book_cover_big.gifWhile the quantum mechanical framework was being developed after Plank’s discovery in 1901, physicists were wrestling with the dual character of light (wave or particle?). Thomas Young’s double slit experiment in 1803, where interference patterns were observed, seemed to show without doubt that light was a wave phenomenon. However, Planck’s interpretation of black body radiation as light quanta, followed by Einstein’s explanation of the photoelectronic effect, both contradicted the light-as-wave theory. Additionally, a shocking discovery was made by Compton in 1925. Compton found that when he let X-rays (a form of light with extremely short wavelengths) collide head-on with a bundle of electrons, the X-rays were scattered as if they were particles. This phenomenon became known as the “Compton scattering experiment.”

At about that time, French physicist Louis de Broglie combined two simple formulas: Plank’s light quanta expression (E = hν, with ν as the frequency) and Einstein’s famous energy‑mass equation (E = mc2). This led to another simple equation: λ = h/mc, with λ as wavelength. This equation really tells us that all matter has wave properties. However, since the mass, m, of most everyday visible objects is so large, their wavelengths are too small for us to notice any wave effect. But when we consider the small masses of atomic particles such as electrons and protons, their wavelengths become relevant and start to play a role in the phenomena we observe.

All this brought Erwin Schrödinger to the conclusion that electrons should be considered waves, and he developed a famous wave equation that very successfully described the behavior of electrons in a hydrogen atom. Schrödinger’s equation used a wave function to describe the probability of finding a rapidly moving electron at a certain time and place. In fact, the equation confirmed many ideas that Bohr used to build his empirical atom model. For instance, the equation correctly predicted that the lowest energy level of an atom could allow only two electrons, while the next level was limited to eight electrons, and so on. In the year 1933 Schrödinger was awarded the Nobel Prize for his wave equation.

Schrödinger had, as did Planck and Einstein, an extensive background in thermodynamics. From 1906 to 1910, he studied at the University of Vienna under Boltzmann’s successor, Fritz Hasenöhrl. Hasenöhrl was a great admirer of Boltzmann and in 1909 he republished 139 of the latter’s scientific articles in three volumes [Hasenöhrl, 1909]. It was through Hasenöhrl that Schödinger became very interested in Boltzmann’s statistical mechanics. He was even led to write of Boltzmann, “His line of thoughts may be called my first love in science. No other has ever thus enraptured me or will ever do so again [Schrödinger 1929].Later he published books, (Statistical Thermodynamics and What’s Life), and several papers on specific heats of solids and other thermodynamic issues. [1]

 © 2009 Copyright John Schmitz


[1] Taken from “The Second Law of Life”:http://www.elsevierdirect.com/product.jsp?isbn=9780815515371

book_cover_big.gifThe human body can deliver lots of work. Consider, for instance, the athlete running a marathon, or the cyclist racing in the Tour de France. We also know that human body temperature is normally 37°C and that usually the environment is cooler, say 20°C. From this we could suggest that there is some resemblance between a heat engine, in which the body is the heat source, and the cooler environment could act as a heat sink. So let’s make a few simple calculations to see how closely the body resembles a heat engine. We know that the efficiency of a heat engine is determined by the temperatures of the heat source (the body temperature, Tbody = 310K) and the heat sink (the environmental temperature, Tsink  = 293K):

  Efficiency = [Tbody – Tsink]/Tbody = [310-293]/310 = 5.5%

 Thus, based on this temperature difference, the body would be able to achieve only 5.5% efficiency. Fortunately, scientific studies already have estimated the human body’s efficiency [1] in other ways. One study reasons that for an average man to produce 75 Watts of power, he will need to breathe about one liter of oxygen per minute. That liter of O2 is combusted in body cells to form carbon dioxide (CO2). It has also been determined that one liter of oxygen generates in this way about 300 Watts of power. Thus, we can conclude that the efficiency of the human “engine” is 75/300 = 25%. What causes the difference between the 5.5% efficiency as calculated above, and the 25% from the combustion determination? The explanation is that the human body cannot be considered a heat engine. The work is not generated in the same way as a steam engine, which directly transforms heat into work and lower-temperature waste heat. Instead, the human body is more like a fuel cell, where chemical energy is transformed into work (see also Whitt et. al.). For this kind of transformation, one obviously cannot use the efficiency formula of a heat engine.

 


[1] Whitt, F.R. and Wilson, D.G., Bicycling Science, MIT Press, Cambridge (1976)

book_cover_big.gifEinstein, like Planck, was very fluent in thermodynamic theory. Before 1905, Einstein published several papers on thermodynamic topics. One of these dealt with the fundamentals of thermodynamic theory [Einstein, 1903]. In this work, he studied whether the thermodynamic laws could be derived from a minimum amount of elementary assumptions. In 1905[1] he published a study in which he explained the photoelectric phenomenon. In that explanation, he not only used the results of Planck’s discrete energy packets for the black body radiation description, but fully acknowledged Boltzmann’s work, calling the expression S = k lnW  “the principle of Boltzmann.”

How highly Einstein regarded thermodynamics can be appreciated in the following quote:

 “A law is more impressive the greater the simplicity of its premises, the more different are the kinds of things it relates, and the more extended its range of applicability. (..) It is the only physical theory of universal content, which I am convinced, that within the framework of applicability of its basic concepts will never be overthrown.”

Einstein is best known for his invention of relativistic theory where time is no longer invariable[2]. Less remembered is that he searched his whole life for a theory that could unify the electromagnetic theory of Faraday and Maxwell on one hand, and the mechanical theory of the material particles of Newton on the other. For instance, Newton unified the observations of falling objects on earth with the fact that the earth and planets orbited the sun. He did this by using a single concept – namely, gravity – to explain both phenomena. Maxwell showed that seemingly quite different magnetic and electric observations could be described by a single theory of electromagnetic waves.

Around 1900 several outstanding physicists were working to explain Planck’s black body radiation. Planck had to introduce quantum theory to explain the experimental observation of the relationship between energy and wavelength. Einstein did not like this explanation, since it introduced yet another theory rather then unifying existing theories. Einstein was convinced that the answers could be found in thermodynamics, since this theory was based on structure-independent assumptions. Indeed, the special theory of relativity can be considered as a theory of principles analogous to the theory of thermodynamics [Klein, 1967].

What brought Einstein to his Special Theory of Relativity was his idea (conceived when he was 16 years old!) that the velocity of light must be the same for all observers, regardless of their respective speeds. He derived this conclusion from Maxwell’s electromagnetic equations and so kept his mind puzzled for a long time. His familiarity with thermodynamic theory also gave him a lot of inspiration. We can appreciate the challenge he found from two questions (taken from the publication of Martin Klein: “Thermodynamics in Einstein’s Thought”; Science, Vol 157, 509 (1967).  In essence what the classical thermodynamic accomplishment was, was to find mathematical expressions to the dilemma:

“What must the laws of nature be like so that it is impossible to construct a perpetual motion machine from either the first or the second kind?”

This question refers to the empirical fact that perpetual machines have never been observed that could violate the first principle that energy cannot be added or destroyed in an isolated system, or contradict the second principle that entropy always increases for spontaneous processes in, again an isolated system. Similarly, while developing the Special Theory of Relativity, Einstein wondered:

“What must the laws of nature be like so that there are no privileged observers?”

This question refers to the fact that the speed of light is the same for all observers, regardless of how fast their platform (a planet, a rocket, or an angel’s wings) is going. Therefore, one must derive expressions that will obey the principle of the constancy of light speed. In the same way that classical thermodynamics does not worry about why energy is conserved or why entropy increases, so Einstein didn’t try to puzzle out why the speed of light was constant, but merely accepted it as fact. Once accepted, the equations that describe this assumption are pretty straightforward!

Thus, the Special Theory of Relativity can be viewed as a theory of principles analogous to thermodynamics, and not as a constructive theory – as, for instance, gravity or the kinetic gas theory[3]. This means that no model is needed (like a model of an atom in the case of quantum mechanics) in either the Special Theory of Relativity or in thermodynamics, in order to arrive at the end results of both theories. The nice thing is that both theories can live on indefinitely with little risk of needing adjustment because of new insights. That is, in fact, what we’ve seen: both thermodynamics and the Special Theory of Relativity have not changed since their conception. [4]

Taken from:

“The Second Law of Life, Energy, Technology and the Future of Earth As We Know It”

http://www.elsevier.com/wps/find/bookdescription.cws_home/715243/description#description]

© Copyright 2009 John Schmitz

 


[1] 1905 was also the year Einstein published his Special Theory of Relativity, along with his articles on the photoelectric effect, the explanation of Brownian movement, and an article where he stated his famous equation, E=mc2. Because of Einstein’s overwhelming amount of important material in one year, 1905 is sometimes called Annus Mirabilis (the MiracleYear) [Bushev, Michael, “A Note on Einstein’s Annus Mirabilis”, Annales de la Fondation Louis de Broglie, Vol 25, no 3 (2000)].

[2] Einstein worked for several years at the Swiss patent office in Bern. During that period, because of the ongoing electrification and synchronization of clocks in the cities and across the countries, many patent applications came in that proposed all sort of ingenious ways to implement the synchronization. Because of that Einstein saw of course many proposals dealing with these kinds of problems and that may have very well triggered his interest in time, see also footnote 72, [Galison, Peter, Einstein’s Clocks, Poincaré’s Maps, Empires of Time; W.W. Norton & Company, Inc., New York (2004)].

[3] The kinetic gas theory starts with the existence of gas molecules, their continuous motion, and their finite dimensions. Then, by applying Newton’s mechanical kinetic theory it is possible to derive a relation among the macroscopic gas parameters: pressure, temperature, and volume. In this way a model can be built that has predictive and verifiable power.

[4] I feel that a few more words are needed here. Einstein himself pointed out in an article in 1919 in the Times of London that a theory of principle is based on empirical observations without the need for a particular model whereas a constructive model will first make assumptions about a fundamental structure then will built a mathematical description of that structure that hopefully will give relationships between the empirically observed parameters. In his own words: “Thus the science of thermodynamics seeks by analytical means to deduce necessary conditions, which separate events have to satisfy, from the universally experienced fact that perpetual motion is impossible”. Thus, classical thermodynamics can be regarded as a theory of principles, whereas statistical thermodynamics (i.e., Boltzmann approach) should be categorized as a constructive theory. In 1904 it was Poincaré who made a similar classification in scientific theories in his book The Value of Science.

book_cover_big.gifA few blogs ago,  I wrote about the life cycle analysis (LCA) of Compact Fluorescence Lamps (CFL’s,)[1]. CFL’s do “consume” during their life indeed about 5 times less electricity than incandescent light bulbs (and CFL’s live about 4 times longer). However, the manufacturing of CFL’s is much more complicated and therefore environmentally more demanding than classical bulbs and rightfully the question was raised that when you sum it all up would the environmental advantage still hold? After a careful and detailed LCA, a team of Australian researchers came with the answer: a big yes!

However,  it was pointed out by the researchers at the University of Ghent[2], Belgium, that one needs to look not just at the environmental impact (for  factors such as global warming, ozone depletion, toxics emission, acidification, etc.) of a certain product but also need to take into account  resources such as organic and inorganic, fuel and feedstock, renewable and non-renewable, energy and materials. It is here where thermodynamics kicks in using the concept of entropy[3] (as already suggested by Nicholas Georgescu-Roegen[4] quite a while ago). Entropy, can be used to describe the degradation of resources during the manufacturing and actually usage of products. One can say, very roughly, that the faster and further away from equilibrium a certain production process is done, the more energy is degraded and made not-available anymore to do further work. This is described by an increase in entropy and is non-reversible, i.o.w. high quality energy (such as energy contained in fossil fuels for that matter) is turned into low quality energy (heat).

This sort of analysis is then used to study the environmental impact of bio-foods versus large scale agriculture produced foods. And sure enough you can find situations where bio-foods (because of their poor yields or their transport over large distances) have more negative impact on the environment than have traditional produced foods. It was found[5] that if bio-beans are locally produced they are environmentally better than conventional produced beans. But when the beans needed to get transported from other areas to make it to our stores the balance can easily change and even reverse the situation! Bio-potatoes are always worse than conventional potatoes because they have such a lower yield per surface area land[6].

Therefore, before drawing conclusions on the impact of a given process or product on the environment or resources a careful evaluation (LCA) needs to be done. Such an evaluation is not a trivial matter at all and can only be done by qualified people.

 

© Copyright 2009, John Schmitz

 


[1] https://secondlawoflife.wordpress.com/2008/10/05/compact-fluorescence-lamps/

[2] http://pubs.acs.org/doi/abs/10.1021/es071719a

[3] As a matter of fact a concept of « exergy » is used but it has a very close relationship to entropy

[4] https://secondlawoflife.wordpress.com/2007/04/28/nicholas-georgescu-roegen/

[5] http://www.standaard.be/Artikel/Detail.aspx?artikelId=4I2B40SO

[6] See also: https://secondlawoflife.wordpress.com/2007/07/28/entropy-and-the-food-chain-part-i/ and https://secondlawoflife.wordpress.com/2007/08/22/entropy-and-the-foodchain-part-ii/

Nice review on www.libproject.net:

It is thought that of all the animals on planet earth, there is only one that can build a fire and has developed a realization of itself so that it can ask and answer the questions: Who am I? What is this fire that burns within me and before me? Why does the flame rise, and why am I warmed before this fire of time? John Schmitz’s book on thermodynamics is designed for the mature general science reader who has developed a general knowledge of the physical science literature that does not require mathematics beyond the arithmetic of writing a bank check. The overall objective of this short book is to introduce the reader to the thermodynamic concept of entropy and its many ramifications ranging from the micro-quantum world to the gross dynamic relativity construction of the universe. To prepare the reader for this entropy concept he lays down a foundation which closely follows the early historic development of thermodynamics. In preparations for reading this book one should first carefully read through the two-page table of contents. Dr. Schmitz makes statements and/or asks questions which he then answers in the text of the book drawing the reader into his web of understanding which demonstrates the beauty and his love of thermodynamics. One very quickly realizes that in writing this book the author has given quality time in considering carefully the answers to his questions. There are footnotes that are well worth reading which amplify selected points including historic events with specific dates. You will find yourself going back to the table of contents and index pages to pick up action items in your reading. Indeed, before you start reading this book you should browse the table of contents to determine the extent and usages of entropy.

Taken from: http://libproject.net/science/the-second-law-of-life.html

book_cover_big.gifRecently a Harvard University scientist, Alex Wissner-Gross, was quoted in TimesOnLine  that each computer search of the internet could produce as much as 7 gram of CO2 (the journalists of TimesOnLine compared that to boiling a kettle of water that would produce about 15 gram of CO2).[1] Google responded that the calculation was not right as an average search would only last about 0.2 second and that that would then equate to about 0.2 gram of CO2.[2] Clarifications later on revealed that Google referred to a one time search hit whereas Wissner-Gross referred to a complete search that encompasses several hits. Further more Google pointed out that the company has several environmental footprint reducing initiatives underway.

But it remains of course interesting to know how much energy the ICT infrastructure needs. It has been suggested[3] that this could be up to 2% of the world’s total greenhouse emissions (comparable to the amount produced by air transportation).

Closer to ourselves: who knows how much energy your PC at home takes up? Well I did not know the answer and I have monitored my PC  for a week. I simply hooked up a kWh meter between the outlet and the PC/printer/external HD/scanner assembly. The lucky number is: 6.3 kWh per week. At night I switch the PC off and during day time I put the PC in standby after 20 minutes of idle time. I also compared this figure with my freezer/fridge combination:

  1.             PC                                 6.3     kWh/week              327 kWh/year
  2.             Freezer/Fridge       38.1   kWh/week           1981  kWh/year

Then also good to know is that the electricity need of an average Belgian family is about 3500kWh per year.[4]

What we conclude from this that indeed PC’s and accessories do require a substantial amount of energy that is not small compared to other household appliances. A critical look at standby regimes and shutting down overnight seems to be wise.

© Copyright John Schmitz

 


[1] http://technology.timesonline.co.uk/tol/news/tech_and_web/article5489134.ece

[2] http://googleblog.blogspot.com/2009_01_01_googleblog_archive.html

[3] Recent Gartner report, see reference 1

[4] http://www.vreg.be/nl/04_prive/05_meteropneming/04_verbruik.asp

 

book_cover_big.gifAround 1900, Planck was an expert in classical thermodynamics and wrote many articles and books about that theory. The concept of entropy especially held his interest, but he published also in the fields of dilute solutions and thermoelectricity. Of course, being a time-oriented fellow, he was familiar with the results of Boltzmann’s works. However, being a physicist of the “old school,” he was raised without having the concept of atoms in his scientific toolkit. In 1891, for instance, he and Ostwald had a discussion with Boltzmann at a conference where Planck stated that thermodynamic methods without the incorporation of atomistic models were sufficient to explain those days’ physical observations. Also, Planck was not very pleased with the statistical approach of Boltzmann [1]. His main objection was that Boltzmann’s statistical approach allowed that the change of entropy for spontaneous processes could become negative (i.e., an entropy decrease), although at an extremely low probability (see Chapter 3 for more details on this topic).

But Planck was wrestling at the turn of the century with understanding black body radiation behavior. Since 1861, when Kirchhoff[2] first described a black body, the radiation behavior was studied and described by a slew of well-known physicists such as Wien, Stefan, and Boltzmann. However, all these attempts led only to a radiation law that had very limited applicability. The breakthrough in Planck’s understanding came when he started to use Boltzmann’s statistical approach. In fact, it was Planck who wrote the current well-known form of the Boltzmann equation, S = k lnW, in his famous 1901 article[3] . It was in this text that Planck proposed that the radiation might consist of small packets (quanten) of size hv. This was the beginning of quantum mechanical theory. Planck struggled a long time with his own thoughts, since they were so in contrast with the classical belief of continuous energy. For some time he saw his quanten approach merely as a mathematical trick, but slowly became convinced that energy in nature was indeed discrete, rather than a continuum. It also took some time before his ideas were accepted in the scientific community[4]. It was no less than Einstein who used the quanta principle to explain the photoelectronic effect, as we will see shortly.


[1] Flamm, Dieter, “Einführung zu Ludwig Boltzmanns Entropy und Wahrscheinlichkeit”, this is an introduction of Entropie und Warscheinlichkeit, 1872-1905 von Ludwig Boltzman in Ostwalds Klassiker der Exakten Wissenschaften, Band 286, Verlag Harri Deutsch, Frankfurt am Main (2000). This book is contains a nice compilation of the most important articles from Boltzmann in original version.

[2] It’s likely that Planck got his interest in black body radiation from Kirchhoff, who was his teacher. In 1889, he succeeded Kirchhoff as professor at the University of Berlin.

[3] Planck, Annalen der Physik 1901

[4] Interestingly, Planck once remarked that a new theory gets accepted not because its opponents become convinced, but because they eventually die and new generations of scientists, unhindered by historic baggage, simply assume the theory is true (provided that it is still supported by experimental facts)!

© Copyright 2009 John Schmitz