Rudolf Clausius

File:Rudolf Clausius.jpg

Rudolf Clausius - founding thermodynamicist and originator of the concept of entropy.

Rudolf Julius Emanuel Clausius (January 2, 1822 – August 24, 1888), was a German physicist and mathematician and is considered one of the central founders of the science of thermodynamics. By his restatement of Sadi Carnot's principle known as the Carnot cycle, he put the theory of heat on a truer and sounder basis. His most important paper, on the mechanical 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.

Life

Clausius was born in Köslin in the Province of Pomerania, the son of the Rev. C.E.G. Clausius, a clergyman and educator. He started his education at a school established by his father. After a few years, he went to the Gymnasium in Stettin. Clausius entered the University of Berlin in 1844 where he studied Mathematics and Physics with, among others, Heinrich Magnus, Johann Dirichlet and Jakob Steiner. He also studied history with Leopold von Ranke. He graduated in 1844, and earned a doctorate from the University of Halle in 1847 with a dissertation on the optical effects of the earth's atmosphere.

Clausius's doctoral thesis on the refraction of light proposed that the blue sky observed during the day, and various shades of red at sunrise and sunset (among other phenomena) are due to reflection and refraction of light. Later, Lord Rayleigh would show that it was in fact due to the scattering of light, but regardless, Clausius used a far more mathematical approach than his predecessors.

Thermodynamics

Clausius became professor of physics at the Royal Artillery and Engineering School in Berlin in 1850, and privatdozent at the Berlin university.

His most famous paper, On the Moving Force of Heat and the Laws of Heat which may be Deduced Therefrom was published in 1850, and dealt with the laws governing the relationship between heat and mechanical work. In this paper, he noted that there was an apparent contradiction between the concept of conservation of energy championed by James Joule, Hermann Helmholtz and William Thomson, and Nicolas Léonard Sadi Carnot's principle outlined in a paper he published in 1824. Clausius restated the two laws of thermodynamics to overcome this contradiction. The first states that when heat is destroyed, an eqivalent amount of motive power is produced. The second notes that there is a maximum amount of motive power that can be produced in a process where heat moves from a hotter to a colder body. This paper gained him the attention of the scientific community, and is often considered as having established the field of thermodynamics on a firm footing.

Using these principles, 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.

In 1855 Clausius became professor at the Zürich Polytechnic, and in a paper written a year later, he clarified the conditions upon which he had earlier based the second law. Instead of relying on an argument denying the possibility of perpetual motion, he used a different axiom:

Heat can never pass from a colder to a warmer body without some other change, connected therewith, occurring at the same time. <<<Bricmont, J. 2001. Chance in physics: foundations and perspectives. Berlin: Springer. 29. ISBN 3540420568.>>>

Kinetic theory of gases

In 1857, Clausius contributed to the field of kinetic theory of gases, which is based on the assumption that a gas consists of small particles in rapid motion. These particles are usually interpreted as being the same as the chemical molecules of the particular gas under consideration. Clausius refined August Krönig's very simple gas-kinetic model to include not only motion of translation, but also of rotation and vibration. In 1858 he introduced a fundamental concept of the kinetic theory called the mean free path of a particle—the average distance a molecule travels before it collides with another molecule. He also introduced statistical arguments and probability into his calculations, something that had not been done by his predecessors. Clausius took into account the likelihood that molecules in a gas would be moving at many different speeds at different moments. Earlier formulae, including Joule's expression for the velocity of a gas molecule in 1848, were based on a simplified model that considered only the average velocity of the molecules.

Clausius's work was improved upon by James Clerk Maxwell, who not only vastly improved and applied the statistical arguments first introduced by Clausius, but also estimated the actual distance of the mean free path based on experiments on the rates of diffusion and viscocity for gases. Maxwell's calculation, made in 1860, was used by Josef Loschmidt in 1865 to derive the first estimate of the size of a molecule based on the kinetic theory.

In 1862, Clausius criticized some aspects of Maxwell's derivation of the velocity distribution of molecules in a gas, leading Maxwell to revise his original calculations in works published in 1866 and 1867.

Entropy

In 1864, Clausius published a version of his collected papers, and year later, introduced the word entropy into the lexicon of physicists, it being a quanity purely mathematical in character, but which is generally found to increase in any process involving heat transfer and the accompanying production of motive power. Clausius chose the word "entropy" because the meaning, from Greek, en+tropein, is content transformative or transformation content. Scientists, including Clausius, attempted to find a physical interpretation for this quantity, and it became a fundamental concept in all subsequent treatments of the subject.

In 1867, Clausius accepted a professorship in Würzburg and two years later, one at the University of Bonn.

Dispute with Boltzmann

At the outbreak of the Franco-Prussian war in 1870, he organized an ambulance corps, and was wounded in battle. This left him with a lasting disability. He was awarded the Iron Cross for his services. A year later, after returning to his research, he formulated a demonstration of the dynamical principles behind the second law of thermodynamics in a paper entitled On the reduction of the second law of thermodynamics to general mechanical principles. This had been done in 1866 by Ludwig Boltzmann, who commented rather condescendingly on Clausius's belated results:

"I think I have established my priority. At the end I wish to express my pleasure because an authority like Dr. Clausius contributes to the dissemination of the ideas contained in my papers on the mechanical theory of heat." <<<Bricmont, J. 2001. Chance in physics: foundations and perspectives. Berlin: Springer. 30. ISBN 3540420568.>>>

But the route Clausius used to arrive at his conclusions was somewhat different, and in Clausius's mind, superior, to that of Boltzmann. Clausius used a concept called disgregation as a starting point, and not entropy, as Boltzmann had done. He thus believed that he had achieved greater generality in his results.

Maxwell, however, saw the efforts of both scientists as misdirected, as he believed that the fundamental treatment of the kinetic theory involved a statistical component that had little to do with conventional mechanics.

Later work

In his treatment of the molecular explanation of the second law, Clausius announced the virial theorem, which states that the average kinetic energy of a system of molecules over time is simply related to the average potential energy of the system. This theorem found applications beyond the kinetic theory of gases, and is often applied in astronomical research where a system of mutually gravitating bodies is considered. <<<Kittel, Charles. 1958. Elementary statistical physics. New York: Wiley. 223.>>>

Clausius's wife, Adelheid Rimpham, died in childbirth in 1875, leaving him to raise their six children. He continued to teach, but had less time for research thereafter. In 1877, he explored a novel approach to the equations of electromagnetism, and derived a formula for the force acting between two charges moving relative to one another. Darrigol, Olivier. 2000. Electrodynamics from Ampère to Einstein. Oxford: Oxford University Press. 213-214. ISBN 0198505949.

Clausius died in Bonn on August 24, 1888.

Legacy

Clausius was the first to make a clear statement of the first and second laws of thermodynamics. He later pioneered the use of rudimentary statistics in an attempt to show how these laws can be explained by the kinetic theory of gases. His initial efforts in this direction were quickly overtaken by scientists who were perhaps more able to apply complex mathematics to the task. Maxwell, Boltzmann, later joined by J. Willard Gibbs, established the field of statistical mechanics on a firm footing.

This did not stop Clausius from continuing to be involved in the debate among scientists as to the nature of the first and second laws, nor did it prevent him from making major contributions, such as the virial theorem. He was, however, overshadowed, perhaps to an unreasonable degree, by his illustrious competitors. This may be because he eventually distanced himself from the statistical view those scientists championed. Clausius attempted to demonstrate the second law of thermodynamics by employing William Rowan Hamilton's elegantly formulated principle of least action, and insisted in a dynamical, and not a statistical, interpretation, another reason why he may have received less attention in the history of the subject than he deserved.

Still, that Clausius was the first to use the term entropy, an essential concept in thermodynamics, cannot be denied. His work has immortalized him in the various equations and concepts that bear his name and stamp.

Tributes

• He was elected a Fellow of the Royal Society of London in 1868 and received its Copley Medal in 1879.
• He received the Huygens Medal in 1870.
• He received the Poncelet Prize in 1883.
• He received an honorary doctorate from the University of Würzburg in 1882.
• The Clausius crater on the Moon was named in his honor.

Quotes

The following are two famous quotes made by Clausius in 1865:

“

The energy of the universe is constant.

”

“

The entropy of the universe tends to a maximum.

”

See also

• Thermodynamics

References

ISBN links support NWE through referral fees

<<We need at least 3 reliable references here, properly formatted.>>

• Leff, Harvey S., and Andrew F. Rex. 2003. Maxwell's demon 2 entropy, classical and quantum information, computing. Bristol: Institute of Physics. 58-70. ISBN 0585492379.
• Bricmont, J. 2001. Chance in physics: foundations and perspectives. Berlin: Springer. ISBN 3540420568.
• Purrington, Robert D. 1997. Physics in the nineteenth century. New Brunswick, N.J.: Rutgers University Press. 136-141. ISBN 0585039208.
• Kittel, Charles. 1958. Elementary statistical physics. New York: Wiley. 222-224.

External links

• Revival of Kinetic Theory by Clausius
• Clausius biography in The MacTutor History of Mathematics archive

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