air resistance]] and [[friction]]. The chemical energy has been converted into kinetic energy, the energy of motion, but the process is not completely efficient and produces heat within the cyclist. The kinetic energy in the moving cyclist and the bicycle can be converted to other forms. For example, the cyclist could encounter a hill just high enough to coast up, so that the bicycle comes to a complete halt at the top. The kinetic energy has now largely been converted to gravitational potential energy that can be released by freewheeling down the other side of the hill. Since the bicycle lost some of its energy to friction, it never regains all of its speed without additional pedaling. The energy is not destroyed; it has only been converted to another form by friction. Alternatively, the cyclist could connect a [[Bottle dynamo| OtherAnions = dynamo]] to one of the wheels and generate some electrical energy on the descent. The bicycle would be traveling slower at the bottom of the hill than without the generator because some of the energy has been diverted into electrical energy. Another possibility would be for the cyclist to apply the brakes, in which case the kinetic energy would be dissipated through friction as [[Calcium bicarbonateheat]]. Like any physical quantity that is a function of velocity, the kinetic energy of an object depends on the relationship between the object and the observer's [[frame of reference]]. Thus, the kinetic energy of an object is not [[Galilean invariance| OtherCations = invariant]]. [[Magnesium carbonateSpacecraft]]<br />use chemical energy to launch and gain considerable kinetic energy to reach [[Strontium carbonateorbital speed|orbital velocity]]<br />. In an entirely circular orbit, this kinetic energy remains constant because there is almost no friction in near-earth space. However, it becomes apparent at re-entry when some of the kinetic energy is converted to heat. If the orbit is [[Barium carbonateelliptic orbit|elliptical]]or [[hyperbolic trajectory| OtherCompounds = hyperbolic]], then throughout the orbit kinetic and [[Calcium sulfatepotential energy]]are exchanged; kinetic energy is greatest and potential energy lowest at closest approach to the earth or other massive body, while potential energy is greatest and kinetic energy the lowest at maximum distance. Without loss or gain, however, the sum of the kinetic and potential energy remains constant. }}Kinetic energy can be passed from one object to another. In the game of [[billiards]], the player imposes kinetic energy on the cue ball by striking it with the cue stick. If the cue ball collides with another ball, it slows down dramatically, and the ball it hit accelerates its speed as the kinetic energy is passed on to it. [[Collisions]] in billiards are effectively [[elastic collision]]s, in which kinetic energy is preserved. In [[inelastic collision]]s, kinetic energy is dissipated in various forms of energy, such as heat, sound, binding energy (breaking bound structures).}}[[File:CalciteFlywheel]]s have been developed as a method of [[flywheel energy storage|energy storage]]. This illustrates that kinetic energy is also stored in rotational motion. Several mathematical descriptions of kinetic energy exist that describe it in the appropriate physical situation.pngFor objects and processes in common human experience, the formula ½mv² given by [[Newtonian mechanics|thumbNewtonian (classical) mechanics]] is suitable. However, if the speed of the object is comparable to the speed of light, [[special relativity|right|Crystal structure of calciterelativistic effects]] become significant and the relativistic formula is used. If the object is on the atomic or [[sub-atomic scale]], [[quantum mechanical]]effects are significant, and a quantum mechanical model must be employed.

==Chemistry=Kinetic energy of rigid bodies===Calcium carbonate shares the typical properties of other carbonates. Notably,* it reacts with In [[acidclassical mechanics]]s, releasing [[carbon dioxide]]::CaCO₃the kinetic energy of a ''point object'' (s) + 2H⁺(aq) → Ca²⁺(aq) + CO₂(g) + H₂O (lan object so small that its mass can be assumed to exist at one point)* it releases carbon dioxide upon heating, called or a non-rotating [[thermal decompositionrigid body]] reaction, or depends on the [[calcinationmass]] (to above 840&nbsp;°C in of the case of CaCO₃), to form body as well as its [[calcium oxidespeed]], commonly called . The kinetic energy is equal to 1/2 the [[quicklimeMultiplication|product]], with reaction [[enthalpy]] 178 kJ/moleof the mass and the square of the speed. In formula form::CaCO₃ (s) → CaO (s) + CO₂ (g)

Calcium carbonate will react with water that is saturated with carbon dioxide to form the soluble [[calcium bicarbonate]].:CaCO<submath>3E_\text{k} =\tfrac{1}{2} mv^2 </submath> + COwhere <submath>2m</submath> + His the mass and <submath>2v</submath>O → Cais the speed (HCO₃or the velocity)₂of the body. In [[SI]] units, mass is measured in [[kilogram]]s, speed in [[metres per second]], and the resulting kinetic energy is in [[joule]]s.

This reaction is important in For example, one would calculate the [[erosion]] kinetic energy of [[carbonate rock]]an 80&nbsp;kg mass (about 180&nbsp;lbs) traveling at 18&nbsp;metres per second (about 40&nbsp;mph, or 65&nbsp;km/h) as:<math>E_\text{k} = \frac{1}{2} \cdot 80 \,\text{kg} \cdot \left(18 \, forming [[cavern]]\text{m/s}\right)^2 = 12960 \, and leads to [[hard water]] in many regions\text{J} = 12.96 \,\text{kJ}</math>

An unusual form of calcium carbonate is the hexahydrateWhen you throw a ball, you do [[ikaitework (physics)|work]]on it to give it speed as it leaves your hand. The moving ball can then hit something and push it, CaCO₃·6H₂Odoing work on what it hits. Ikaite The kinetic energy of a moving object is stable only below 6&nbsp;°Cequal to the work required to bring it from rest to that speed, or the work the object can do while being brought to rest: '''net force × displacement = kinetic energy''', i.e.,

:<math>F s ==Preparation==The vast majority of calcium carbonate used in industry is extracted by mining or quarrying. Pure calcium carbonate (e.g. for food or pharmaceutical use), can be produced from a pure quarried source (usually [[marble]]).\tfrac{1}{2} mv^2</math>

AlternativelySince the kinetic energy increases with the square of the speed, calcium carbonate is prepared from [[calcium oxide]]an object doubling its speed has four times as much kinetic energy. Water is added For example, a car traveling twice as fast as another requires four times as much distance to give [[calcium hydroxide]] then [[carbon dioxide]] is passed through stop, assuming a constant braking force. As a consequence of this solution to precipitate quadrupling, it takes four times the desired calcium carbonate, referred work to in double the industry as precipitated calcium carbonate (PCC):<ref name="PCC">{{cite web|title = Precipitated Calcium Carbonate |accessdate = 11 January 2014|url = http://www.lime.org/uses_of_lime/other_uses/precip_ccspeed.asp}}</ref>

The kinetic energy of an object is related to its [[momentum]] by the equation: CaO + H₂O → Ca(OH)₂:<chemmath>Ca(OH)E_\text{k} = \frac{p^2 + CO2 -> CaCO3(v) + H2O}{2m}</chemmath>

==Structure==where:The thermodynamically stable form of CaCO:<submath>3p\;</submath> under normal conditions is hexagonal β-CaCO₃, (the mineral [[calcite]]).<ref name ="Ropp">{{cite book|last=R C Ropp Elsevier|title=Encyclopedia of the alkaline earth compounds|publisher=Elsevier|isbn=9780444595508|pages=359–370}}momentum:</refmath> Other forms can be prepared, the denser,(2.83 g/cc) orthorhombic λ-CaCO₃ ( the mineral [[aragonite]]) and μ-CaCO₃, occurring as the mineral [[vaterite]].<ref name ="Ropp"/> The aragonite form can be prepared by precipitation at temperatures above 85&nbspm\;°C, the vaterite form can be prepared by precipitation at 60&nbsp;°C.<ref name ="Ropp"/> Calcite contains calcium atoms coordinated by 6 oxygen atoms, in aragonite they are coordinated by 9 oxygen atoms.<ref name ="Ropp"/math> The vaterite structure is not fully understood.<ref name="DemichelisRaiteri2013">{{cite journal|last1=Demichelis|first1=Raffaella|last2=Raiteri|first2=Paolo|last3=Gale|first3=Julian D.|last4=Dovesi|first4=Roberto|title=The Multiple Structures mass of Vaterite|journal=Crystal Growth & Design|volume=13|issue=6|year=2013|pages=2247–2251|issn=1528-7483|doi=10.1021/cg4002972}}</ref> Magnesium carbonate MgCO₃ has the calcite structure, whereas strontium and barium carbonate (SrCO₃ and BaCO₃) adopt the aragonite structure, reflecting their larger ionic radii.<ref name ="Ropp"/>body

[[File:Calcium carbonate chunks.JPG|thumb|Calcium carbonate chunks from clamshell]]<math> E_\text{t} =\tfrac{1}{2} mv^2 </math>

===Geological sources===where::<math>m\;</math> is the mass of the body:<math>v\;</math> is the speed of the [[Calcite]], [[aragonite]] and [[vaterite]] are pure calcium carbonate minerals. Industrially important source rocks which are predominantly calcium carbonate include [[limestone]], [[chalk]], [[marble]] and [[travertinecenter of mass]]of the body.

[[File:SilfurbergThe kinetic energy of any entity depends on the reference frame in which it is measured.jpg|thumb|Calcite is However the most stable polymorph total energy of calcium carbonatean isolated system, i.e. It one in which energy can neither enter nor leave, does not change over time in the reference frame in which it is transparent measured. Thus, the chemical energy converted to opaquekinetic energy by a rocket engine is divided differently between the rocket ship and its exhaust stream depending upon the chosen reference frame. A transparent variety This is called the [[Iceland sparOberth effect]] (shown here) . But the total energy of the system, including kinetic energy, fuel chemical energy, heat, etc., is used for optical purposesconserved over time, regardless of the choice of reference frame. Different observers moving with different reference frames would however disagree on the value of this conserved energy.{{clarify|date=January 2018}}]]

===Biological sources===Eggshells, snail shells and most seashells are predominantly calcium carbonate and can be used as industrial sources The kinetic energy of such systems depends on the choice of reference frame: the reference frame that gives the minimum value of that chemical.<ref>{{cite web |title=How are seashells created? |author=Horne, Francis |date=23 October 2006 |work=Scientific American |accessdate=25 April 2012 |url=http://www.scientificamerican.com/article.cfm?id=how-are-seashells-created}}</ref> Oyster shells have enjoyed recent recognition as a source energy is the [[center of dietary calciummomentum]] frame, but are also a practical industrial sourcei.<ref>{{cite web |url=http://www.webmd.com/drugs/drug-16642-Natural+Oyster+Shell+Calcium+Oral.aspx?drugid=16642&drugname=Natural+Oyster+Shell+Calcium+Oral| title=WebMD: Oyster shell calcium |publisher=WebMD| accessdate=25 April 2012}}</ref><ref>{{cite web |title=Oyster Shell Calcium Carbonate|publisher=Caltron Clays &amp Chemicals|url=http://caltronclayse.the reference frame in/Oyster_CCwhich the total momentum of the system is zero.html}}</ref> Dark green vegetables such as broccoli and kale contain dietarily significant amounts This minimum kinetic energy contributes to the [[invariant mass]] of calcium carbonate, however, they are not practical the system as an industrial source.<ref>{{cite journal|year=1993 |title=Absorbability of Calcium from Brassica Vegetables: Broccoli, Bok Choy, and Kale |journal=Journal of Food Science |volume=58 |issue=6 |pages=1378–1380|doi=10.1111/j.1365-2621.1993.tb06187.x|last1=Heaney|first1=R.P.|last2=Weaver|first2=C.M.|last3=Hinders|first3=SM.|last4=Martin|first4=B.|last5=Packard|first5=P.Ta whole.}}</ref>

===Extraterrestrial=Derivation====Beyond Earth, strong evidence suggests The work done in accelerating a particle with mass ''m'' during the infinitesimal time interval ''dt'' is given by the presence dot product of calcium carbonate on [[Mars]]. Signs of calcium carbonate have been detected at more than one location (notably at [[Gusev crater|Gusev]] ''force'' '''F''' and [[Huygens (crater)|Huygens]] craters). This provides some evidence for the past presence of liquid water.infinitesimal ''displacement ''d'''x''''':<refmath>\mathbf{F} \cdot d \mathbf{cite journal| last1x} =Boynton |first1\mathbf{F} \cdot \mathbf{v} d t =WV| last2\frac{d \mathbf{p}}{d t} \cdot \mathbf{v} d t =Ming |first2\mathbf{v} \cdot d \mathbf{p} =DW| last3=Kounaves |first3=SP| last4=Young |first4=SM| last5=Arvidson |first5=RE| last6=Hecht |first6=MH| last7=Hoffman |first7=J| last8=Niles |first8=PB| last9=Hamara |first9=DK| last10=Quinn| first10=R. C.| last11=Smith| first11=P. H.| last12=Sutter| first12=B| last13=Catling| first13=D. C.| last14=Morris| first14=R. V.| title=Evidence for Calcium Carbonate at the Mars Phoenix Landing Site| url=http://planetary.chem.tufts.edu/Boynton%20etal%20Science%202009v325p61.pdf| journal=Science |volume=325 |issue=5936 |pages= 61–64| year=2009 |pmid=19574384 |bibcode=2009Sci...325...61B| display-authors=3| doi=10.1126/science.1172768| doi-broken-date=2017-01-31 \mathbf{v}\cdot d (m \mathbf{v})\,,</ref><ref name=Clark2007math>{{cite journal| author1where we have assumed the relationship '''p'''&nbsp;=Clark| year=2007| title=Evidence for montmorillonite or its compositional equivalent in Columbia Hills&nbsp;''m''&nbsp;'''v''' and the validity of [[Newton's Second Law]]. (However, Mars| journal=also see the special relativistic derivation [[Journal Kinetic energy#Relativistic kinetic energy of Geophysical Researchrigid bodies|below]]| volume=112 |pages=E06S01| doi=10.1029/2006JE002756| last2=Arvidson| first2=R. E.| last3=Gellert| first3=R.| last4=Morris| first4=R. V.| last5=Ming| first5=D. W.| last6=Richter| first6=L.| last7=Ruff| first7=S. W.| last8=Michalski| first8=J. R.| last9=Farrand| first9=W. H.| last10=Yen| first10=A.| last11=Herkenhoff| first11=K. E.| last12=Li| first12=R.| last13=Squyres| first13=S. W.| last14=Schröder| first14=C.| last15=Klingelhöfer| first15=G.| last16=Bell| first16=J. F.| bibcode = 2007JGRE..112.6S01C| displayauthors=3 | url=http://dspace.stir.ac.uk/bitstream/1893/17119/1/Clark2007_Evidence_for_montmorillonite_or_its_compositional_equivalent_in_Columbia_Hills_Mars.pdf}}</ref>)

==Geology==Carbonate is found frequently in geologic settings and constitutes an enormous Applying the [[carbon cycle|carbon reservoirproduct rule]]. Calcium carbonate occurs as [[aragonite]], [[calcite]] and [[dolomite]]. The [[carbonate mineral]]s form the rock typeswe see that:: [[limestone]], [[chalk]], [[marble]], [[travertine]], [[tufa]], and others<math> d(\mathbf{v} \cdot \mathbf{v}) = (d \mathbf{v}) \cdot \mathbf{v} + \mathbf{v} \cdot (d \mathbf{v}) = 2(\mathbf{v} \cdot d\mathbf{v}).</math>

In warmTherefore, clear tropical waters [[coral]]s are more abundant than towards the poles where the waters are cold. Calcium carbonate contributors, including [[plankton]] (such as [[coccolith]]s and planktic [[foraminifera]]assuming constant mass so that ''dm''=0), [[coralline algae]]we have, [[sea sponge|sponges]], [[brachiopod]]s, [[echinoderm]]s, [[bryozoa]] and [[Mollusc shell|mollusks]], are typically found in shallow water environments where sunlight and filterable food are more abundant. Cold-water carbonates do exist at higher latitudes but have a very slow growth rate. The [[calcification]] processes are changed by [[ocean acidification]]:<math> \mathbf{v} \cdot d (m \mathbf{v}) = \frac{m}{2} d (\mathbf{v} \cdot \mathbf{v}) = \frac{m}{2} d v^2 = d \left(\frac{m v^2}{2}\right).</math>

Where the [[oceanic crust]] Since this is [[Subduction|subducted]] under a [[continental platetotal differential]] sediments will be carried down to warmer zones in (that is, it only depends on the final state, not how the [[asthenosphere]] particle got there), we can integrate it and [[lithosphere]]call the result kinetic energy. Under these conditions calcium carbonate decomposes Assuming the object was at rest at time 0, we integrate from time 0 to produce [[carbon dioxide]] which, along with other gases, give rise time t because the work done by the force to bring the object from rest to velocity ''v'' is equal to the work necessary to explosive [[volcano|volcanic eruptions]]do the reverse::<math> E_\text{k} = \int_0^t \mathbf{F} \cdot d \mathbf{x} = \int_0^t \mathbf{v} \cdot d (m \mathbf{v}) = \int_0^v d \left(\frac{m v^2}{2}\right) = \frac{m v^2}{2}.</math>

===Carbonate compensation depth===The This equation states that the kinetic energy (''E''_k) is equal to the [[carbonate compensation depthintegral]] of the [[dot product]] of the [[velocity]] (CCD'''v''') is the point in the ocean where the rate of precipitation of calcium carbonate is balanced by a body and the rate [[infinitesimal]] change of dissolution due to the conditions present. Deep in the ocean, the temperature drops and pressure increasesbody's [[momentum]] ('''p'''). Calcium carbonate It is unusual in assumed that its solubility increases the body starts with decreasing temperature. Increasing pressure also increases the solubility of calcium carbonate. The carbonate compensation depth can range from 4–6&nbsp;km below sea levelno kinetic energy when it is at rest (motionless).

===Role in taphonomyRotating bodies===Calcium carbonate can [[taphonomy|preserve fossils]] If a rigid body Q is rotating about any line through [[permineralization]]. Most of the vertebrate fossils center of the mass then it has [[Two Medicine Formationrotational energy|''rotational kinetic energy'']]—a [[geologic formation]] known for its [[duck-billed dinosaur]] eggs—are preserved by CaCO(<submath>3E_\text{r}\,</submath> permineralization.<ref name="twoturn" /> This type ) which is simply the sum of preservation conserves high levels the kinetic energies of detailits moving parts, even down to the microscopic level. However, it also leaves specimens vulnerable to [[weathering]] when exposed to the surface.<ref name="twoturn">Trexler, D. (2001) [httpsand is thus given by://books.google.com/books?id=mgc6CS4EUPsC&pg=PA98 "Two Medicine Formation, Montana: geology and fauna"], pp. 298–309 in ''Mesozoic Vertebrate Life'', Tanke, D. H., and Carpenter, K. (eds), Indiana University Press. {{ISBN|0-253-33907-3}}</ref>

[[Trilobite]] populations were once thought to have composed the majority of aquatic life during the [[Cambrian]], due to the fact that their calcium carbonate-rich shells were more easily preserved than those of other species,:<refmath>E_\text{r} = \int_Q \frac{v^2 dm}{Cite book|url2} =https://www.nap.edu/catalog/11630/out-of-thin-air-dinosaurs-birds-and-earths-ancient-atmosphere|title\int_Q \frac{(r \omega)^2 dm}{2} =Out of Thin Air: Dinosaurs, Birds, and Earth's Ancient Atmosphere|last\frac{\omega^2}{2} \int_Q {r^2}dm =Ward|first\frac{\omega^2}{2} I =Peter|date=|publisher=|year=|isbn=9780309666121|location=|pages=|language=en|doi=10.17226/11630\begin{matrix} \frac{1}{2}\end{matrix}I \omega^2 </refmath> which had purely chitinous shells.

The main use ===Kinetic energy of systems===A system of calcium carbonate is in bodies may have internal kinetic energy due to the construction industry, either as a building material or limestone aggregate for road building or as an ingredient relative motion of cement or as the starting material for bodies in the preparation of builder's lime by burning in a kilnsystem. HoweverFor example, because of weathering mainly caused by in the [[acid rainSolar System]]the planets and planetoids are orbiting the Sun. In a tank of gas,<ref>{{cite web|title = Effects the molecules are moving in all directions. The kinetic energy of Acid Rain|publisher = US Environmental Protection Agency|accessdate = 14 March 2015|url = http://www.epa.gov/acidrain/effects/materials.html}}</ref> calcium carbonate (in limestone form) the system is no longer used for building purposes on its own, but only as a raw/primary substance for building materialsthe sum of the kinetic energies of the bodies it contains.

Calcium carbonate A macroscopic body that is also used in stationary (i.e. a reference frame has been chosen to correspond to the purification of body's [[ironcenter of momentum]] from ) may have various kinds of [[iron ore]] in a [[blast furnaceinternal energy]]at the molecular or atomic level, which may be regarded as kinetic energy, due to molecular translation, rotation, and vibration, electron translation and spin, and nuclear spin. The carbonate is calcined These all contribute to the body''in situ'' to give calcium oxides mass, which forms as provided by the special theory of relativity. When discussing movements of a slag with various impurities presentmacroscopic body, and separates from the purified ironkinetic energy referred to is usually that of the macroscopic movement only.<ref>{{cite web|title = Blast Furnace|publisher = Science Aid|accessdate = 30 December 2007|url = http://www.scienceaid.co.uk/chemistry/industrial/blastfurnaceHowever all internal energies of all types contribute to body's mass, inertia, and total energy.html}}</ref>

In the [[oil industry]], calcium carbonate is added to [[drilling fluid]]s as a formation-bridging and filtercake-sealing agent; it is also a weighting material which increases the density ===Frame of drilling fluids to control the downhole pressure. Calcium carbonate is added to swimming pools, as a [[pH]] corrector for maintaining [[alkalinity]] and offsetting the acidic properties of the disinfectant agent.{{citation needed|datereference===June 2015}}

It The speed, and thus the kinetic energy of a single object is also used as frame-dependent (relative): it can take any non-negative value, by choosing a raw material in the refining of sugar from suitable [[sugar beetinertial frame of reference]]; It is calcined . For example, a bullet passing an observer has kinetic energy in a kiln with anthracite to produce calcium oxide and carbon dioxidethe reference frame of this observer. This burnt lime The same bullet is then slaked in sweet water stationary to produce a calcium hydroxide suspension for an observer moving with the same velocity as the precipitation of impurities in raw juice during [[carbonatation]]bullet, and so has zero kinetic energy.<ref>{{cite book|title=Introduction to the theory of relativity|first1=Francis Weston|last1=McGinnisSears|first1first2=R.ARobert W.|titlelast2=Beet-Sugar TechnologyBrehme|publisher=Beet Sugar Development FoundationAddison-Wesley|pageyear=1781968|editionpage=2nd127}}, [https://books.google.com/books?id=cpzvAAAAMAAJ&dq=%22in+its+own+rest+frame%22+%22kinetic+energy%22&q=%22in+its+own+rest+frame%22 Snippet view of page 127]</ref>By contrast, the total kinetic energy of a system of objects cannot be reduced to zero by a suitable choice of the inertial reference frame, unless all the objects have the same velocity. In any other case, the total kinetic energy has a non-zero minimum, as no inertial reference frame can be chosen in which all the objects are stationary. This minimum kinetic energy contributes to the system's [[invariant mass]], which is independent of the reference frame.

Calcium carbonate has traditionally been The total kinetic energy of a major component of blackboard chalk. However, modern manufactured chalk is mostly system depends on the [[gypsuminertial frame of reference]], hydrated [[calcium sulfate]] CaSO₄·2H₂O. Calcium carbonate : it is the sum of the total kinetic energy in a main source for growing [[Seacretecenter of momentum frame]], or and the kinetic energy the total mass would have if it were concentrated in the [[Biorockcenter of mass]]. Precipitated calcium carbonate (PCC), pre-dispersed in slurry form, is a common filler material for latex gloves with the aim of achieving maximum saving in material and production costs.<ref name=precaco3>{{cite web|title=Precipitated Calcium Carbonate uses |url=http://www.aristocratholding.com/calris-5.html |deadurl=yes |archiveurl=https://web.archive.org/web/20140725032803/http://www.aristocratholding.com/calris-5.html |archivedate=25 July 2014 }}</ref>

Fine ground calcium carbonate (GCC) is an essential ingredient in the microporous film used in [[diapers]] and some building films as the pores are nucleated around the calcium carbonate particles during the manufacture of the film by biaxial stretching. GCC or PCC is used as a filler in paper because they are cheaper than wood fiber. In terms of market volume, GCC are the most important types of fillers currently used.This may be simply shown: let <refmath>[http://www.ceresana.com/en/market-studies/additives/fillers/ Market Study Fillers, 2nd ed., published by Ceresana, September 2011]\textstyle\mathbf{V}</refmath> Printing and writing paper can contain 10–20% calcium carbonate. In North America, calcium carbonate has begun to replace [[Kaolinite|kaolin]] in be the relative velocity of the production center of glossy paper. Europe has been practicing this as alkaline [[papermaking]] or acid-free papermaking for some decades. PCC used for paper filling and paper coatings is precipitated and prepared mass frame ''i'' in a variety of shapes and sizes having characteristic narrow particle size distributions and equivalent spherical diameters of 0.4 to 3 micrometresthe frame ''k''.Since <math>\textstyle v^2 = (v_i + V)^2 = (\mathbf{v}_i + \mathbf{V}) \cdot (\mathbf{v}_i + \mathbf{V}) = \mathbf{v}_i \cdot \mathbf{v}_i + 2 \mathbf{v}_i \cdot \mathbf{V} + \mathbf{V} \cdot \mathbf{citation needed|dateV} =June 2015v_i^2 + 2 \mathbf{v}_i \cdot \mathbf{V}+ V^2</math>,

Calcium carbonate is widely used as an extender in paints,:<ref name = reademath>E_\text{k} = \int \frac{cite web|title = Calcium Carbonate Powder|publisher = Reade Advanced Materials |date=4 February 2006|accessdate = 30 December 2007|url = http://www.reade.com/Products/Minerals_and_Ores/calcium_carbonate.htmlv^2}{2}</ref> in particular matte emulsion paint where typically 30% by weight of the paint is either chalk or marble. It is also a popular filler in plastics.<ref name dm = reade/> Some typical examples include around 15 to 20% loading of chalk in [[Polyvinyl chloride|unplasticized polyvinyl chloride]] (uPVC) drain pipe, 5 to 15% loading of stearate coated chalk or marble in uPVC window profile. [[Polyvinyl chloride|PVC]] cables can use calcium carbonate at loadings of up to 70 phr (parts per hundred parts of resin) to improve mechanical properties (tensile strength and elongation) and electrical properties (volume resistivity).\int \frac{v_i^2}{citation needed|date=June 20152}dm + \mathbf{V} [[Polypropylene]] compounds are often filled with calcium carbonate to increase rigidity, a requirement that becomes important at high use temperatures.<ref name= Imerys>\cdot \int \mathbf{v}_i dm + \frac{cite web|url=http://www.imerys-perfmins.com/calcium-carbonate/eu/calcium-carbonate-plastic.htm |title=Calcium carbonate in plastic applications |accessdate=1 August 2008 |publisher=Imerys Performance MineralsV^2}{2}</ref> Here the percentage is often 20–40%\int dm. It also routinely used as a filler in [[Thermosetting plastic|thermosetting resins]] (sheet and bulk molding compounds)<ref name = Imerys/math> and has also been mixed with [[acrylonitrile butadiene styrene|ABS]], and other ingredients, to form some types of compression molded "clay" poker chips.{{citation needed|date=June 2015}} Precipitated calcium carbonate, made by dropping [[calcium oxide]] into water, is used by itself or with additives as a white paint, known as [[whitewashing]].{{citation needed|date=June 2015}}

Calcium carbonate However, let <math> \int \frac{v_i^2}{2} dm = E_i </math> the kinetic energy in the center of mass frame, <math> \int \mathbf{v}_i dm </math> would be simply the total momentum that is added to a wide range by definition zero in the center of trade and [[do it yourself]] adhesives, sealantsmass frame, and decorating fillerslet the total mass: <math> \int dm = M </math>.Substituting, we get:<ref name = reade>[http://> Ceramic tile adhesives typically contain 70 to 80% limestonewww.phy.duke. Decorating crack fillers contain similar levels of marble or dolomiteedu/~rgb/Class/intro_physics_1/intro_physics_1/node64. It is also mixed with putty html Physics notes - Kinetic energy in setting [[stained glassthe CM frame]] windows, and as a resist to prevent glass from sticking to kiln shelves when firing glazes and paints at high temperature.{{citation neededwebarchive|url=https://web.archive.org/web/20070611231147/http://www.phy.duke.edu/~rgb/Class/intro_physics_1/intro_physics_1/node64.html |date=June 20152007-06-11 }}. [[Duke University|Duke]].edu. Accessed 2007-11-24.</ref>

In [[ceramics (art)|ceramics]]/glazing applications, calcium carbonate is known as ''whiting'',:<ref name = reade/math> and is a common ingredient for many glazes in its white powdered form. When a glaze containing this material is fired in a kiln, the whiting acts as a [[Ceramic flux|flux]] material in the glaze. Ground calcium carbonate is an [[abrasive]] (both as scouring powder and as an ingredient of household scouring creams), in particular in its calcite form, which has the relatively low hardness level of 3 on the [[Mohs scale of mineral hardness]], and will therefore not scratch [[glass]] and most other [[ceramic]]s, [[Vitreous enamel|enamel]], [[bronze]], [[iron]], and [[steel]], and have a moderate effect on softer metals like [[aluminium]] and [[copper]]. A paste made from calcium carbonate and [[deionized water]] can be used to clean [[tarnish]] on [[silver]].<ref nameE_\text{k} ="Make it Shine">E_i + \frac{M V^2}{cite web|title = Ohio Historical Society Blog: Make It Shine|publisher = Ohio Historical Society |url = http://ohiohistory.wordpress2}.com/2011/06/02/making-it-shine/}}</refmath>

===Health and dietary applications===[[File:500 mg calcium supplements with vitamin D.jpg|thumb|500-milligram calcium supplements made from calcium carbonate]]Calcium carbonate Thus the kinetic energy of a system is widely used medicinally as an inexpensive dietary calcium supplement for [[antacid|gastric antacid]]<ref name = medline>{{cite web|work = Medline Plus|publisher = [[National Institutes lowest to center of Health]]|title = Calcium Carbonate |date=1 October 2005|accessdate = 30 December 2007|url = https://www.nlm.nih.gov/medlineplus/druginfo/medmaster/a601032.html |archiveurl = https://web.archive.org/web/20071017031324/http://www.nlm.nih.gov/medlineplus/druginfo/medmaster/a601032momentum reference frames, i.html <!-- Bot retrieved archive --> |archivedate = 17 October 2007}}</ref> (e.g., [[Tums]]). It may be used as a [[phosphate binder]] for frames of reference in which the treatment center of mass is stationary (either the [[hyperphosphatemiacenter of mass frame]] (primarily in patients with or any other [[chronic renal failurecenter of momentum frame]]). It In any different frame of reference, there is also used additional kinetic energy corresponding to the total mass moving at the speed of the center of mass. The kinetic energy of the system in the pharmaceutical industry as an inert [[Excipient|fillercenter of momentum frame]] for [[Tablet is a quantity that is invariant (pharmacyall observers see it to be the same)|tablets]] and other [[pharmaceuticals]].<ref>{{cite book|author1=Lieberman, Herbert A. |author2=Lachman, Leon |author3=Schwartz, Joseph B. |title = Pharmaceutical Dosage Forms: Tablets|year = 1990|isbn = 0-8247-8044-2|page=153|publisher = Dekker|location = New York}}</ref>

Calcium carbonate ===Rotation in systems===It sometimes is used in convenient to split the production total kinetic energy of calcium oxide as well as toothpaste and has seen a resurgence as a food preservative body into the sum of the body's center-of-mass translational kinetic energy and color retainer, when used in or with products such as organic apples.<ref>the energy of rotation around the center of mass ([[http://chemistry.about.com/od/foodcookingchemistry/a/cadditives.htm Food Additives – Names Starting with Crotational energy]]. Chemistry.about.com (10 April 2012). Retrieved 2012-05-24.</ref>:

Excess calcium from supplements, fortified food and high-calcium diets, can cause [[milk-alkali syndrome]], which has serious toxicity and can be fatal. In 1915, Bertram Sippy introduced the "Sippy regimen" of hourly ingestion of milk and cream, and the gradual addition of eggs and cooked cereal, for 10 days, combined with alkaline powders, which provided symptomatic relief for peptic ulcer disease. Over the next several decades, the Sippy regimen resulted in [[renal failure]], [[alkalosis]], and [[hypercalcaemia]], mostly in men with peptic ulcer disease. These adverse effects were reversed when the regimen stopped, but it was fatal in some patients with protracted vomiting. Milk-alkali syndrome declined in men after effective treatments for [[peptic ulcer]] disease arose. During the past 15 years, it has been reported in women taking calcium supplements above the recommended range of 1.2 to 1.5&nbsp;g daily, for prevention and treatment of osteoporosis, and is exacerbated by [[dehydration]]. Calcium has been added to over-the-counter products, which contributes to inadvertent excessive intake. Excessive calcium intake can lead to [[hypercalcemia]], complications of which include vomiting, abdominal pain and altered mental status.:<refmath>E_\text{k} = E_t + E_\text{cite journal|title=Clinical problem-solving, back to basics|author=Gabrielyr} \, Ilan |journal=New England Journal of Medicine|year=2008|volume=358|pmid=18450607|doi=10.1056/NEJMcps0706188|issue=18|last2=Leu|first2=James P.|last3=Barzel|first3=Uriel S.|pages=1952–6}}</refmath>

As a [[food additive]] it is designated E170,where::''E''<refsub>{{cite web|title=Food-Info.net : E-numbers : E170 Calcium carbonate|url=http://www.food-info.net/uk/e/e170.htm}} 080419 food-info.netk</refsub> and it has an INS number of 170. Used as an acidity regulator, anticaking agent, stabiliser or colour it is approved for usage in the EU,<ref>UK Food Standards Agencytotal kinetic energy: {{cite web |url=http://www.food.gov.uk/safereating/chemsafe/additivesbranch/enumberlist |title=Current EU approved additives and their ''E Numbers |accessdate=27 October 2011}}''</refsub> USAt<ref/sub>US [[Food and Drug Administration]]is the translational kinetic energy: {{cite web|url=http://www.fda.gov/Food/FoodIngredientsPackaging/FoodAdditives/FoodAdditiveListings/ucm091048.htm |title=Listing of Food Additives Status Part I |accessdate=27 October 2011 |deadurl=yes |archiveurl=https://web.archive.org/web/20130314104055/http://www.fda.gov/Food/FoodIngredientsPackaging/FoodAdditives/FoodAdditiveListings/ucm091048.htm |archivedate=14 March 2013 |df=dmy }}''E''</refsub> and [[Australia]] and [[New Zealand]].r<ref>Australia New Zealand Food Standards Code{{cite web |url=http://www.comlaw.gov.au/Details/F2011C00827 |title=Standard 1.2.4 – Labelling of ingredients |accessdate=27 October 2011}}</refsub> It is used in some [[soy milk]] and [[almond milk]] products as a source of dietary calcium; one study suggests that calcium carbonate might be as [[bioavailable]] as the calcium in cow's milk.<ref>{{Cite journal| pmid = 16177199| year = 2005| author1 = Zhao| first1 = Y| title = Calcium bioavailability of calcium carbonate fortified soymilk is equivalent to cow's milk rotational energy'' or ''angular kinetic energy'' in young women| journal = The Journal of Nutrition| volume = 135| issue = 10| pages = 2379–82| last2 = Martin| first2 = B. R.| last3 = Weaver| first3 = C. M.}}</ref> Calcium carbonate is also used as a [[firming agent]] in many canned or bottled vegetable products.the rest frame

===Agricultural use===[[Agricultural lime]], powdered chalk or limestone, Thus the kinetic energy of a tennis ball in flight is used as a cheap method for neutralising acidic soil, making it suitable for planting.<ref name="Oates2008">{{cite book|first=J. A. H.|last=Oates|title=Lime and Limestone: Chemistry and Technologythe kinetic energy due to its rotation, Production and Uses|url=https://books.googleplus the kinetic energy due to its translation.com/books?id=MVoEMNI5Vb0C&pg=PA111|date=11 July 2008|publisher=John Wiley & Sons|isbn=978-3-527-61201-7|pages=111–3}}</ref>

===Household use=Relativistic kinetic energy of rigid bodies==Calcium carbonate is a key ingredient {{See also|Mass in many household cleaning powders like [[Comet (cleanser)]] special relativity|Tests of relativistic energy and is used as a scrubbing agent.momentum}}

In 1989, a researcher, Ken Simmons, introduced CaCO₃ into the Whetstone Brook in With ''m'' being an object's [[Massachusettsrest mass]].<ref>{{cite news|agency = [[Associated Press]]|title = Limestone Dispenser Fights Acid Rain in Stream |date=13 June 1989|url = https://query.nytimes.com/gst/fullpage.html?res=950DEFD9173FF930A25755C0A96F948260|work = The New York Times}}</ref> His hope was that the calcium carbonate would counter the acid in the stream from acid rain , '''v''' and ''v'' its velocity and save the trout that had ceased to spawn. Although his experiment was a successspeed, it did increase and ''c'' the amount speed of aluminium ions light in vacuum, we use the area of the brook that was not treated with the limestone. This shows that CaCO₃ can be added to neutralize the effects of acid rain in [[river]] ecosystems. Currently calcium carbonate is used to neutralize acidic conditions in both soil and water.expression for linear momentum <ref name=envmath>\mathbf{{cite web|title=Environmental Uses for Calcium Carbonate|url=http://www.congcal.com/markets/environmental/|publisher=Congcal|accessdate=5 August 2013p}}</ref><ref>{{cite journal|author = Schreiber, R. K. |title = Cooperative federal-state liming research on surface waters impacted by acidic deposition|year = 1988|journal =Water, Air, & Soil Pollution|volume = 41|issue = 1|pages = 53–73|doi=10.1007/BF00160344|url=https://link.springer.com/article/10.1007%2FBF00160344|doi-broken-date = 2017-01-31}}</ref><ref>m\gamma \mathbf{{cite web|title = Effects of low pH and high aluminum on Atlantic salmon smolts in Eastern Maine and liming project feasibility analysis|year = 2006|author1=Kircheis, Dan |author2=Dill, Richard |publisher = National Marine Fisheries Service and Maine Atlantic Salmon Commission|url = http://www.mainesalmonrivers.org/pages/Liming%20Project%20Rpt.pdf|format = reprinted at Downeast Salmon Federation}v}</refmath> Since the 1970s, such ''liming'' has been practiced on a large scale in Sweden to mitigate acidification and several thousand lakes and streams are limed repeatedly.where <refmath>{{Cite journal |doi\gamma = 10.10071/s10933\sqrt{1-006-9014-9 |title= Liming placed in a long-term perspective: A paleolimnological study of 12 lakes in the Swedish liming program |journal= Journal of Paleolimnology |volume= 37 |issue= v^2/c^2 |pages= 247–258 |year= 2006 |last1= Guhrén |first1= M. |last2= Bigler |first2= C. |last3= Renberg |first3= I. |bibcode= 2007JPall..37..247G }}</refmath>.

Calcium carbonate [[Integration by parts|Integrating by parts]] yields:<math>E_\text{k} = \int \mathbf{v} \cdot d \mathbf{p}= \int \mathbf{v} \cdot d (m \gamma \mathbf{v}) = m \gamma \mathbf{v} \cdot \mathbf{v} - \int m \gamma \mathbf{v} \cdot d \mathbf{v} = m \gamma v^2 - \frac{m}{2} \int \gamma d (v^2)</math>Since <math>\gamma = (1 - v^2/c^2)^{-1/2}\!</math>,:<math>\begin{align}E_\text{k} &= m \gamma v^2 - \frac{- m c^2}{2} \int \gamma d (1 - v^2/c^2) \\ &= m \gamma v^2 + m c^2 (1 - v^2/c^2)^{1/2} - E_0\end{align}</math><math>E_0</math> is also used in a [[constant of integration]] for the [[flue gas desulfurisationindefinite integral]] applications eliminating harmful SO.Simplifying the expression we obtain:<submath>\begin{align}E_\text{k} &= m \gamma (v^2 + c^2 (1 - v^2/c^2)) - E_0 \\ &= m \gamma (v^2 + c^2 - v^2) - E_0 \\ &= m \gamma c^2 - E_0\end{align}</math><math>E_0</math> is found by observing that when <math>\mathbf{v }= 0 , \ \gamma = 1\!</submath> and NO<submath>E_\text{k} = 0 \!</math>, giving:<math>E_0 = m c^2\,</submath> emissions from coal and other fossil fuels burnt resulting in large fossil fuel power stations.the formula:<ref namemath>E_\text{k} = m \gamma c^2 - m c^2 =env\frac{m c^2}{\sqrt{1 - v^2/c^2}} - m c^2</math>

==Calcination equilibrium==[[Calcination]] of [[limestone]] using [[charcoal]] fires to produce [[calcium oxide|quicklime]] has been practiced since antiquity by cultures all over This formula shows that the world. The temperature at which limestone yields calcium oxide is usually given work expended accelerating an object from rest approaches infinity as 825&nbsp;°C, but stating an absolute threshold is misleading. Calcium carbonate exists in equilibrium with calcium oxide and [[carbon dioxide]] at any temperature. At each temperature there is a [[partial pressure]] of carbon dioxide that is in equilibrium with calcium carbonate. At room temperature the equilibrium overwhelmingly favors calcium carbonate, because velocity approaches the equilibrium CO₂ pressure is only a tiny fraction speed of the partial CO₂ pressure in air, which light. Thus it is about 0.035 kPaimpossible to accelerate an object across this boundary.

At temperatures above 550&nbsp;°C the equilibrium CO₂ pressure begins to exceed the CO₂ pressure in air. So above 550&nbsp;°C, calcium carbonate begins to outgas CO₂ into air. However, in a charcoal fired kiln, the concentration The mathematical by-product of CO₂ will be much higher than it this calculation is in air. Indeed, if all the [[oxygenmass-energy equivalence]] in the kiln is consumed in the fire, then the partial pressure of CO₂ in the kiln can be as high as 20 kPa.<ref name="solvaypcc2007">{{cite web|title = Solvay Precipitated Calcium Carbonate: Production|publisher = Solvay S. A. |date=9 March 2007|accessdate = 30 December 2007|url = http://www.solvaypcc.com/safety_environment/0,0,1000044-_EN,00.html}}</ref>formula—the body at rest must have energy content

The table shows that this partial pressure is not achieved until the temperature is nearly 800&nbsp;°C. For the outgassing of CO:₂ from calcium carbonate to happen at an economically useful rate, the equilibrium pressure must significantly exceed the ambient pressure of CO<submath>E_\text{rest} = E_0 = m c^2\!</submath>. And for it to happen rapidly, the equilibrium pressure must exceed total atmospheric pressure of 101 kPa, which happens at 898&nbsp;°C.{{clear right}}

{| class="wikitable"|+ {{chembox header}} |Equilibrium pressure of COAt a low speed (<submath>2v</submath> over CaCO₃ (P) vs. temperature (T).<ref name=crcmath>{{RubberBible86th}}c</refmath>|-|'''P (kPa)'''||0, the relativistic kinetic energy is approximated well by the classical kinetic energy.055||0.13||0.31||1.80||5.9||9.3||14||24||34||51||72 ||80||91||101||179||901||3961|-|'''T (°C)'''||550||587||605||680||727||748||777||800||830||852||871||881||891||898||937||1082||1241|}This is done by [[binomial approximation]] or by taking the first two terms of the [[Taylor expansion]] for the reciprocal square root:

:<math>E_\text{k} \approx m c^2 \left(1 + \frac{1}{2} v^2/c^2\right) - m c^2 ==Solubility==\frac{1}{2} m v^2</math>

===With varying COSo, the total energy <submath>2E_k</submath> pressure===[[File:CanarySpring.jpg|thumb|right|[[Travertine]] calcium carbonate deposits from a [[hot spring]]]]Calcium carbonate is poorly soluble in pure water (47&nbsp;mg/L can be partitioned into the rest mass energy plus the Newtonian kinetic energy at normal atmospheric CO₂ partial pressure as shown below)low speeds.

The equilibrium of its solution is given by the equation When objects move at a speed much slower than light (with dissolved calcium carbonate e.g. in everyday phenomena on Earth), the first two terms of the right)::{| width="500"| style="width:50%; height:30px;"| CaCO₃ {{eqm}} Ca²⁺ + CO₃²⁻| ''K''_sp = 3series predominate.7×10⁻⁹ to 8.7×10⁻⁹ at 25&nbsp;°C|}The next term in the Taylor series approximation

where the [[solubility product]] for [Ca:<supmath>E_\text{k} \approx m c^2\left(1 +<\frac{1}{2} v^2/sup>] [CO_{c^2 + \frac{3}²⁻] is given as anywhere from ''K''_sp = 3.7×10⁻⁹ to ''K''_sp = }{8.7×10<sup>−9<} v^4/sup> at 25&nbsp;°C, depending upon the data source.<ref name c^4\right) - m c^2 = crc/><ref> \frac{1}{cite web|title = Selected Solubility Products and Formation Constants at 25 °C|publisher = [[California State University, Dominguez Hills]]|url = http://www.csudh.edu/oliver/chemdata/data-ksp.htm}2}</ref> What the equation means is that the product of molar concentration of calcium ions ([[mole (unit)|moles]] of dissolved Ca^{m v^2+} per liter of solution) with the molar concentration of dissolved CO<sub>\frac{3<}{8} m v^4/sub>²⁻ cannot exceed the value of ''K''_sp. This seemingly simple solubility equation, however, must be taken along with the more complicated equilibrium of [[carbon dioxide]] with [[water]] (see [[carbonic acid]]). Some of the CO₃<sup>2−c^2</supmath> combines with H⁺ in the solution according to:

:is small for low speeds. For example, for a speed of {{convert|10|km/s| width="500"mph| styleabbr="width:50%; height:25px;"| HCO₃⁻ {{eqmon}} H<sup>+<the correction to the Newtonian kinetic energy is 0.0417&nbsp;J/sup> + CO₃<sup>2−<kg (on a Newtonian kinetic energy of 50&nbsp;MJ/sup> kg) and for a speed of 100&nbsp;km/s it is 417&nbsp;| ''K''<sub>a2<J/sub> = kg (on a Newtonian kinetic energy of 5.61×10⁻¹¹ at 25&nbsp;°C|}GJ/kg).

HCO₃⁻ The relativistic relation between kinetic energy and momentum is known as the [[bicarbonate]] ion. [[Calcium bicarbonate]] is many times more soluble in water than calcium carbonate—indeed it exists ''only'' in solution.given by

Some of the HCO₃⁻ combines with H:<supmath>E_\text{k} = \sqrt{p^2 c^2 +m^2 c^4} - m c^2</supmath> in solution according to:

This can also be expanded as a [[Taylor series]], the first term of which is the simple expression from Newtonian mechanics:<ref>{{cite web |url=http://farside.ph.utexas.edu/teaching/qmech/Quantum/node107.html |title=Fine Structure of Hydrogen |first=Richard |last=Fitzpatrick | widthdate="500"20 July 2010 | stylework="width:50%; height:25px;"Quantum Mechanics |H<sub>2accessdate=20 August 2016}}</subref>CO:<sub>3</submath> E_\text{k} \approx \frac{p^2}{eqm2 m}- \frac{p^4} H⁺ + HCO_{{8 m^3}⁻ &nbsp;&nbsp;| ''K''_a1 = c^2} .5×10<sup>−4</supmath> at 25&nbsp;°C|}This suggests that the formulae for energy and momentum are not special and axiomatic, but concepts emerging from the equivalence of mass and energy and the principles of relativity.

Some of ===General relativity==={{see also|Schwarzschild geodesics}}Using the Hconvention that:<submath>g_{\alpha \beta} \, u^{\alpha} \, u^{\beta} \, = \, - c^2</sub>CO<submath>3</sub> breaks up into water and dissolved carbon dioxide according to:

:{| width="500"where the [[four-velocity]] of a particle is| style="width:50%; height:25px;"| H<submath>2</sub>O + CO₂(dissolved) u^{\alpha} \, = \, \frac{d x^{eqm\alpha}} H<sub>2{d \tau} </submath>CO₃ &nbsp;&nbsp;| ''K''_h = 1.70×10⁻³ at 25&nbsp;°C|}

And dissolved carbon dioxide and <math>\tau \,</math> is the [[proper time]] of the particle, there is also an expression for the kinetic energy of the particle in equilibrium with atmospheric carbon dioxide according to:[[general relativity]].

:{| width="500"If the particle has momentum| style="width:45%;"|<math chem>\frac{P_p_{\ce{CO2}}}{[\ce{CO2}]beta}\ , =\ k_, m \ce, g_{H\beta \alpha}</math>| where ''k''_H = 29.76 atm/(mol/L) at 25&nbsp;°C ([[Henry's law|Henry constant]])\, <math chem>P_u^{\ce{CO2}alpha}</math> being the CO₂ partial pressure.|}

For ambient air, <math chem>P_{\ce{CO2}}</math> is around 3.5×10⁻⁴ atmospheres (or equivalently 35 [[Pascal (unit)|Pa]]). The last equation above fixes the concentration of dissolved COas it passes by an observer with four-velocity ''u''_2obs as a function of <math chem>P_{\ce{CO2}}</math>, independent of then the concentration of dissolved CaCO₃. At atmospheric partial pressure expression for total energy of CO₂, dissolved CO₂ concentration is 1.2×10⁻⁵ moles/liter. The equation before that fixes the concentration of H₂CO₃ particle as observed (measured in a function of [COlocal inertial frame) is:<submath>2</sub>]. For [CO₂]E \, =1.2×10⁻⁵\, it results in [H₂CO₃]=2.0×10⁻⁸ moles per liter. When [H₂CO₃] is known- \, the remaining three equations together withp_{| class="wikitable floatright"|+ \beta} \, u_{\text{chembox headerobs}} |Calcium ion solubility as a function of [[carbon dioxide|CO₂]] [[partial pressure]] at 25&nbsp;°C ^{{math|1=(''K''_sp = 4.47×10⁻⁹)}}|-!<math chem>\scriptstyle P_\ce{CO2beta}</math> (atm)![[pH]]![Ca²⁺] (mol/L)|-| 10⁻¹² ||12.0||5.19 × 10⁻³|-| 10⁻¹⁰ ||11.3||1.12 × 10⁻³|-| 10⁻⁸ ||10.7||2.55 × 10⁻⁴|-| 10⁻⁶ ||9.83||1.20 × 10⁻⁴|-| 10⁻⁴ ||8.62||3.16 × 10⁻⁴|-| 3.5 × 10⁻⁴||8.27||4.70 × 10⁻⁴|-| 10⁻³ ||7.96||6.62 × 10⁻⁴|-| 10⁻² ||7.30||1.42 × 10⁻³|-| 10⁻¹ ||6.63||3.05 × 10⁻³|-| 1 ||5.96||6.58 × 10⁻³|-| 10 ||5.30||1.42 × 10⁻²|}

and the kinetic energy can be expressed as the total energy minus the rest energy:{| width="450"| style="width:50%; height:25px;"| H<submath>2</sub>O E_{k} \, = \, - \, p_{\beta} \, u_{\text{eqmobs}}^{\beta} H⁺ + OH⁻| ''K'' = 10<sup>−14\, - \, m \, c^2 \, .</supmath> at 25&nbsp;°C|}

Consider the case of a metric that is diagonal and spatially isotropic (which is true for all aqueous solutions''g''_tt,''g''_ss,''g''_ss,''g''_ss). Since:<math>u^{\alpha} = \frac{d x^{\alpha}}{d t} \frac{d t}{d \tau} = v^{\alpha} u^{t} \, and the fact that the solution must be electrically neutral,</math>

:2[Cawhere ''v''^2+α] + [His the ordinary velocity measured w.r.t. the coordinate system, we get:<supmath>+</sup>] -c^2 = g_{\alpha \beta} u^{\alpha} u^{\beta} = [HCO₃⁻] g_{t t} (u^{t})^2 + g_{s s} v^2[CO₃^{2−(u^{t})^2 \,.}] + [OH<sup>−</supmath>]

make it possible to solve simultaneously Solving for the remaining five unknown concentrations (note that the above form of the neutrality equation is valid only if calcium carbonate has been put in contact with pure water or with a neutral pH solution; in the case where the initial water solvent pH is not neutral''u''^t gives:<math>u^{t} = c \sqrt{\frac{-1}{g_{t t} + g_{s s} v^2}} \, the equation is modified).</math>

The table on the right shows the result Thus for [Ca²⁺] and [H⁺] (in the form of pH) as a function of ambient partial pressure of CO₂ stationary observer (''Kv''_sp = 4.47×10⁻⁹ has been taken for the calculation0).* At atmospheric levels of ambient CO₂ the table indicates the solution will be slightly alkaline with a maximum CaCO₃ solubility of 47&nbsp;mg/L.* As ambient CO₂ partial pressure is reduced below atmospheric levels, the solution becomes more and more alkaline. At extremely low :<math chem>P_u_{\cetext{CO2obs}}</math>, dissolved CO₂, bicarbonate ion, and carbonate ion largely evaporate from the solution, leaving a highly alkaline solution of [[calcium hydroxide]], which is more soluble than CaCO₃. Note that for <math chem>P_^{t} = c \cesqrt{CO2}} = 10^\frac{-121} \mathrm{atmg_{t t}}} \,</math>, the [Ca²⁺] [OH⁻]² product is still below the solubility product of Ca(OH)₂ (8×10⁻⁶). For still lower CO₂ pressure, Ca(OH)₂ precipitation will occur before CaCO₃ precipitation.* As ambient CO₂ partial pressure increases to levels above atmospheric, pH drops, and much of the carbonate ion is converted to bicarbonate ion, which results in higher solubility of Ca²⁺.

The effect of and thus the latter is especially evident in daykinetic energy takes the form:<math>E_\text{k} = -tom g_{tt} u^t u_{\text{obs}}^t -day life of people who have hard water. Water in aquifers underground can be exposed to levels of CO_{m c^2 = m c^2 \sqrt{\frac{g_{tt}}{g_{tt} + g_{ss} v^2}} - m c^2} much higher than atmospheric. As such water percolates through calcium carbonate rock\, the CaCO₃ dissolves according to the second trend. When that same water then emerges from the tap, in time it comes into equilibrium with CO₂ levels in the air by outgassing its excess CO<sub>2</submath>. The calcium carbonate becomes less soluble as a result and the excess precipitates as lime scale. This same process is responsible for the formation of [[stalactites]] and [[stalagmite]]s in limestone caves.

Two hydrated phases of calcium carbonate, [[monohydrocalcite]], CaCOFactoring out the rest energy gives::₃·H<submath>E_\text{k} = m c^2 \left( \sqrt{\frac{g_{tt}}{g_{tt} + g_{ss} v^2</sub>O and [[ikaite]]}} - 1 \right) \, CaCO_3.·6H<submath>2</sub>O, may [[precipitate]] from water at ambient conditions and persist as metastable phases.

=== With varying pH, temperature and salinityThis expression reduces to the special relativistic case for the flat-space metric where: CaCO<submath>3</sub> scaling in swimming pools ===[[File:CaCO3-pH.gif|thumb|altg_{t t} =Effects of salinity and pH on the maximum calcium ion level before scaling is anticipated at 25 C and 1 mM bicarbonate (e.g. in swimming pools)]][[File:CaCO3-Temp.gif|thumb|alt=Effects of temperature and bicarbonate concentration on the maximum calcium ion level before scaling is anticipated at pH 7 and 5,000 ppm salinity (e.g. in swimming pools)]]In contrast to the open equilibrium scenario above, many swimming pools are managed by addition of [[sodium bicarbonate]] (NaHCO₃) to about c^2 mM as a buffer\, then control of pH through use of HCl, NaHSO<sub>4</submath>, Na₂CO₃, NaOH or chlorine formulations that are acidic or basic. In this situation, dissolved inorganic carbon ([[total inorganic carbon]]) is far from equilibrium with atmospheric CO₂. Progress towards equilibrium through outgassing of CO₂ is slowed by (i) the slow reaction [[Carbonic acid|H₂CO_3:]] ⇌ CO₂(aq) + H₂O;<refmath>g_{{Cite journal | doi s s} = 10.1021/jp909019u| pmid = 20039712| title = Comprehensive Study of the Hydration and Dehydration Reactions of Carbon Dioxide in Aqueous Solution| journal = The Journal of Physical Chemistry A| volume = 114| issue = 4| pages = 1734–40| year = 2010| last1 = Wang | first1 = X. | last2 = Conway | first2 = W1 \,. | last3 = Burns | first3 = R. | last4 = McCann | first4 = N. | last5 = Maeder | first5 = M. | bibcode = 2010JPCA..114.1734W}}</refmath> (ii) limited aeration in a deep water column and (iii) periodic replenishment of bicarbonate to maintain buffer capacity (often estimated through measurement of [[alkalinity|‘total alkalinity’]]).

In this situation, the dissociation constants for the much faster reactions HNewtonian approximation to general relativity:<submath>g_{t t} = - \left( c^2</sub>CO₃ ⇌ H⁺ + HCO₃^‾ ⇌ 2 H⁺ + CO₃²⁻ allow the prediction of concentrations of each dissolved inorganic carbon species in solution\Phi \right) \, from the added concentration of HCO<sub>3</submath>:<supmath>−</sup> (which constitutes more than 90% of [[Bjerrum plot]] species from pH 7 to pH 8 at 25&nbsp;°C in fresh water).<ref nameg_{s s} ="Mook 2000">Mook, W. (2000) [http://www1 -naweb.iaea.org/napc/ih/documents/global_cycle/vol%20I/cht_i_09.pdf "Chemistry of carbonic acid in water"], pp. 143–165 in ''Environmental Isotopes in the Hydrological Cycle: Principles and Applications''. INEA/UNESCO: Paris.</ref> Addition of HCO₃⁻ will increase CO₃²⁻ concentration at any pH. Rearranging the equations given above, we can see that [Ca^{\frac{2 \Phi}{c^2+}] = Ksp / [CO₃²⁻], and [CO₃²⁻] = K_a2 × [HCO₃⁻] / [H⁺]. Therefore} \, when HCO₃⁻ concentration is known, the maximum concentration of Ca<sup>2+</supmath> ions before scaling through CaCO₃ precipitation can be predicted from the formula:

:Ca²⁺_max = (K_sp / K_a2) × (where Φ is the Newtonian [H⁺[gravitational potential] / [HCO₃⁻]). This means clocks run slower and measuring rods are shorter near massive bodies.

The solubility product for CaCO₃ ==Kinetic energy in quantum mechanics=={{further|Hamiltonian (K_spquantum mechanics) and the dissociation constants for the dissolved inorganic carbon species (including K_a2) are all substantially affected by temperature and [[salinity]],<ref name="Mook 2000" /> with the overall effect that Ca²⁺_max increases from fresh to salt water, and decreases with rising temperature, pH, or added bicarbonate level, as illustrated in the accompanying graphs.}}

The trends In [[quantum mechanics]], observables like kinetic energy are illustrative for pool management, but whether scaling occurs also depends on other factors including interactions with Mg²⁺, Brepresented as [[Operator (OHphysics)₄⁻ and other ions in the pool, as well as supersaturation effects.<ref>{{cite journal|author=Wojtowicz, Joperators]]. A. |year=1998|title= Factors affecting precipitation For one particle of calcium carbonatemass ''m'', the kinetic energy operator appears as a term in the [[Hamiltonian (quantum mechanics)|journal= Journal Hamiltonian]] and is defined in terms of the Swimming Pool and Spa Industry |volume=3 |issue=1|pages= 18–23|url=http://jspsi.poolhelp.com/ARTICLES/JSPSI_V3N1_pp18-23.pdf}}more fundamental momentum operator </refmath>\hat p<ref/math>{{cite journal|author=Wojtowicz, J. A. |year=1998|title= Corrections, potential errors, and significance of The kinetic energy operator in the saturation index|journal= Journal of the Swimming Pool [[Relativistic quantum mechanics#Non-relativistic and Spa Industry |volume=3 |issue=1relativistic Hamiltonians|pages=37–40|url=http://jspsi.poolhelp.com/ARTICLES/JSPSI_V3N1_pp37non-40.pdf}}</ref> Scaling is commonly observed in electrolytic chlorine generators, where there is a high pH near the cathode surface and scale deposition further increases temperature. This is one reason that some pool operators prefer borate over bicarbonate relativistic]] case can be written as the primary pH buffer, and avoid the use of pool chemicals containing calcium.<ref>Birch, R. G. (2013) [http://members.iinet.net.au/~jorobbirch/BABES.pdf BABES: a better method than "BBB" for pools with a salt-water chlorine generator.] iinet.net.au</ref>

===Solubility in a strong or weak acid solution===Solutions of [[strong acid|strong]] ([[hydrochloric acid|HCl]]), moderately strong ([[sulfamic acid|sulfamic]]) or [[weak acid|weak]] ([[acetic acid|acetic]], [[citric acid|citric]], [[sorbic acid|sorbic]], [[lactic acid|lactic]], [[phosphoric acid|phosphoric]]) acids are commercially available. They are commonly used as [[descaling agent]]s to remove [[limescale]] deposits. The maximum amount of CaCO:<submath>3</sub> that can be "dissolved" by one liter of an acid solution can be calculated using the above equilibrium equations\hat T = \frac{\hat p^2}{2m}.* In the case of a strong monoacid with decreasing acid concentration [A] = [A<sup>−</supmath>], we obtain (with CaCO₃ molar mass = 100 g):

{| border="1" cellspacing="0" cellpadding="4" style="margin: 0 0 0 0.5em; background: white; border-collapse: collapse; border-color: #C0C090;" class="wikitable"|-! width="160" {{chembox header}} |[A] (mol/L)| 1| 10Notice that this can be obtained by replacing <supmath>−1p</supmath>| 10by <supmath>−2\hat p</supmath>in the classical expression for kinetic energy in terms of [[momentum]],| 10⁻³| 10⁻⁴| 10<sup>−5:</supmath>| 10⁻⁶| 10⁻⁷| 10⁻¹⁰|-! width="160" {E_\text{chembox header}k} |Initial pH| 0.00||1.00||2.00||3.00||4.00||5.00||6.00||6.79||7.00|-! width="160" \frac{p^2}{chembox header}2m} |Final pH| 6.75||7.25||7.75||8.14||8.25||8.26||8.26||8.26||8.27|-! width="160" {{chembox header}} |Dissolved CaCO₃<br /math>(g/[[liter|L]] of acid)| 50.0||5.00||0.514||0.0849||0.0504||0.0474||0.0471||0.0470||0.0470|}

where In the initial state is the acid solution with no Ca²⁺ (not taking into account possible CO₂ dissolution) and the final state is the solution with saturated Ca²⁺. For strong acid concentrations, all species have a negligible concentration in the final state with respect to Ca²⁺ and A⁻ so that the neutrality equation reduces approximately to 2[Ca²⁺[Schrödinger picture] = [A⁻] yielding , <math>\scriptstyle[\mathrm{Ca}^{2+}] \simeq \frac{[\mathrm{A}^-]}{2}hat p</math>. When takes the concentration decreases, [HCOform <submath>3-i\hbar\nabla </submath>⁻] becomes non-negligible so that where the preceding expression derivative is no longer valid. For vanishing acid concentrations, one can recover the final pH taken with respect to position coordinates and the solubility of CaCO₃ in pure water.* In the case of a weak monoacid (here we take acetic acid with p''K''_A = 4.76) with decreasing total acid concentration [A] = [A⁻]+[AH], we obtain:hence

{| border="1" cellspacing="0" cellpadding="4" style="margin: 0 0 0 0.5em; background: white; border-collapse: collapse; border-color: #C0C090;" class="wikitable"|-! width="160" {{chembox header}} |[A] (mol/L)| 1| 10<supmath>−1</sup>| 10⁻²| 10⁻³| 10⁻⁴| 10⁻⁵| 10⁻⁶| 10⁻⁷| 10⁻¹⁰|\hat T = -! width="160" \frac{{chembox header}} |Initial pH| \hbar^2.38||2.88||3.39||3.91||4.47||5.15||6.02||6.79||7.00|-! width="160" {{chembox header}} |Final pH| 6.75||7.25||7.75||8.14||8.25||8.26||8.26||8.26||8.27|-! width="160" {{chembox header2m}} |Dissolved CaCO₃<br />(g/[[liter|L]] of acid)| 49.5||4.99||0.513||0.0848||0.0504||0.0474||0.0471||0.0470||0.0470|}For the same total acid concentration, the initial pH of the weak acid is less acid than the one of the strong acid; however, the maximum amount of CaCO₃ which can be dissolved is approximately the same. This is because in the final state, the pH is larger than the p''K''_A, so that the weak acid is almost completely dissociated, yielding in the end as many H⁺ ions as the strong acid to "dissolve" the calcium carbonate.* The calculation in the case of [[phosphoric acid]] (which is the most widely used for domestic applications) is more complicated since the concentrations of the four dissociation states corresponding to this acid must be calculated together with [HCO₃⁻], [CO₃²⁻], [Ca^{\nabla^2+}], [H⁺] and [OH⁻]. The system may be reduced to a seventh degree equation for [H<sup>+</supmath>] the numerical solution of which gives

The expectation value of the electron kinetic energy, <math>\langle\hat{| border="1" cellspacing="0" cellpadding="4" style="margin: 0 0 0 0.5em; background: white; border-collapse: collapse; border-color: #C0C090;" class="wikitable"|-! width="160" {{chembox header}T} |[A] (mol/L)| 1| 10^{−1\rangle</supmath>, for a system of ''N'' electrons described by the [[Wave function| 10wavefunction]] <supmath>−2\vert\psi\rangle</supmath>is a sum of 1-electron operator expectation values:| 10:<supmath>−3}| 10⁻⁴| 10⁻⁵| 10⁻⁶| 10⁻⁷| 10⁻¹⁰|-! width\langle\hat{T}\rangle ="160" \bigg\langle\psi \bigg\vert \sum_{i=1}^N \frac{chembox header-\hbar^2}} |Initial pH| 1.08||1.62||{2.25||3.05||4.01||5.00||5.97||6.74||7.00|-! width="160" {m_\text{chembox headere}} |Final pH| 6.71||7.17||7.63||8.06||8.24||8.26||8.26||8.26||8.27|\nabla^2_i \bigg\vert \psi \bigg\rangle = -! width="160" \frac{\hbar^2}{2 m_\text{chembox headere}} |Dissolved CaCO\sum_{i=1}^N \bigg\langle\psi \bigg\vert \nabla^2_i \bigg\vert \psi \bigg\rangle</math>where <submath>3m_\text{e}</submath> is the mass of the electron and <math>\nabla^2_i<br /math>(g/is the [[liter|LLaplacian]] operator acting upon the coordinates of acid)| 62.0||7.39||0.874||0.123||0.0536||0.0477||0the ''i''^th electron and the summation runs over all electrons.0471||0.0471||0.0470|}

where The [A] = [H₃PO₄Density functional theory|density functional] + [H₂PO₄⁻] + [HPOformalism of quantum mechanics requires knowledge of the electron density ''only'', i.e., it formally does not require knowledge of the wavefunction. Given an electron density <submath>4\rho(\mathbf{r})</submath>²⁻] + [PO₄³⁻] , the exact N-electron kinetic energy functional is unknown; however, for the total acid concentration. Thus phosphoric acid is more efficient than specific case of a monoacid since at the final almost neutral pH1-electron system, the second dissociated state concentration [HPOkinetic energy can be written as:<submath>4T[\rho] = \frac{1}{8} \int \frac{ \nabla \rho(\mathbf{r}) \cdot \nabla \rho(\mathbf{r}) }{ \rho(\mathbf{r}) } d^3r </submath>where <supmath>2−T[\rho]</supmath>] is not negligible (see known as the [[phosphoric acid#pH and composition of a phosphoric acid aqueous solutionCarl Friedrich von Weizsäcker|phosphoric acidvon Weizsäcker]])kinetic energy functional.

{{div colPortal|colwidth=22emEnergy}}* [[CuttleboneEscape velocity]]* [[CuttlefishJoule]]* [[GessoKE-Munitions]]* [[LimescaleProjectile#Typical projectile speeds|Kinetic energy per unit mass of projectiles]]* [[MarbleProjectile#Kinetic projectiles|Kinetic projectile]]* [[Ocean acidificationParallel axis theorem]]* [[Potential energy]]* [[Recoil]] ==Notes=={{div col endreflist}}

*{{reflistcite web |30emurl = http://www.physicsclassroom.com/class/energy/Lesson-1/Kinetic-Energy | title = Kinetic Energy | accessdate = 2015-07-19 | author = Physics Classroom | year = 2000 }}*[[Oxford Dictionary]] 1998*{{cite web | url = http://www-history.mcs.st-andrews.ac.uk/Mathematicians/Coriolis.html | title = Biography of Gaspard-Gustave de Coriolis (1792-1843) | accessdate = 2006-03-03 | author = School of Mathematics and Statistics, University of St Andrews | year = 2000 }}*{{cite book | last = Serway | first = Raymond A. |author2=Jewett, John W. | title = Physics for Scientists and Engineers | edition = 6th | publisher = Brooks/Cole | year = 2004 | isbn = 0-534-40842-7 }}*{{cite book | last = Tipler | first = Paul | title = Physics for Scientists and Engineers: Mechanics, Oscillations and Waves, Thermodynamics | edition = 5th | publisher = W. H. Freeman | year = 2004 | isbn = 0-7167-0809-4 }}*{{cite book | last = Tipler | first = Paul |author2=Llewellyn, Ralph | title = Modern Physics | edition = 4th | publisher = W. H. Freeman | year = 2002 | isbn = 0-7167-4345-0 }}

* {{ICSC|1193|11}}* {{PubChemLink|516889}}* [[ATC codes]]: {{ATC|A02|AC01}} and {{ATC|A12|AA04Commonscat-inline}}* [http://calcium-carbonatewww.orgkineticenergys.uk/calciumcom kinetic energy] -carbonate.asp The British Calcium Carbonate Association – What what it is calcium carbonate]* [https://www.cdc.gov/niosh/npg/npgd0090.html CDC – NIOSH Pocket Guide to Chemical Hazards – Calcium Carbonate] {{Calcium compounds}}{{Antacids}}{{Drugs for treatment of hyperkalemia and hyperphosphatemia}}how it works

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