Rudolf Clausius

{{short description|German physicist and mathematician (1822–1888)}} {{Redirect|Clausius|the lunar crater|Clausius (crater)}} {{Use dmy dates|date=July 2025}}

{{Infobox scientist |name = Rudolf Clausius |image = Rudolf Clausius 01.jpg |birth_name = Rudolf Julius Emanuel Clausius |birth_date = {{birth date|1822|1|02|df=yes}} |birth_place = Köslin, Province of Pomerania, Prussia |death_date = {{death date and age|1888|08|24|1822|1|02|df=yes}} |death_place = Bonn, Rhine Province, Prussia, German Empire |ethnicity = |field = Physics |work_institutions = |alma_mater = |doctoral_advisor = |doctoral_students = |known_for = {{ubl|Chemical thermodynamics|First law of thermodynamics|Second law of thermodynamics|Originator of the concept of entropy|Entropy production|Disgregation|Ideal gas law|Kinetic theory of gases|Virial theorem|Clausius model|Clausius theorem|Clausius–Mossotti relation|Clausius–Clapeyron relation|Clausius–Duhem inequality}} |influences = |influenced = |prizes ={{ubl|Poncelet Prize (1882)|Copley Medal (1879)|ForMemRS (1868)}} |signature = Rudolf Clausius signature.svg }}

'''Rudolf Julius Emanuel Clausius''' ({{IPA|de|ˈʁuːdɔlf ˈklaʊzi̯ʊs}};<ref>{{cite book|author1=Dudenredaktion|last2=Kleiner|first2=Stefan|last3=Knöbl|first3=Ralf|year=2015|orig-year=First published 1962|title=Das Aussprachewörterbuch|trans-title=The Pronunciation Dictionary|url=https://books.google.com/books?id=T6vWCgAAQBAJ|language=de|edition=7th|location=Berlin|publisher=Dudenverlag|isbn=978-3-411-04067-4|pages=280, 744}}</ref><ref>{{cite book|last1=Krech|first1=Eva-Maria|last2=Stock|first2=Eberhard|last3=Hirschfeld|first3=Ursula|last4=Anders|first4=Lutz Christian|title=Deutsches Aussprachewörterbuch|trans-title=German Pronunciation Dictionary|url=https://books.google.com/books?id=E-1tr_oVkW4C&q=deutsches+ausspracheworterbuch|language=de|year=2009|publisher=Walter de Gruyter|location=Berlin|isbn=978-3-11-018202-6|pages=416, 884}}</ref> 2 January 1822 – 24 August 1888) was a German physicist and mathematician and is considered one of the central founding fathers of the science of thermodynamics.<ref>{{Citation | author=Cardwell, D.S.L. | title=From Watt to Clausius: The Rise of Thermodynamics in the Early Industrial Age | location=London | publisher=Heinemann | year=1971 | isbn=978-0-435-54150-7}}</ref> By his restatement of Sadi Carnot's principle known as the Carnot cycle, he gave the theory of heat a truer and sounder basis. His most important paper, "On the Moving Force of Heat",<ref name="Theory of Heat"/> published in 1850, first stated the basic ideas of the second law of thermodynamics. In 1865 he introduced the concept of entropy. In 1870 he introduced the virial theorem, which applied to heat.<ref>{{cite journal | last = Clausius | first = RJE | year = 1870 | title = On a Mechanical Theorem Applicable to Heat | journal = Philosophical Magazine |series=4th Series | volume = 40 | pages = 122–127}}</ref>

==Life== Clausius was born in Köslin (now Koszalin, Poland) in the Province of Pomerania in Prussia. His father was a Protestant pastor and school inspector,<ref>Emilio Segrè (2012). ''From Falling Bodies to Radio Waves: Classical Physicists and Their Discoveries''. Courier Dover Publications. p. 228</ref> and Rudolf studied in the school of his father. In 1838, he went to the Gymnasium in Stettin. Clausius graduated from the University of Berlin in 1844 where he had studied mathematics and physics since 1840 with Gustav Magnus, Peter Gustav Lejeune Dirichlet, and Jakob Steiner. He also studied history with Leopold von Ranke. During 1848, he got his doctorate from the University of Halle on optical effects in Earth's atmosphere. In 1850 he became professor of physics at the Royal Artillery and Engineering School in Berlin and Privatdozent at the Berlin University. In 1855 he became professor at the ETH Zürich, the Swiss Federal Institute of Technology in Zürich, where he stayed until 1867. During that year, he moved to Würzburg and two years later, in 1869 to Bonn.<ref>{{cite web |title=Rudolf Clausius, Prof. Dr. |url=https://www.physik.uzh.ch/de/institut/emeriti/RudolfClausius.html |website=physik.uzh.ch |publisher=Universität Zürich |access-date=18 June 2021 |language=de}}</ref>

In 1870 Clausius organized an ambulance corps in the Franco-Prussian War. He was wounded in battle, leaving him with a lasting disability. He was awarded the Iron Cross for his services.

His wife, Adelheid Rimpau died in 1875, leaving him to raise their six children. In 1886, he married Sophie Sack, and then had another child. Two years later, on 24 August 1888, he died in Bonn, Germany.<ref name="Cropper2004">{{cite book|first=William H.|last=Cropper|title=Great Physicists: The Life and Times of Leading Physicists from Galileo to Hawking|chapter-url=https://books.google.com/books?id=UqbxZpELwHYC&pg=PA93|access-date=25 March 2014|year=2004|publisher=Oxford University Press|isbn=978-0-19-517324-6|pages=93–105|chapter=The Road to Entropy Rudolf Clausius}}</ref>

==Work== Clausius's PhD thesis concerning the refraction of light proposed that we see a blue sky during the day, and various shades of red at sunrise and sunset (among other phenomena) due to reflection and refraction of light. Later, Lord Rayleigh would show that it was in fact due to the scattering of light.

His most famous paper, ''Ueber die bewegende Kraft der Wärme'' ("On the Moving Force of Heat and the Laws of Heat which may be Deduced Therefrom")<ref>{{cite journal | last=Clausius |first=R. | title =Ueber die bewegende Kraft der Wärme und die Gesetze, welche sich daraus für die Wärmelehre selbst ableiten lassen |url=http://gallica.bnf.fr/ark:/12148/bpt6k15164w/f518.table | journal =Annalen der Physik | volume =79 |issue=4 | pages=368–397, 500–524| year =1850 | doi=10.1002/andp.18501550403|bibcode = 1850AnP...155..500C |hdl=2027/uc1.$b242250 | hdl-access=free}}. See English Translation: [https://archive.org/details/londonedinburghd02lond On the Moving Force of Heat, and the Laws regarding the Nature of Heat itself which are deducible therefrom]. Phil. Mag. (1851), series 4, '''2''', 1–21, 102–119. Also available on [https://books.google.com/books?id=JbwdWbbM1KgC&pg=RA1-PA1 Google Books].</ref> was published in 1850, and dealt with the mechanical theory of heat. In this paper, he showed there was a contradiction between Carnot's principle and the concept of conservation of energy. Clausius restated the two laws of thermodynamics to overcome this contradiction. This paper made him famous among scientists. (The third law was developed by Walther Nernst, during the years 1906–1912).

Clausius's most famous statement of the second law of thermodynamics was published in German in 1854,<ref>{{cite journal|last=Clausius|first=R.|title=Ueber eine veränderte Form des zweiten Hauptsatzes der mechanischen Wärmetheoriein|journal=Annalen der Physik und Chemie|year=1854|volume=93|issue=12|pages=481–506|url=http://gallica.bnf.fr/ark:/12148/bpt6k15178k/f499.image|access-date=25 June 2012|doi=10.1002/andp.18541691202|bibcode=1854AnP...169..481C}}</ref> and in English in 1856.<ref>{{cite journal|last=Clausius|first=R.|title=On a Modified Form of the Second Fundamental Theorem in the Mechanical Theory of Heat|journal=Phil. Mag.|date=August 1856|volume=12|series=4|issue=77|pages=81–98|url=https://archive.org/stream/londonedinburghd12lond#page/80/mode/2up|access-date=25 June 2012|doi=10.1080/14786445608642141}}</ref> {{blockquote | Heat can never pass from a colder to a warmer body without some other change, connected therewith, occurring at the same time.}}

During 1857, Clausius contributed to the field of kinetic theory after refining August Krönig's very simple gas-kinetic model to include translational, rotational and vibrational molecular motions. In this same work he introduced the concept of 'Mean free path' of a particle.<ref>{{Citation | author=Clausius, R. | title =Über die Art der Bewegung, die wir Wärme nennen | url =http://gallica.bnf.fr/ark:/12148/bpt6k15185v/f371.table | journal =Annalen der Physik | volume =100 | issue =3 | pages =353–379 | year =1857|doi=10.1002/andp.18571760302 |bibcode = 1857AnP...176..353C }}</ref><ref>{{Citation | author=Clausius, R. | title =Ueber die Wärmeleitung gasförmiger Körper | url =http://gallica.bnf.fr/ark:/12148/bpt6k15200x/f13.table | journal =Annalen der Physik | volume =115 | issue =1 | pages =1–57 | year =1862 |doi=10.1002/andp.18621910102 |bibcode = 1862AnP...191....1C }}</ref><ref>Clausius, R. (1864), [http://gallica.bnf.fr/notice?N=FRBNF37278069 ''Abhandlungen über die Mechanische Wärmetheorie'']. Electronic manuscript from the Bibliothèque nationale de France.</ref>

Clausius deduced the Clausius–Clapeyron relation from thermodynamics. This relation, which is a way of characterizing the phase transition between two states of matter such as solid and liquid, had originally been developed in 1834 by Émile Clapeyron.<gallery> File:Clausius-1-1.jpg|1864 edition of Clausius's ''Abhandlungen über die mechanische Wärmetheorie'', volume I File:Clausius-1-2.jpg|Title page of an 1864 edition of Clausius's ''Abhandlungen über die mechanische Wärmetheorie'', volume I File:Clausius-2-1.jpg|1879 English translation of Clausius's ''The Mechanical Theory of Heat'' File:Clausius-2-2.jpg|Title page of an 1879 English translation of Clausius's ''The Mechanical Theory of Heat'' </gallery>

===Entropy=== {{Main|History of entropy}}{{See also|History of thermodynamics#Rudolf Clausius}} In 1865, Clausius gave the first mathematical version of the concept of entropy, and also gave it its name.<ref name="Cropper2004"/> Clausius chose the word because the meaning (from Greek ἐν ''en'' "in" and τροπή ''tropē'' "transformation") is "''content transformative''" or "''transformation content''" ("''Verwandlungsinhalt''").<ref name="Theory of Heat">{{cite book|last=Clausius|first=R.|title=The Mechanical Theory of Heat – with its Applications to the Steam Engine and to Physical Properties of Bodies|year=1867|publisher=John van Voorst|location=London|url=https://archive.org/details/mechanicaltheor04claugoog|quote=editions:PwR_Sbkwa8IC.|access-date=19 June 2012}} Contains English translations of many of his other works.</ref><ref>{{Citation | author=Clausius, R. | title =Ueber verschiedene für die Anwendung bequeme Formen der Hauptgleichungen der mechanischen Wärmetheorie | url =http://gallica.bnf.fr/ark:/12148/bpt6k152107/f369.table | journal =Annalen der Physik | volume =125 | issue =7 | pages =353–400 | year =1865 |doi=10.1002/andp.18652010702|bibcode = 1865AnP...201..353C }}</ref><ref name="Cooper">{{cite book|last1=Cooper|first1=Leon N.|title=An Introduction to the Meaning and Structure of Physics|date=1968|publisher=Harper|page=331}}</ref>{{Blockquote|text=I prefer going to the ancient languages for the names of important scientific quantities, so that they may mean the same thing in all living tongues. I propose, accordingly, to call S the entropy of a body, after the Greek word 'transformation'. I have designedly coined the word entropy to be similar to 'energy', for these two quantities are so analogous in their physical significance, that an analogy of denomination seemed to me helpful.|author=Rudolf Clausius|title=Ueber verschiedene für die Anwendung bequeme Formen der Hauptgleichungen der mechanischen Wärmetheorie}}He used the now abandoned unit 'Clausius' (symbol: '''Cl''') for entropy.<ref>{{Cite journal|last1=Huang|first1=Mei-Ling|last2=Hung|first2=Yung-Hsiang|last3=Chen|first3=Wei-Yu|date=1 October 2010|title=Neural Network Classifier with Entropy Based Feature Selection on Breast Cancer Diagnosis|journal=Journal of Medical Systems|language=en|volume=34|issue=5|pages=865–873|doi=10.1007/s10916-009-9301-x|pmid=20703622|s2cid=6658005|issn=1573-689X}}</ref> :1 Clausius (Cl) = 1 calorie/degree Celsius (cal/°C) = 4.1868 joules per kelvin (J/K)

The landmark 1865 paper in which he introduced the concept of entropy ends with the following summary of the first and second laws of thermodynamics:<ref name="Theory of Heat" /> {{blockquote |The energy of the universe is constant.<br /> The entropy of the universe tends to a maximum.}}

Leon Cooper<ref name="Cooper" /> added that in this way he succeeded in coining a word that meant the same thing to everybody: nothing.

==Tributes== [[File:Prawa termodynamiki clausiusa pk.jpg|thumbnail|upright=1.1|Memorial stone in front of the Koszalin University of Technology in Poland, with the laws of thermodynamics as formulated by Clausius]] * Honorary Membership of the Institution of Engineers and Shipbuilders in Scotland in 1859.[http://www.iesis.org/honorary-fellows.html IESIS Institution of Engineers and Shipbuilders in Scotland] * Iron Cross of 1870 * Fellow of the Royal Society of London in 1868 and received its Copley Medal in 1879. * Member of the Royal Swedish Academy of Sciences in 1878. * Huygens Medal in 1870. * Foreign Member of the Accademia Nazionale dei Lincei in Rome in 1880 * Member of the German Academy of Sciences Leopoldina in 1880 * Poncelet Prize in 1883. * Honorary doctorate from the University of Würzburg in 1882. * Foreign Member of the Royal Netherlands Academy of Arts and Sciences in 1886.<ref>{{cite web|url=http://www.dwc.knaw.nl/biografie/pmknaw/?pagetype=authorDetail&aId=PE00004619 |title=R.J.E. Clausius (1822–1888) |publisher=Royal Netherlands Academy of Arts and Sciences |access-date=21 July 2015}}</ref> * Pour le Mérite for Arts and Sciences in 1888 * The lunar crater Clausius named in his honor. * Elected an honorary member of the Manchester Literary and Philosophical Society in 1886<ref>{{cite book | title = Memoirs and Proceedings of the Manchester Literary & Philosophical Society | series = Fourth Series | volume = II | date = 1889 | publisher = The Manchester Literary & Philosophical Society | location = Manchester | page = 1 }}</ref> * A memorial in his home town of Koszalin in 2009

==Publications== * {{cite book|last=Clausius|first=R.|title=The Mechanical Theory of Heat – with its Applications to the Steam Engine and to Physical Properties of Bodies|year=1867|publisher=John van Voorst|location=London|url=https://archive.org/details/mechanicaltheor04claugoog|quote=editions:PwR_Sbkwa8IC.}} English translations of nine papers.

==See also== *Hans Peter Jørgen Julius Thomsen, one of the founders of the thermochemistry.

==References== {{Reflist}}

==External links== {{wikiquote}} {{Commons category|Rudolf Clausius}} *[https://www.math.umd.edu/~lvrmr/History/Revival.html Revival of Kinetic Theory by Clausius] * {{MacTutor Biography|id= Clausius}} *{{Cite EB1911|wstitle=Clausius, Rudolf Julius Emmanuel}} *[https://www.ebsco.com/research-starters/history/clausius-and-second-law-thermodynamics EBSCO] * {{Gutenberg author | id=35970| name=Rudolf Clausius}} * {{Internet Archive author |sname=Rudolf Clausius}}

{{DEFAULTSORT:Clausius, Rudolf}} Category:1822 births Category:1888 deaths Category:People from Koszalin Category:Academic staff of ETH Zurich Category:Thermodynamicists Category:German military personnel of the Franco-Prussian War Category:19th-century German physicists Category:German fluid dynamicists Category:People from the Province of Pomerania Category:Recipients of the Iron Cross (1870) Category:Recipients of the Copley Medal Category:Recipients of the Pour le Mérite (civil class) Category:Humboldt University of Berlin alumni Category:Academic staff of the University of Bonn Category:Academic staff of the University of Würzburg Category:Foreign members of the Royal Society Category:Foreign associates of the National Academy of Sciences Category:Members of the Royal Netherlands Academy of Arts and Sciences Category:Members of the Royal Swedish Academy of Sciences Category:German theoretical physicists Category:Prussian Army personnel Category:German fellows of the Royal Society