9 julio, 2024

Rudolf Clausius: who he was, biography and contributions to science

Who was Rudolf Clausius?

Rudolf Clausius (1822-1888) was a German physicist and mathematician who formulated the second law of thermodynamics and is considered by many to be one of the founders of thermodynamics.

Together with him, characters such as William Thomson and James Joule significantly developed this branch of science whose foundation is attributed to the Frenchman Sadi Carnot.

Clausius’s work had a strong impact on the development of theories proposed by other leading physicists. An example is the case of the theories of James Maxwell, who openly recognized the influence of Clausius in his own work.

The most relevant contributions of Rudolf Clausius were related to the results of his research on the effect of heat on different fluids and materials.

Biography of Rudolf Clausius

Birth and early years

Rudolf Clausius was born on January 2, 1822 in Köslin, in Pomerania, Germany. Rudolf’s father professed the Protestant faith and had a school; that was where this scientist got his first training from him.

Subsequently, he entered the gymnasium in the city of Stettin (written in German as szczecin) and there he continued part of his training.

university studies

In 1840 he entered the University of Berlin, from which he graduated four years later, in 1844. There he studied physics and mathematics, two disciplines in which Clausius proved to be quite adept from a very early age.

After this academic experience, Clausius entered the University of Halle, where he obtained a doctorate in 1847 thanks to work on the optical effects that are generated on planet Earth as a consequence of the existence of the atmosphere.

From this work, which had some flaws in terms of focus, it became clear that Clausius had clear gifts for mathematics and that his abilities responded perfectly to the field of theoretical physics.

Principles of thermodynamics

After obtaining his doctorate in 1850, Clausius obtained a position as professor of physics at the Royal School of Engineering and Artillery in Berlin; he was there until 1855.

In addition to this position, Clausius also practiced at the University of Berlin as a privatizeda professor who could give classes to the students, but whose fees were not granted by the university, but rather the students themselves were the ones who paid for these classes.

1850 was also the year that Rudolf Clausius published what would be his most important work: On the forces of motion caused by heat.

Teaching and kinetic theory

In 1855 Clausius changed gear and obtained a teaching position at the Swiss Federal Institute of Technology, based in Zurich.

In 1857 he focused on studying the field of kinetic theory; It was at this time that he began to experiment with the concept of the «mean free path of a particle».

This term refers to the distance that exists between two encounters, one after the other, of the molecules that make up a gas. This contribution was also very relevant to the field of physics.

Clausius was at the Swiss Federal Institute of Technology for several years, until 1867, and there he devoted himself to giving physics lessons. That same year he moved to Würzburg, where he also worked as a teacher.

In 1868 he obtained a membership in the Royal Society of London. He was teaching in Würzburg until 1869, the year in which he went on to teach Physics at the University of Bonn, in Germany. In this university he taught until the end of his life.

war participation

In the context of the Franco-Prussian War, Clausius was about 50 years of age. At that time he organized several of his students into a volunteer ambulance corps that served in that conflict, which took place between the years 1870 and 1871.

As a consequence of this heroic action, Clausius received the Iron Cross, thanks to the service he rendered to the German army.

And also thanks to this participation, Clausius had a war wound on his leg, which later caused him discomfort, present until the end of his life.


In 1870 Rudolf Clausius obtained the Huygens Medal and in 1879 he received the Copley Medal, an award given by the Royal Society of London to those who have made relevant contributions in the field of biology or physics.

In 1878 he was made a member of the Royal Swedish Academy of Sciences, and in 1882 he received an honorary doctorate from the University of Wüzburg.

In 1883 he received the Poncelet prize, an award granted by the French Academy of Sciences to all those scientists who have made significant contributions in the field of science in general.

Finally, one of the most momentous recognitions made to this German scientist is that a crater on the Moon was named after him: the Clausius crater.


Rudolf Clasius died on August 24, 1888 in Bonn, in his native Germany. Two years earlier, in 1886, he had married Sophie Stack.

In the last years of his life, he put research aside a bit to dedicate himself to his children; In addition, the wound suffered in the war did not allow him to move as easily as in other times.

His field of research at that time, electrodynamic theory, took a backseat due to all this context. Despite this, Clausius continued to teach at the university level until his death.

One advantage he had was that he was able to enjoy the approval given by the most important scientists of the time, such as William Thomson, James Maxwell and Josiah Gibbs, among many others.

These illustrious scientists and the science community in general recognized him at the time as the man who founded thermodynamics. Even today this discovery is recognized as the most important and transcendental.

Contributions of Rudolf Clausius

foundation of thermodynamics

Considered one of the fathers of thermodynamics, Clausius provided important bases for the development of its fundamental propositions.

Some relevant figures in physics claimed that it was the work of Clausius that ensured the foundations of thermodynamics with clear definitions and defined borders.

Clausius’s attention was focused on the nature of molecular phenomena. From the study of these phenomena resulted the propositions that he himself formulated about the laws of thermodynamics.

Contribution to the kinetic theory of gases

Clausius’s work on individual gas molecules was decisive in the development of the kinetic theory of gases.

This theory was developed by James Maxwell in 1859 based on the work of Clausius. It was criticized in principle by Clausius and thanks to these criticisms Maxwell updated his theory in 1867.

Clausius’s main contribution in this field was the development of a criterion to distinguish atoms and molecules, showing that gas molecules were complex bodies with moving constituent parts.

Second law of thermodynamics

Clausius was the one who introduced the term «Entropy» in thermodynamics and used this concept to study processes, both reversible and irreversible, in this area of ​​knowledge.

Clausius allowed the concept of entropy to be related to the concept of energy dissipation as “Siamese” concepts due to their close relationship.

This marked a substantial difference with similar concepts that tried to describe the same phenomena.

The concept of entropy, as Clausius proposed it, was little more than a hypothesis in his time. Eventually, Clausius was proven correct.

The Clausius Mathematical Method

One of Clausius’s contributions to science was the development of a mathematical method that played a crucial role in thermodynamics. This method was useful in its application to the mechanical theory of heat.

This contribution by Clausius is often overlooked, mainly due to the confusing way in which its author presented it.

However, many authors consider that these confusions were common among physicists and this is not a reason to dismiss it.

mechanical theory of heat

Clausius developed what was called the mechanical theory of heat. This was one of his most important contributions to thermodynamics.

The basis of this theory considered heat as a form of movement.

This allowed us to understand that the amount of heat needed to heat and expand the volume of a gas depends on the way in which said temperature and said volume change during the process.


Daub E. Entropy and Dissipation. Historical Studies in the Physical Sciences. 1970; 2(1970): 321–354.
Ketabgian T. (2017). The Energy of Belief: The Unseen Universe Spirit of Thermodynamics. In Strange Science (pp. 254–278).
Klein M. Gibbs on Clausius. Historical Studies in the Physical Sciences. 1969; 1(1969): 127–149.
Sciences AA Rudolf Julius Emanuel Clausius. Proceedings of the American Academy of Arts and Sciences. 1889; 24:458–465.
Wolfe E. Clausius and Maxwell’s Kinetic Theory of Gases. Historical Studies in the Physical Sciences. 1970; 2:299–319.
Yagi E. Clausius’s Mathematical Method and the Mechanical Theory of Heat. Historical Studies in the Physical Sciences. 1984; 15(1): 177–195.

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