[juanrga]

I have just uploaded a new draft: International System of Units (SI)

http://juanrga.com/en/knowledge/a1112051134v1.html

After definition and a short historical introduction, I discuss the base units, the relevant derived units that receive special names, the SI and binary prefixes, and the Non-SI units accepted for use with the SI.

The draft finishes with a discussion of several relevant topics often ignored in usual textbooks and encyclopedias, such as coherence of the SI, difficulties with current definitions of the base units, political and economic issues behind the USA alternative spelling, and others. Notice that the International Union of Pure and Applied Chemistry (IUPAC) does not recommend USA official spellings.

Any comment, correction, suggestion is welcomed. Among the specific doubts that I have are the following ones:

I have read criticism to the role of the mole as SI basic unit, and some voices to eliminate the concept of mol outside of the SI and even of chemistry

Price, Gary (2010). "Failures of the global measurement system. Part 1: the case of chemistry". Accreditation and Quality Assurance 15 (7): 421–427.

Johansson, Ingvar (2010). "Metrological thinking needs the notions of parametric quantities, units, and dimensions.". Metrologia 47 (3): 219–230.

Cooper, G; Humphry, S (2010). "The ontological distinction between units and entities". Synthese. doi:10.1007/s11229-010-9832-1.

But, as noted in the draft, I fail to consider their criticism seriously, because I find many flaws in their (mostly philosophical) 'arguments'. It seems I am not alone and I have find a list of rebuttals to those 'arguments' in

de Bièvre, P.; Peiser, H.S. (1992). 'Atomic Weight'—The Name, Its History, Definition, and Units. Pure Appl. Chem. 64 (10): 1535–43.

Is some chemist aware of additional criticism or failures of the concept of mole?

In the draft I wrote:

Although becquerel is the preferred unit to be used in nuclear and radioscience; the units gray, sievert, and katal are admitted for reasons of safeguarding human health

Could some nuclear chemist or other to confirm this?

Thank you.

[juanrga]

I have just uploaded a new draft: Scientific notation

I could not find any decent reference on the history of scientific notation and it seems that nobody knows when the term «scientific notation» was invented. If you know something, please let me know.

In my presentation of this topic I ignored the typical sections about how multiply, sum... numbers in scientific notation, because I assumed that my audience knows how to multiply, sum... any real number {*}. If you disagree with my didactic, please let me know.

However, I have added two corrections to the Appendix A.1 Exponential notation in the textbook Chemistry, The Central Science. The first that exponential notation and scientific notation are not synonyms. The second that the coefficient a in scientific notation can be negative.

I have emphasized other advantages of scientific notation beyond being a compactly notation for very large or very small numbers. And I have also emphasized that «billion» does not mean 10⁹ for everyone. In my country, as in many others European countries, a billion is 10¹². I suppose this info must be relevant for USA readers.

I have also emphasized in this draft that zero number cannot be represented in scientific notation because the absolute value of the coefficient a is always larger than or equal to 1. That is, 0 x 10⁰ = 0 x 10¹ = ... is not scientific notation. I found this mistake about the zero in a known mathematical encyclopedia and I have corrected it in this draft.

{*} In my country, we know this kind of stuff already with 14-15 years.

[billnotgatez]

This is WIKI

it seems not to discuss the history

http://en.wikipedia.org/wiki/Scientific_notation

[juanrga]

This is WIKI

it seems not to discuss the history

http://en.wikipedia.org/wiki/Scientific_notation

Yes, neither the appendix A.1 in the chemistry textbook cited above does.

It is curious that scientific notation was a tool so standard that you can find it in calculators and, however, we cannot find any serious reference about its history, who invented it, when was used by the first time...

[juanrga]

I have uploaded a new draft: Scientific Constants

After a minimalist historical introduction --which explains why the symbol L is also recommended for the Avogadro constant--,  there is a definition of scientific constant, kind of scientific constants (fundamental vs derived, defined vs measured), some examples, and a long table with last CODATA values.

The table includes the numerical value of the Faraday constant to be used in coulometric chemical measurements when the relevant current is measured in terms of representations of the volt and ohm based in the Josephson and quantum Hall effects.

There is little room for improvement in this topic. However, I have emphasized that c₀ is a scalar that measures speed, not velocity (a vector); that some so-named astrophysical constants are not constants, but time-varying parameters; and why the recommended value of true constants can vary in time.

Notice that the recommended value for Avogadro constant in 2006 is not the value recommended today. Chemistry textbooks need to be updated.

Comments and corrections are welcomed.

[fledarmus]

This is WIKI

it seems not to discuss the history

http://en.wikipedia.org/wiki/Scientific_notation

Yes, neither the appendix A.1 in the chemistry textbook cited above does.

It is curious that scientific notation was a tool so standard that you can find it in calculators and, however, we cannot find any serious reference about its history, who invented it, when was used by the first time...

I think you will find that the history of scientific notation corresponds with the history of the slide rule.

This device allowed for mechanical calculation of a lot of mathematical operations including multiplication and division, natural logs and exponents, and trig functions. However, it only gave numbers between 1 and 10. Scientific notation put every number into a form that was between 1 and 10 - you did the number calculation on the slide rule, and the exponent calculations either in your head or on paper.

When all the calculations were being done on a slide rule, it was much easier just to leave all the numbers in scientific notation than to convert them back and forth.

[juanrga]

I think you will find that the history of scientific notation corresponds with the history of the slide rule.

This device allowed for mechanical calculation of a lot of mathematical operations including multiplication and division, natural logs and exponents, and trig functions. However, it only gave numbers between 1 and 10. Scientific notation put every number into a form that was between 1 and 10 - you did the number calculation on the slide rule, and the exponent calculations either in your head or on paper.

When all the calculations were being done on a slide rule, it was much easier just to leave all the numbers in scientific notation than to convert them back and forth.

Thank you for this interesting comment.

[juanrga]

The second improved version of my paper Non-redundant and natural variables definition of heat valid for open systems is now available for download (PDF file).

Although an unambiguous definition of heat is available in the classical thermodynamics for closed systems, the question of how best to define heat transfer in open systems is not yet settled. After an introduction to the basic formalism of modern thermodynamics, this article reviews the different definitions of heat for open systems used by Callen, Casas-Vázquez, DeGroot, Fox, Haase, Jou, Kondepudi, Lebon, Mazur, Misner, Prigogine, Smith, Thorne, and Wheeler, emphasizing their main pros and cons. A posterior section deals with the main objective of this article and introduces a new definition of heat that avoids the main difficulties of the existent definitions, providing us (i) a complete distinction between open and closed systems, (ii) high non-redundancy, (iii) natural variables for the thermodynamic potentials, and (iv) a sound and complete but intuitive generalization of classical thermodynamic expressions. The application of the new definition of heat to termoelectricity is used for showing new advantages over the previous definitions, including corrections to misleading and contradictory expressions for the density of production of entropy obtained by other authors for solid conductors. Finally, some consequences of this generalization of classical thermodynamic expressions to open systems are given and misleading recent comments done in black hole literature are corrected.

Using the new definition of heat, the first law of classical thermodynamics is generalized to open systems as
$$\mathrm{d} E = \delta Q + \delta W + \sum_k \left( \frac{T S}{N_k} \right) \delta_e N_k$$
and the second law as
$$\mathrm{d} S \geq \frac{\delta Q}{T} + \sum_k \left( \frac{S}{N_k} \right) \delta_e N_k .$$
Experts readers will notice that the term ##\sum_k (S/N_k) \delta_e N_k## in the generalization of the second law is similar to the term ##\mathrm{d}_{matter}S## introduced by the Brussels school leaded by Prof. Prigogine; however, the new definition has several advantages, specially for systems in presence of fields (e.g., electrochemical cells).

Comments, mistakes, etc. are welcomed.

[juanrga]

I have uploaded a new draft: Axiomatic systems

It includes the definition and main elements of an axiomatic system, a bit of history, examples of axiomatic systems in physics, and more.

The presentation is made from the point of view of a scientist. That is, I do not present axiomatic systems per se, but axiomatic systems as an invaluable tool for the scientist.

Physicists have a strong tendency to axiomatize their discipline. However, the lack of axiomatization in chemistry is, in my opinion, one of its weak points. This weakness is not only present at research level, but at educative level.

For instance, textbooks in quantum chemistry (e.g., Levine) present the axioms (postulates) of quantum mechanics; however, textbooks in chemical thermodynamics still present the subject in a 19th-century-style via heat engines, early empirical laws, and all that ancient stuff.

The modern axiomatic formulation of thermodynamics is by far better. I give in this draft advantages of the axiomatic formulations of scientific theories.

An example of the advantage of an axiomatic formulation was shown recently in this forum. Someone asked why does one have to use external p to calculate work. In my first response to the OP, I stated that I found the use of external pressure disturbing: "For me p would be the pressure of the system".

I did not explain then why I was disturbed. This is because the Tisza & Callen axioms of thermodynamics imply that p has to be the pressure of the system or otherwise the thermodynamic theory is internally inconsistent.

In all the chemical thermodynamic and physical chemistry textbooks that I know thermodynamics is presented in a non-axiomatic form. And all those textbooks claim that p in thermodynamic work has to be external pressure. The contradiction is evident!

In subsequent responses to the OP in why does one have to use external p to calculate work I posted my finding and study of the Chemical education paper «Thermodynamic Calculation of Work for some irreversible processes», Journal of Chemical Education 2005: 82(6), 874-877 by Gary L. Bertrand.

Where Bertrand presents two recent experiments that disagree with the usual formula
$$W=-\int P_{ext}\mathrm{d}V$$
found in chemical literature, whereas ##W=-\int P_{gas}\mathrm{d}V## gives the correct results in agreement with experiments. He reports that only a textbook in chemical engineering gives the correct expression for the work ##W=-\int P_{gas}\mathrm{d}V##.

As most of you, I was also said by my teachers of chemical thermodynamic and physical chemistry that p is the external pressure. They were wrong. Now I understand better the Tisza & Callen axiomatic approach to thermodynamics and I am ready to say that this old dispute about what is the correct definition of work, --a fundamental question which has been debated by many people (see the introduction in Bertrand paper and the references cited) during years--, could be solved in five minutes by the axiomatic formulation of thermodynamics described in the celebrated textbook by Callen, without any need to perform expensive experiments as those reported by Bertrand in his recent paper.

I would like to know what other chemists think about axiomatic systems and if you think that the disciplines of chemistry would be axiomatized or not.

As always comments and corrections to the draft are welcomed.

[juanrga]

New draft The hierarchical structure of matter is ready.

I gave some examples of entities: elementary particle, nuclei, atom, molecule, complex, macromolecule, cell...

I have avoided nuclide, because as explained in this thread, it is confusing and, indeed, different authors give completely different meanings to this term. Recently, I have found another textbook that contradicts the IUPAC's definition of nuclide. The textbook is Modern Nuclear Chemistry by Loveland, Morrissey & Seaborg.

I have also avoided the IUPAC term molecular entity, which in my opinion is also confusing {*} and maybe unneeded. I follow closely IUPAC conventions in the rest of the article and in the other articles.

The article includes a presentation of Jean Marie Lehn's integrationism and the death of reductionism, Prigogine's work in extension of particle physics, emergent properties, and Anderson's More is different. I chose a methane molecule as example of emergence. A methane molecule is more than a collection of quarks and electrons!

The beautiful protein-art is from Rutgers (with permission).

I have included the discussion in this other thread for criticizing physicists' belief that water is made of H₂O molecules. As virtually any chemist student know water also contains H₃O⁺ and OH⁻ ions, and those are very important to understand its chemical properties.

Please correct me in anything that you find wrong, incomplete or where you merely disagree.

{*} E.g. a molecule is defined as different than an atom, because IUPAC define molecule as an "electrically neutral entity consisting of more than one atom", but an atom is considered a molecular entity by the IUPAC. The conclusion is that atoms are not molecules but are molecular entities. This IUPAC terminology is, at best, strange.

[juanrga]

I have just uploaded the new draft Open, closed, and isolated systems

The part discussing the terminology used in atoms in molecules theory will be changed following suggestions by Prof. Cherif F. Matta.

I would also add that a well-know chemist has confirmed me that one of the drafts cited above in this thread will be used in a future new edition of a standard chemistry textbook. Therefore this work is not void  

[juanrga]

The draft about Open, closed, and isolated systems has been updated and moved to here.

It includes new references, extended discussion of conservation laws and improvement made by Prof. Cherif F. Matta regarding the terminology used in the atoms in molecules theory. E.g. an atom is defined as a proper open system...

I have just uploaded a new draft Stochastic scientific quantities and states

It includes the usual material plus recent material (as stochastic Schrödinger equations), which is not usually covered in the quantum chemical literature.

Again comments, suggestions, and criticism are welcomed.

[juanrga]

This is a discussion about scientific states (physical, chemical, biological...) which is not usual in textbook and other resources (an exception seems to be quantum mechanics textbooks, which devote some space to discuss what is a quantum state).

Among material not covered in basic textbooks and encyclopedias I would emphasize that I introduce a hierarchical description of states first developed by Joel Keizer; a rejection of the "Bayesian interpretation of physics" over the basis of recent advances in statistical dynamics; and the proposal for substituting the term "physical states of matter" by the more adequate and precise term "phase of matter" (I include a link to a NASA page that is already using the new terminology). I also emphasize that p in thermodynamics state (T,p,N) is the pressure of the system (many textbooks got this wrong and claim that p is the pressure of surrounds).

Comments, doubts, and suggestions to include material are welcomed.

I am specially interested in your opinion about abandoning the ambiguous terms "state of matter" and "physical state of matter".

[juanrga]

The work Eight Assumptions of Modern Physics Which Are Not Fundamental has been selected Finalist in the FQXI Essay Contest. Physical chemists and those with a predilection by foundational questions would check the parts about quantum theory, because the Schrödinger equation is only an approximation to a more general quantum formulation. Precisely the nonlinear extension of the Schrödinger equation solves several paradoxes of theoretical chemistry such as the paradox of the molecular shape.

Regarding the online free encyclopedia, a new article about descriptive science is just available.