Blog #14 - Rudolf Clausius and the Virial Theorem

Rudolf Clausius and the Virial Theorem 

Rudolf Clausius was a German born physicist and mathematician who forever changed the rules of thermodynamics, mathematics, and eventually astronomy with his findings regarding the way heat moved through systems and how it affected an amorphous term known as energy. Before serving in the Franco-Prussian war in 1870 and injuring himself (leading to a decrease in his ability to research) Clausius became one of the world's foremost scientists in the development of heat transfer and thermodynamics. Early in his career he developed a more sound mathematical model for the carnot cycle. Then in 1850 he published his landmark work On the Moving Force of Heat which alongside what would eventually be known as the Second Law of Thermodynamics Clausius published his work on the virial theorem.

In it's most simple form, the virial theorem is listed as:

Which states that the kinetic energy of a system is directly related to the potential energy of a system which can be represented by the force on the kth particle which is at a position r from a central location. This equation takes on many forms including electromagnetic versions, special relativity versions, and quantum mechanical versions. Overall the virial theorem helps relate the average kinetic energy over time in a system to the average potential energy over time of a system. This equation can be expanded to systems with many bodies in a variety of positions, coordinate planes, and physical situations.

With Clausius' ground breaking work, later developments such as Kepler's 3 Laws of Motion, electron movement within particles, and the discovery of dark matter were all formed. The scale of the virial theorem seems to hold for most scenarios and the beautifully simple equation has an incredibly impactful footprint on the history of physics and astronomy.