The Law of Conservation of Energy

Hermann von Helmholtz is a famous name in thermodynamics[1] although he also made famous inventions in the fields of ophthalmology, electrochemistry and acoustics. It was Helmholtz who formulated very clearly, using conclusions reached by Kelvin, Joule and Clausius earlier,  the existence of the law of conservation of energy or of “force” (as energy was called at that time) around 1850. In the winter of 1862, he delivered a series of lectures at Carlsruhe on the topic of the “Conservation of Force”. He started with an introduction in which he managed to elaborate on this theme without using any mathematical formula[2]. Below I will give a brief summary of the main points of this introduction (which can be found on numerous web sites[3]).

He starts of by showing that gravity, the most fundamental of all forces,  can be used to do work[4]. For instance a weight can drive a clock by sinking. Although the weight will have lost it capability to perform work when it reaches the floor, it will not loose its weight: gravity remains. The amount of work can then be determined by the weight times the distance travelled.

Heat can also produce work such as occurs in a steam engine. Here he recalls the point that heat must not be considered as a substance but merely as an movement of internal particles (realize that we are still about 50 years before atoms become widely accepted!). For quite a while it was considered that the amount of heat was constant (for instance, the required amount of heat required to melt a piece of ice is the same amount that one needs to extract when the resulting water is converted to ice again). However, he explains that as soon as heat is converted into work, that an equivalent amount of heat is destroyed. The relationship between heat and work was established by the work of Clausius and Joule. Many other examples exist where work is generated at the cost of something:

• a raised weight can do work but while doing that it must sink and no longer do work
• a stretched spring can do work but will become loose
• the velocity of a mass can do work but will eventually come to rest
• chemical forces (=energy) can do work but they will get exhausted
• electrical force can do work but will consume chemical or mechanical forces

Helmholtz concluded that all natural forces (energy) can do work but they are at the same time exhausted to the degree of work performed. He then formulated that the total quantity of all forces capable of doing work in the whole universe remains constant. He compared this with the laws of constant mass or constant chemical elements (both were of course to be found less constant after the theory of relativity and the discovery of radioactivity!!).

Finally he touches briefly on the topic of perpetual motion and states that force cannot be produced from nothing: something must be consumed. I strongly recommend reading Helmholtz’ introduction.

See also: https://secondlawoflife.wordpress.com/2007/12/28/the-origin-and-development-of-the-energy-principle/

Copyright © 2008 John Schmitz

---

[1] Hermann von Helmholtz (1821-1888) reported on July 23 in 1847 on the principle of conservation of energy and showed that he had acquired a deep understanding of this principle. He was, together with Rudolf Clausius, the founder of what was called the Berlin School of Thermodynamics where he succeeded Magnus as the director of the Physical Institute. The influence of this school on the development of thermodynamics was crucial. It is almost unbelievable how many famous scientists were connected to this school. To name a few: Walter Nernst, Max Planck, Albert Einstein, Erwin Schrödinger and Leo Szilard.

[2] Although Helmholtz himself had a very good knowledge of mathematics

[3] See for instance: http://www.bartleby.com/30/125.html

[4] Work is simply defined here as lifting a weight.

 

The Origin and Development of the Energy Principle

Today everybody knows that energy can not be created or destroyed. We know this principle as the law of conservation of energy  (or the First Law of thermodynamics). Today we use this law in many situations perhaps without always realizing this. However, there was a time that there was great confusion about what energy, work and heat exactly was and their relation. It was the German physician Mayer who first formulated in 1842 a statement that can be considered as the predecessor of today’s energy law. At the occasion of the 100th anniversary of Mayer’s discovery, a small (91 pages) book was published in 1943 by Prof. Jacob Clay, a physics professor at the university of Amsterdam, entitled: “Onstaan en ontwikkeling van het Energie Beginsel”[1] (the book is in Dutch and the title can be translated by “Origin and Development of the Energy Principle”). The book contains some interesting historical elaborations of how the energy law developed. Because the book is not so easy to get anymore, I will summarize the chapter where Clay describes how Mayer got to his energy law.

Julius Robert Mayer, born in 1814 in Heilbronn (Germany, not too far from the French border) who, after several world voyages, became a medical doctor in 1841 also in Heilbronn. He was probably driven to understand energy issues by the question how chemical energy was transformed in living beings to do things like work[2] and generate heat. Mayer got convinced that perpetual engines did not exist (“…. das mechanische Arbeit sich nicht aus Nichts erzeugen lasse.” translated as “mechanical work can not be created from nothing”). Also, while studying processes where changes happened (such as the decrease of velocity of moving bodies and the simultaneous appearance of heat) Mayer was searching for something that would be constant. His inspiration for the existence of a  constant factor came from his colleagues in chemistry who used the law of conservation of mass (formulated in 1789 by Antoine Lavoisier) quite successfully. Mayer observed that “lebende Kraft” (literally “living force” but nowadays what we call  that kinetic energy) could be transformed into heat[3]. In addition he noted that the amount of heat needed to warm a given quantity of gas was larger at constant volume (no work from the PDV term!) than when heated at constant pressure. This led him to formulate the equivalence of work (or energy) and heat and he made a first estimate of this equivalency factor (which today is known at 1 calorie = 4.184 Joule).

The contributions by Mayer were for quite some years neglected by the scientific community. One reason was that he did not very clearly present his thoughts[4]. In addition he had competition  from an English beer brewer: John Prescot Joule who arrived  -somewhat later though- to similar conclusions but who was better connected to institutes such as the French Scientific Academy[5].

However, from 1862 onwards Mayer’s work became more and more acknowledged and he won several prestigious awards underlining the importance of his contributions. In 1847 Hermann von  Helmholtz published his famous article entitled: “Ueber die Erhaltung der Kraft” (“On the conservation of energy”) and this can be seen as an important milestone of the development of the First Law of thermodynamics. I will come back to that article soon.

See also: https://secondlawoflife.wordpress.com/2008/03/24/the-law-of-conservation-of-energy/

Copyright © 2008  John Schmitz

---

[1] Prof. Dr. J. Clay, Onstaan en ontwikkeling van het energy-beginsel; N.V. Servire, The Hague (1943)

[2] With work we mean here the ability of a system to lift weights.

[3] This fact was actually already noted in 1798 by Count Rumford who observed that a lot of heat was generated in boring cannon barrels.

[4] He confused force and work for instance. Therefore, Johann Poggendorf, who was the editor of the Annalen der Physik, refused to place his article in 1841.

[5] The Academy published a letter from Joule on the energy topic in 1847 in their Comptes Rendus.