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Entropy
This isn’t a webpage or lesson plan, at this point.
Right now it is just my online notes on entropy
Main ideas
two types of entropy
Rod Vance, on Physics.Stackexchange.com, writes:
There are two definitions of entropy, which physicists believe to be the same (modulo the dimensional Boltzman scaling constant) and a postulate of their sameness has so far yielded agreement between what is theoretically foretold and what is experimentally observed. There are theoretical grounds, namely most of the subject of statistical mechanics, for our believing them to be the same, but ultimately their sameness is an experimental observation
- (Boltzmann / Shannon): Given a thermodynamic system with a known macrostate, the entropy is the size of the document, in bits, you would need to write down to specify the system’s full quantum state. Otherwise put, it is proportional to the logarithm of the number of full quantum states that could prevail and be consistent with the observed macrostate. Yet another version: it is the (negative) conditional Shannon entropy (information content) of the maximum likelihood probability distribution of the system’s microstate conditioned on the knowledge of the prevailing macrostate;
- (Clausius / Carnot): Let a quantity δQδQ of heat be input to a system at temperature TT. Then the system’s entropy change is δQTδQT. This definition requires background, not the least what we mean by temperature; the well-definedness of entropy (i.e. that it is a function of state alone so that changes are independent of path between endpoint states) follows from the definition of temperature, which is made meaningful by the following steps in reasoning: (see my answer here for details). (1) Carnot’s theorem shows that all reversible heat engines working between the same two hot and cold reservoirs must work at the same efficiency, for an assertion otherwise leads to a contradiction of the postulate that heat cannot flow spontaneously from the cold to the hot reservoir. (2) Given this universality of reversible engines, we have a way to compare reservoirs: we take a “standard reservoir” and call its temperature unity, by definition. If we have a hotter reservoir, such that a reversible heat engine operating between the two yields TT units if work for every 1 unit of heat it dumps to the standard reservoir, then we call its temperature TT. If we have a colder reservoir and do the same (using the standard as the hot reservoir) and find that the engine yields TT units of work for every 1 dumped, we call its temperature T−1T−1. It follows from these definitions alone that the quantity δQTδQT is an exact differential because ∫badQT∫abdQT between positions aa and bb in phase space must be independent of path (otherwise one can violate the second law). So we have this new function of state “entropy” definied to increase by the exact differential dS=δQ/TdS=δQ/T when the a system reversibly absorbs heat δQδQ.
As stated at the outset, it is an experimental observation that these two definitions are the same; we do need a dimensional scaling constant to apply to t
http://physics.stackexchange.com/questions/131170/what-is-entropy-really
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textbooks
apps
? Phet
microstates
External links
Entropy Sites — A Guide. Frank L. Lambert, Professor Emeritus
Entropy (order and disorder) (Wikipedia)
What Is Entropy? By Johannes Koelman
What is entropy? Thermodynamics of chemical equilibrium
Learning Standards
2016 Massachusetts Science and Technology/Engineering Curriculum Framework
High School Chemistry
PS3.A and 3.B Definition and conservation of energy and energy transfer
HS-PS3-4b. Provide evidence from informational text or available data to illustrate that the transfer of energy during a chemical reaction in a closed system involves changes in energy dispersal (enthalpy change) and heat content (entropy change) while assuming the overall energy in the system is conserved.
Mass Science Curriculum 2006
6. States of Matter, Kinetic Molecular Theory, and Thermochemistry
Central Concepts: Gas particles move independently of each other and are far apart. The behavior of gas particles can be modeled by the kinetic molecular theory. In liquids and solids, unlike gases, particles are close to each other. The driving forces of chemical reactions are energy and entropy. The reorganization of atoms in chemical reactions results in the release or absorption of heat energy.
6. States of Matter, Kinetic Molecular Theory, and Thermochemistry
6.5 Recognize that there is a natural tendency for systems to move in a direction of disorder or randomness (entropy).
SAT Subject Test in Chemistry
Thermochemistry: Including conservation of energy, calorimetry and specific heats, enthalpy (heat) changes associated with phase changes and chemical reactions, heating and cooling curves, entropy.
AP Chemistry
5.E: Chemical or physical processes are driven by a decrease in enthalpy or an increase in entropy, or both.
5.A.1: Temperature is a measure of the average kinetic energy of atoms and molecules.
5.E: One of the most powerful applications of thermodynamic principles is the ability to determine whether a process corresponding to a physical or chemical change will lie toward the reactant or product side when the process reaches a steady equilibrium state. The standard change in Gibbs free energy, ΔG° = ΔH° – TΔS°, is used to make this determination. If ΔG° < 0, then products are favored at equilibrium, and the forward process is considered to be “thermodynamically favored.” Conversely, if ΔG° > 0, then reactants are favored at equilibrium, and the reverse process is considered to be “thermodynamically favored.” Both the enthalpy change (ΔH°) and the entropy change (ΔS°) are closely related to the structure and nature of the components of the system; for this reason, it is often possible to make qualitative determinations concerning the sign (and magnitude) of ΔG° without explicit calculation…. Importantly, in biochemical systems, some reactions that oppose the thermodynamically favored direction are driven by coupled reactions. Thus, a cell can use energy to create order (a direction that is not thermodynamically favored) via coupling with thermodynamically favored reactions….
5.E.1: Entropy is a measure of the dispersal of matter and energy.
5.E.1: a. Entropy may be understood in qualitative terms rather than formal statistical terms. Although this is not the most rigorous approach to entropy, the use of qualitative reasoning emphasizes that the goal is for students to be able to make predictions about the direction of entropy change, ΔS°, for many typical chemical and physical processes.
b. Entropy increases when matter is dispersed. The phase change from solid to liquid, or from liquid to gas, results in a dispersal of matter in the sense that the individual particles become more free to move, and generally occupy a larger volume. Another way in which entropy increases in this context is when the number of individual particles increases when a chemical reaction precedes whose stoichiometry results in a larger number of product species than reacting species. Also, for a gas, the entropy increases when there is an increase in volume (at constant temperature), and the gas molecules are able to move within a larger space.
c. Entropy increases when energy is dispersed. From KMT, we know that the distribution of kinetic energy among the particles of a gas broadens as the temperature increases. This is an increase in the dispersal of energy, as the total kinetic energy of the system becomes spread more broadly among all of the gas molecules. Thus, as temperature increases, the entropy increases.
5.E.2: a. For the purposes of thermodynamic analysis in this course, the enthalpy and the internal energy will not be distinguished.
b. The phrase “thermodynamically favored” means that products are favored at equilibrium (K > 1).
c. Historically, the term “spontaneous” has been used to describe processes for which ΔG° < 0. The phrase “thermodynamically favored” is used here to avoid misunderstanding and confusion that can occur because of the common connotation of the term “spontaneous,” which students may believe means “immediately” or “without cause.”
d. For many processes, students will be able to determine, either quantitatively or qualitatively, the signs of both ΔH° and ΔS° for a physical or chemical process. In those cases where ΔH° < 0 and ΔS° > 0, there is no need to calculate ΔG° in order to determine that the process is thermodynamically favored.
e. As noted below in 5.E.5, the fact that a process is thermodynamically favored does not mean that it will proceed at a measurable rate.
f. Any process in which both ΔH° > 0 and ΔS° < 0 are not thermodynamically favored, (ΔG° > 0) and the process must favor reactants at equilibrium (K < 1). Because the signs of ΔS° and ΔH° reverse when a chemical or physical process is reversed, this must be the case.
http://www.n-union.k12.oh.us/Downloads/AP%20Chem%20Curriculum%20Map.docx
Four new elements named by IUPAC
IUPAC is naming the four new elements nihonium, moscovium, tennessine, and oganesson.
Nihonium and symbol Nh, for the element 113,
Moscovium and symbol Mc, for the element 115,
Tennessine and symbol Ts, for the element 117, and
Oganesson and symbol Og, for the element 118.
…The guidelines for the naming the elements were recently revised [3] and shared with the discoverers to assist in their proposals. Keeping with tradition, newly discovered elements can be named after:
(a) a mythological concept or character (including an astronomical object),
(b) a mineral or similar substance,
(c) a place, or geographical region,
(d) a property of the element, or
(e) a scientist.
The names of all new elements in general would have an ending that reflects and maintains historical and chemical consistency. This would be in general “-ium” for elements belonging to groups 1-16, “-ine” for elements of group 17 and “-on” for elements of group 18. Finally, the names for new chemical elements in English should allow proper translation into other major languages.
For the element with atomic number 113 the discoverers at RIKEN Nishina Center for Accelerator-Based Science (Japan) proposed the name nihonium and the symbol Nh. Nihon is one of the two ways to say “Japan” in Japanese, and literally mean “the Land of Rising Sun”. The name is proposed to make a direct connection to the nation where the element was discovered. Element 113 is the first element to have been discovered in an Asian country. While presenting this proposal, the team headed by Professor Kosuke Morita pays homage to the trailblazing work by Masataka Ogawa done in 1908 surrounding the discovery of element 43. The team also hopes that pride and faith in science will displace the lost trust of those who suffered from the 2011 Fukushima nuclear disaster.
For the element with atomic number 115 the name proposed is moscovium with the symbol Mc and for element with atomic number 117, the name proposed is tennessine with the symbol Ts. These are in line with tradition honoring a place or geographical region and are proposed jointly by the discoverers at the Joint Institute for Nuclear Research, Dubna (Russia), Oak Ridge National Laboratory (USA), Vanderbilt University (USA) and Lawrence Livermore National Laboratory (USA).
Moscovium is in recognition of the Moscow region and honors the ancient Russian land that is the home of the Joint Institute for Nuclear Research, where the discovery experiments were conducted using the Dubna Gas-Filled Recoil Separator in combination with the heavy ion accelerator capabilities of the Flerov Laboratory of Nuclear Reactions.
Tennessine is in recognition of the contribution of the Tennessee region, including Oak Ridge National Laboratory, Vanderbilt University, and the University of Tennessee at Knoxville, to superheavy element research, including the production and chemical separation of unique actinide target materials for superheavy element synthesis at ORNL’s High Flux Isotope Reactor (HFIR) and Radiochemical Engineering Development Center (REDC).
For the element with atomic number 118 the collaborating teams of discoverers at the Joint Institute for Nuclear Research, Dubna (Russia) and Lawrence Livermore National Laboratory (USA) proposed the name oganesson and symbol Og. The proposal is in line with the tradition of honoring a scientist and recognizes Professor Yuri Oganessian (born 1933) for his pioneering contributions to transactinoid elements research. His many achievements include the discovery of superheavy elements and significant advances in the nuclear physics of superheavy nuclei including experimental evidence for the “island of stability”.
…Ultimately, and after the lapse of the public review, the final Recommendations will be published in the IUPAC journal Pure and Applied Chemistry. The Provisional Recommendation regarding the naming of the four new elements can be found on the IUPAC website at http://www.iupac.org/recommendations/under-review-by-the-public/.
Finally, laboratories are already working on searches for the elements in the 8th row of the periodic table, and they are also working to consolidate the identification of copernicium and heavier elements….
NOVA Absolute Zero
View online: Nova – Absolute Cold
View online (link 2): Nova – Absolute Cold
Air-conditioning, refrigeration, and superconductivity are just some of the ways technology has put cold to use. But what is cold, how do you achieve it, and how cold can it get? We follow the quest for cold from Cornelius Drebbel up to Michael Faraday.
extra! Milestones in cold research and extra! Anatomy of a refrigerator
official website NOVA: Absolute Zero
Transcript (for easy reading) of the show
Questions: please answer the following in complete sentences, demonstrating that you understand the concepts involved.
In this show Andrew Szydlo, a well known chemistry professor, enjoys re-enacting the work of the great court magician & chemist, Cornelius Drebbel, 1600’s France.
1. How did Drebbel (likely) create the world’s first demonstration of indoor air conditioning?
_____
Robert Boyle, famous for his study of gas, temperature and pressure. He systematically worked through a series of ideas about what cold is: Please answer:
2. Does cold come from the air? Is cold transferred by “frigorific” cold-making particles? If not, what does cold come from? How did Boyle show that “cold” was probably not a material?
_____
The first temperature scale to be widely adopted was devised by Gabriel Daniel Fahrenheit. He was a gifted instrument maker who made thermometers for scientists and physicians across Europe.
3. How did he set his lowest temperature? How did he set his other reference temperatures?
_____
In terms of temperature, is there an absolute lower limit? The idea that there might be one, would become a turning point in the history of cold. The story begins with the French physicist Guillaume Amontons. He was doing experiments heating and cooling bodies of air to see how they expand and contract.
4. How did Amotons realize that there must be a lowest possible temperature, an absolute zero? (Explain his reasoning.)
_____
The science of cold was about to suffer a serious setback. A rival theory of heat and cold emerged that was appealing, yet wrong. It was called the caloric theory, and its principle advocate was the great French chemist Antoine Lavoisier, 1700s France. In so many ways he was brilliant, and his careful experiments created much of modern day Chemistry. Lavoisier even developed the theory of conservation of matter. But on the topic of heat and cold, he was mistaken.
5. According to Lavoisier, what was “caloric”? Also, why do you think it is possible for a brilliant scientist to be so correct in so many other areas of science, yet completely incorrect in another area? (This isn’t answered within the program. I am looking for your thoughts.)
_____
One scientist was convinced that Lavoisier was wrong about caloric – and was determined to destroy the caloric theory. His name was Sir Benjamin Thompson, Count Rumford. (*) He was born in America, spied for the British during the Revolution, and after being forced into exile, became an influential government minister in Bavaria. Among his varied responsibilities was the artillery works, and it was here, in the 1790s, that he began to think about how he might be able to disprove the caloric theory.
6. How did he show that heat was not a fluid or material? In Count Rumford’s view, what was heat?
(*) Although his name was Ben Thompson, he is universally known as Count Rumford. What does that even mean? For his efforts in improving the life of people in the nation-state of Bavaria, he was made a Count of the Holy Roman Empire. Thompson took the name “Rumford” for Rumford, New Hampshire, the older name for the town of Concord.
_____
Michael Faraday, who later became famous for his work on electricity and magnetism, would take a critical early step in the long descent towards absolute zero. He was asked to investigate the properties of chlorine using crystals of chlorine hydrate, in 1823.
Faraday took the sealed tube and heated the end containing the chlorine hydrate in hot water. He put the other end in an ice bath. Soon he noticed yellow chlorine gas being given off. Because the gas is being produced, pressure’s building up inside this glass tube!
When Faraday did the experiment, a visitor, Dr. Paris, came by to see what he was up to. Paris pointed out some oily matter in the bottom of the tube. Faraday was curious, and decided to break open the tube…. The explosion sent shards of glass flying. With the sudden release of pressure, the oily liquid vanished.
7. What did Faraday learn about heat, cold, gas and pressure, from this?
Gorgeous CG Reproductions of Classic Scientific Instruments
A new project is creating digital reproductions of the instruments used in key chemistry experiments, in hopes of fostering appreciation for the craftsmanship involved in a new generation of science acolytes.
The photograph above is part of the Beautiful Chemistry outreach project, a collaboration between the University of Science and Technology of China (USTC) and Tsinghua University Press. It is inspired in part by the 19th century German biologist Ernst Haeckel, whose most famous book, Art Forms in Nature, featured stunning illustrations of marine and microscopic life forms.
When the site first launched in 2014, it showcased a series of eye-popping animated videos of chemical reactions, minus such distracting elements as beakers and test tubes. Now it’s back with a new design and a photographic gallery — plus short video teaser, with more to come — of 15 CG reproductions of the apparatus used in some of the most important chemistry breakthroughs from 1660 to 1860.
“In these 200 years, chemistry transformed from practical art and mysterious alchemy to a physical science with great precision,” project leader Yan Liang told Gizmodo via email. “We hope people could look at this period of history from a new angle: the evolution of chemical instruments.” He partnered with CG artists from IHDT.tv to create the reproductions. “We worked very hard to make sure that the instruments we recreated are scientifically accurate,” he said, while still giving the artists sufficient creative freedom…
Feast Your Eyes on These Gorgeous CG Reproductions of Classic Scientific Instruments
KaiserScience 
