The Ups and Down of Friction

Total Page:16

File Type:pdf, Size:1020Kb

The Ups and Down of Friction CERN Courier May 2012 Sciencewatch C OMPILED BY J OHN S WAIN , N ORTHEA S TERN U NIVER S ITY The ups and down of friction The exact nature of friction is still somewhat Nanomeasurement instruments can detect mysterious, despite having long been studied movement to a billionth of a metre. (Image by many physicists and engineers. In the credit: K U Leuven.) 17th century, Guillaume Amontons and Charles-Augustin de Coulomb attributed recording the curves of the up-and-down friction to tiny surface irregularities that motion of the object as it rises and falls mesh and impede horizontal motion, over small irregularities. Remarkably, this necessitating frequent vertical motions. phenomenon – known as lift-up hysteresis – These ideas fell somewhat to the wayside does not appear to have been shown before. in more recent adhesion-based theories Its measurement shows the complexity of of friction but they have recently received techniques to measure hysteresis curves in friction and, say the researchers, confirms renewed support from Farid Al-Bender and the normal displacement (perpendicular the intuition of Amontons and Coulomb. colleagues at the Katholieke Universiteit to the surface) of a sliding object as it is Leuven. pushed along. They tested various materials ● Further reading These researchers used nanoscale (paper, plastic and brass) at different speeds, F Al-Bender et al. 2012 Tribol. Lett. 46 23. Earthshine and life better for the fruit flies, the wasps avoided on other worlds Ice-age plant resurrected laying eggs in the alcoholic larvae. Fruit flies also seem to treat psychological One way to look for life on other planets It may not be quite problems with alcohol. Galit Shohat-Ophir is to look at spectroscopic signals of the the same scenario and colleagues at the University of chemical composition of their atmospheres, as in Jurassic Park, California in San Francisco found that male searching for compounds such as methane but Svetlana Yashina fruit flies are more likely to choose food or molecular oxygen, which are likely to and colleagues at the laced with alcohol after being rejected by a be produced by living things. The catch so Russian Academy of mate (something that might strike a chord far has been that the light from exoplanets Sciences in Puschchino in humans). Alcohol seems to raise levels is faint compared with that emitted by the managed to resurrect of neuropeptide F, a brain chemical that stars they orbit. Now, Michael Sterzik of the a 30,000-year-old Ice also rises after mating. The work suggests European Southern Observatory in Santiago Silene Age flowering plant. treatments for human alcoholism and and colleagues have a clever proposal. Light stenophylla They recovered fruit depression by raising levels of neuropeptide that comes through an atmosphere becomes regenerated tissue of the plant (Silene Y, the human analogue of neuropeptide F. polarized, allowing it to be separated from from tissue of stenophylla) from a unpolarized background. fossil fruit. fossilized squirrel burrow ● Further reading The researchers tested this idea with (Image credit: 38 m underground N F Milan et al. 2012 Current Biology 22 488. the Focal Reducer/Low-Dispersion S Yashina et al.) near the Kolyma river in G Shohat-Ophir et al. 2012 Science 335 1351. Spectrograph at the Very Large Telescope in Siberia. Chile, looking at earthshine reflected from By using growth hormones, the team Storing hydrogen in acid the Moon. They were able to find signatures managed to start the cells dividing again and of oxygen, ozone and water and indications were able to grow viable plants that actually A big challenge in using hydrogen for of vegetation, as well as the fractional bloomed. This sets a new record, shattering energy is how to store it. Jonathan Hull contributions of clouds and ocean surface. the previous record for a 1200-year-old lotus, of Brookhaven National Laboratory and This technique could offer a new way of which was grown in modern times. colleagues have shown that hydrogen can be studying distant planets and searching for stored in an aqueous solution of formic acid, life even before there is a means to go there ● Further reading the acid that burns in ant stings. At normal for a more direct look. S Yashina et al. 2012 Proc. Nat. Acad. Sci. 109 4008. temperatures and pressures – a big plus for this technique – an iridium catalyst can ● Further reading make hydrogen react with carbon dioxide M F Sterzik et al. 2012 Nature 483 64. Milan of Emory University in Atlanta and to make formic acid under slightly alkaline colleagues raised fruit-fly larvae infected conditions. Acidifying the solution releases Alcohol helps fruit flies with parasites from a wasp that lays eggs in pure hydrogen gas at high pressures. them. As many as 80 per cent of the infected People who drink a little whisky in the hopes larvae favoured alcohol-laced food, which ● Further reading of helping a cold may be surprised to find can kill off the parasites, as opposed to just J F Hull 2012 Nature Chemistry, doi:10.1038/ that fruit flies do something similar. Neil 30 per cent of the noninfested ones. Even nchem.1295. 12 CCMay12-Science.indd 12 12/04/2012 15:16 .
Recommended publications
  • A NONSMOOTH APPROACH for the MODELLING of a MECHANICAL ROTARY DRILLING SYSTEM with FRICTION Samir Adly, Daniel Goeleven
    A NONSMOOTH APPROACH FOR THE MODELLING OF A MECHANICAL ROTARY DRILLING SYSTEM WITH FRICTION Samir Adly, Daniel Goeleven To cite this version: Samir Adly, Daniel Goeleven. A NONSMOOTH APPROACH FOR THE MODELLING OF A ME- CHANICAL ROTARY DRILLING SYSTEM WITH FRICTION. Evolution Equations and Control Theory, AIMS, In press, X, 10.3934/xx.xx.xx.xx. hal-02433100 HAL Id: hal-02433100 https://hal.archives-ouvertes.fr/hal-02433100 Submitted on 8 Jan 2020 HAL is a multi-disciplinary open access L’archive ouverte pluridisciplinaire HAL, est archive for the deposit and dissemination of sci- destinée au dépôt et à la diffusion de documents entific research documents, whether they are pub- scientifiques de niveau recherche, publiés ou non, lished or not. The documents may come from émanant des établissements d’enseignement et de teaching and research institutions in France or recherche français ou étrangers, des laboratoires abroad, or from public or private research centers. publics ou privés. Manuscript submitted to doi:10.3934/xx.xx.xx.xx AIMS’ Journals Volume X, Number 0X, XX 200X pp. X–XX A NONSMOOTH APPROACH FOR THE MODELLING OF A MECHANICAL ROTARY DRILLING SYSTEM WITH FRICTION SAMIR ADLY∗ Laboratoire XLIM, Universite´ de Limoges 87060 Limoges, France. DANIEL GOELEVEN Laboratoire PIMENT, Universite´ de La Reunion´ 97400 Saint-Denis, France Dedicated to 70th birthday of Professor Meir Shillor. ABSTRACT. In this paper, we show how the approach of nonsmooth dynamical systems can be used to develop a suitable method for the modelling of a rotary oil drilling system with friction. We study different kinds of frictions and analyse the mathematical properties of the involved dynamical systems.
    [Show full text]
  • Leonardo Da Vinci's Contributions to Tribology
    © 2016. This manuscript version is made available under the CC-BY-NC-ND 4.0 license http://creativecommons.org/licenses/by-nc-nd/4.0/ Published as Wear 360-361 (2016) 51-66 http://dx.doi.org/10.1016/j.wear.2016.04.019 Leonardo da Vinci’s studies of friction Ian M. Hutchings University of Cambridge, Department of Engineering, Institute for Manufacturing, 17 Charles Babbage Road, Cambridge CB3 0FS, UK email: [email protected] Abstract Based on a detailed study of Leonardo da Vinci’s notebooks, this review examines the development of his understanding of the laws of friction and their application. His work on friction originated in studies of the rotational resistance of axles and the mechanics of screw threads. He pursued the topic for more than 20 years, incorporating his empirical knowledge of friction into models for several mechanical systems. Diagrams which have been assumed to represent his experimental apparatus are misleading, but his work was undoubtedly based on experimental measurements and probably largely involved lubricated contacts. Although his work had no influence on the development of the subject over the succeeding centuries, Leonardo da Vinci holds a unique position as a pioneer in tribology. Keywords: sliding friction; rolling friction; history of tribology; Leonardo da Vinci 1. Introduction Although the word ‘tribology’ was first coined almost 450 years after the death of Leonardo da Vinci (1452 – 1519), it is clear that Leonardo was fully familiar with the basic tribological concepts of friction, lubrication and wear. He has been widely credited with the first quantitative investigations of friction, and with the definition of the two fundamental ‘laws’ of friction some two hundred years before they were enunciated (in 1699) by Guillaume Amontons, with whose name they are now usually associated.
    [Show full text]
  • 1 Classical Theory and Atomistics
    1 1 Classical Theory and Atomistics Many research workers have pursued the friction law. Behind the fruitful achievements, we found enormous amounts of efforts by workers in every kind of research field. Friction research has crossed more than 500 years from its beginning to establish the law of friction, and the long story of the scientific historyoffrictionresearchisintroducedhere. 1.1 Law of Friction Coulomb’s friction law1 was established at the end of the eighteenth century [1]. Before that, from the end of the seventeenth century to the middle of the eigh- teenth century, the basis or groundwork for research had already been done by Guillaume Amontons2 [2]. The very first results in the science of friction were found in the notes and experimental sketches of Leonardo da Vinci.3 In his exper- imental notes in 1508 [3], da Vinci evaluated the effects of surface roughness on the friction force for stone and wood, and, for the first time, presented the concept of a coefficient of friction. Coulomb’s friction law is simple and sensible, and we can readily obtain it through modern experimentation. This law is easily verified with current exper- imental techniques, but during the Renaissance era in Italy, it was not easy to carry out experiments with sufficient accuracy to clearly demonstrate the uni- versality of the friction law. For that reason, 300 years of history passed after the beginning of the Italian Renaissance in the fifteenth century before the friction law was established as Coulomb’s law. The progress of industrialization in England between 1750 and 1850, which was later called the Industrial Revolution, brought about a major change in the production activities of human beings in Western society and later on a global scale.
    [Show full text]
  • Redalyc.Guillaume Amontons
    Revista CENIC. Ciencias Químicas ISSN: 1015-8553 [email protected] Centro Nacional de Investigaciones Científicas Cuba Wisniak, Jaime Guillaume Amontons Revista CENIC. Ciencias Químicas, vol. 36, núm. 3, 2005, pp. 187-195 Centro Nacional de Investigaciones Científicas La Habana, Cuba Disponible en: http://www.redalyc.org/articulo.oa?id=181620584008 Cómo citar el artículo Número completo Sistema de Información Científica Más información del artículo Red de Revistas Científicas de América Latina, el Caribe, España y Portugal Página de la revista en redalyc.org Proyecto académico sin fines de lucro, desarrollado bajo la iniciativa de acceso abierto Revista CENIC Ciencias Químicas, Vol. 36, No. 3, 2005. Guillaume Amontons Jaime Wisniak. Department of Chemical Engineering, Ben-Gurion University of the Negev, Beer-Sheva, Israel 84105. [email protected] Recibido: 24 de agosto de 2004. Aceptado: 28 de octubre de 2004. Palabras clave: barómetro, termometría, cero absoluto, higrómetro, telégrafo, máquina de combustión externa, fricción en las máquinas. Key words: barometer, thermometry, absolute zero, hygrometer, telegraph, external-combustion machine, friction in machines. RESUMEN. Guillaume Amontons (1663-1705) fue un experimentador que se de- Many instruments had been de- dicó a la mejora de instrumentos usados en física, en particular, el barómetro y el veloped to measure in a gross man- termómetro. Dentro de ellos se destacan, en particular, un barómetro plegable, ner the humidity of air. Almost all un barómetro sin cisterna para usos marítimos, y un higrómetro. Experimentó systems made use of the hygro- con el termómetro de aire e hizo notar que con dicho aparato el máximo frío sería scopic properties of vegetable or aquel que reduciría el resorte (presión) del aire a cero, siendo así, el primero que animal fibers such as hemp, oats, dedujo la presencia de un cero absoluto de temperatura.
    [Show full text]
  • Rubbing and Scrubbing
    RUBBING AND SCRUBBING he "rubbing and scrub- Tbing department" was Though simply expressed the laws erf T^SSy, much ooff how David Tabor's friction, friction encapsulate a host OI miCrOSCOplC Leonardo's writing on fric- lubrication and wear labora- and nanoscopic phenomena whose tion did not come to light tory was described by certain until the 1960s, which is whv uncharitable colleagues at elucidation has become one of the most the individual more often as- the Cavendish Laboratory in fascinating pursuits in applied physics. sociated with the laws of fric- Cambridge, England, some tion is Guillaume Amontons, 40 years ago. The tables who independently studied have turned. Tribology, as Georg Hahner and Nicholas Spencer both lubricated and unlubri- Tabor named his discipline cated friction at the end of (from the Greek tribos, the 17th century. meaning "rubbing"), has become respectable—even posi- Amontons's observations on friction, as presented to tively modish—in physics departments worldwide. And the Royal Academy of Sciences in Paris on 19 December Tabor, having become the revered elder statesman of this 1699, were as follows flourishing field, is often accorded a place in reference 1 l> That the resistance caused by rubbing increases of even the most hardcore tribo-physics papers.1 or diminishes only in proportion to greater or lesser Although Tabor brought physics to tribology in the pressure (load) and not according to the greater or 1950s, the origins of the field lie in the engineering lesser extent of the surfaces. sciences and stretch back more than 5000 years to the D> That the resistance caused by rubbing is more neolithic period.
    [Show full text]
  • Acta Technica Jaurinensis
    Acta Technica Jaurinensis Győr, Transactions on Engineering Vol. 3, No. 1 Acta Technica Jaurinensis Vol. 3. No. 1. 2010 The Historical Development of Thermodynamics D. Bozsaky “Széchenyi István” University Department of Architecture and Building Construction, H-9026 Győr, Egyetem tér 1. Phone: +36(96)-503-454, fax: +36(96)-613-595 e-mail: [email protected] Abstract: Thermodynamics as a wide branch of physics had a long historical development from the ancient times to the 20th century. The invention of the thermometer was the first important step that made possible to formulate the first precise speculations on heat. There were no exact theories about the nature of heat for a long time and even the majority of the scientific world in the 18th and the early 19th century viewed heat as a substance and the representatives of the Kinetic Theory were rejected and stayed in the background. The Caloric Theory successfully explained plenty of natural phenomena like gas laws and heat transfer and it was impossible to refute it until the 1850s when the Principle of Conservation of Energy was introduced (Mayer, Joule, Helmholtz). The Second Law of Thermodynamics was discovered soon after that explanation of the tendency of thermodynamic processes and the heat loss of useful heat. The Kinetic Theory of Gases motivated the scientists to introduce the concept of entropy that was a basis to formulate the laws of thermodynamics in a perfect mathematical form and founded a new branch of physics called statistical thermodynamics. The Third Law of Thermodynamics was discovered in the beginning of the 20th century after introducing the concept of thermodynamic potentials and the absolute temperature scale.
    [Show full text]
  • Thermodynamic Temperature
    Thermodynamic temperature Thermodynamic temperature is the absolute measure 1 Overview of temperature and is one of the principal parameters of thermodynamics. Temperature is a measure of the random submicroscopic Thermodynamic temperature is defined by the third law motions and vibrations of the particle constituents of of thermodynamics in which the theoretically lowest tem- matter. These motions comprise the internal energy of perature is the null or zero point. At this point, absolute a substance. More specifically, the thermodynamic tem- zero, the particle constituents of matter have minimal perature of any bulk quantity of matter is the measure motion and can become no colder.[1][2] In the quantum- of the average kinetic energy per classical (i.e., non- mechanical description, matter at absolute zero is in its quantum) degree of freedom of its constituent particles. ground state, which is its state of lowest energy. Thermo- “Translational motions” are almost always in the classical dynamic temperature is often also called absolute tem- regime. Translational motions are ordinary, whole-body perature, for two reasons: one, proposed by Kelvin, that movements in three-dimensional space in which particles it does not depend on the properties of a particular mate- move about and exchange energy in collisions. Figure 1 rial; two that it refers to an absolute zero according to the below shows translational motion in gases; Figure 4 be- properties of the ideal gas. low shows translational motion in solids. Thermodynamic temperature’s null point, absolute zero, is the temperature The International System of Units specifies a particular at which the particle constituents of matter are as close as scale for thermodynamic temperature.
    [Show full text]
  • The Gas Laws
    HANDOUT SET GENERAL CHEMISTRY I Periodic Table of the Elements 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 IA VIIIA 1 2 1 H He 1.00794 IIA IIIA IVA VA VIA VIIA 4.00262 3 4 5 6 7 8 9 10 2 Li Be B C N O F Ne 6.941 9.0122 10.811 12.011 14.0067 15.9994 18.9984 20.179 11 12 13 14 15 16 17 18 3 Na Mg Al Si P S Cl Ar 22.9898 24.305 26.98154 28.0855 30.97376 32.066 35.453 39.948 IIIB IVB VB VIB VIIB VIIIB IB IIB 19 20 21 22 23 24 25 26 27 28 29 30 31 32 33 34 35 36 4 K Ca Sc Ti V Cr Mn Fe Co Ni Cu Zn Ga Ge As Se Br Kr 39.0983 40.078 44.9559 47.88 50.9415 51.9961 54.9380 55.847 58.9332 58.69 63.546 65.39 69.723 72.59 74.9216 78.96 79.904 83.80 37 38 39 40 41 42 43 44 45 46 47 48 49 50 51 52 53 54 5 Rb Sr Y Zr Nb Mo Tc Ru Rh Pd Ag Cd In Sn Sb Te I Xe 85.4678 87.62 88.9059 91.224 92.9064 95.94 (98) 101.07 102.9055 106.42 107.8682 112.41 114.82 118.710 121.75 127.60 126.9045 131.29 55 56 57 72 73 74 75 76 77 78 79 80 81 82 83 84 85 86 6 Cs Ba La* Hf Ta W Re Os Ir Pt Au Hg Tl Pb Bi Po At Rn 132.9054 137.34 138.91 178.49 180.9479 183.85 186.207 190.2 192.22 195.08 196.9665 200.59 204.383 207.2 208.9804 (209) (210) (222) 87 88 89 104 105 106 107 108 109 110 111 112 7 Fr Ra Ac** Rf Db Sg Bh Hs Mt *** (223) 226.0254 227.0278 (261) (262) (263) (264) (265) (266) (270) (272) (277) *Lanthanides 58 59 60 61 62 63 64 65 66 67 68 69 70 71 Ce Pr Nd Pm Sm Eu Gd Tb Dy Ho Er Tm Yb Lu 140.12 140.9077 144.24 (145) 150.36 151.96 157.25 158.925 162.50 164.930 167.26 168.9342 173.04 174.967 **Actinides 90 91 92 93 94 95 96 97 98 99 100 101 102 103 Th Pa U Np Pu Am Cm Bk Cf Es Fm Md No Lr 232.038 231.0659 238.0289 237.0482 (244) (243) (247) (247) (251) (252) (257) (258) (259) (260) Mass numbers in parenthesis are the mass numbers of the most stable isotopes.
    [Show full text]
  • The Ideal Gas Law, PV = Nrt, Is a Useful Formula That Was Discovered by Experimental Observation
    Ideal Gas Laws and the Absolute Zero of Temperature (approx. 2 h 15 min.)(6/20/12) Introduction The ideal gas law, PV = nRT, is a useful formula that was discovered by experimental observation. In SI units P stands for pressure in N/m2 (i.e. Pascals); V is for volume in cubic meters; n is the number of moles; R = 8.314 J/mol-K is the universal gas constant; and T is the absolute temperature in Kelvins. This law has been tested on numerous gases and shows remarkable agreement with experiment over a large range of pressures, volumes and temperatures when the number of moles per unit volume is not too high. Equipment One each for each of six constant-temperature stations: • Boyle's Law unit • 2000 ml beaker • metal sphere • thermometer • pitcher for water For specific temperature stations: a bucket of crushed ice; 1 liter room temp. water; 4 large hotplates For Whole Class: eye protection; rulers; grid paper; gloves; stopcock lubricant (one tube for class) Setup: Six teams should fill six 2000 ml beakers halfway with water and maintain their respective temperatures at: 0 °C (mixture of ice and water in equilibrium); room temperature; 40°C; 58°C; 77°C; and 95 °C. (Note for instructor: Crushed ice is available in room 207 (door combination: 0812). Consult your instructor or the other lab groups before selecting your temperature. Begin heating as soon as possible, since reaching the higher temperatures may be time consuming. Some Historical Background In 1643 the Italian physicist Evangelista Torricelli developed a barometer which enabled him to determine that the pressure exerted by Earth’s atmosphere was equal to the pressure at the bottom of a column of mercury 76 cm high (with near vacuum above it).
    [Show full text]
  • Physics 5D - Heat, Thermodynamics, and Kinetic Theory Homework Will Be Posted at the Phys5d Website
    Physics 5D - Heat, Thermodynamics, and Kinetic Theory Homework will be posted at the Phys5D website http://physics.ucsc.edu/~joel/Phys5D. Solutions are due at the beginning of class. Late homework will not be accepted since solutions will be posted on the class website (password: Entropy) just after the homework is due, so that you can see how to do the problems while they are still fresh in your mind. Course Schedule Date Topic Readings 1. Sept 30 Temperature, Thermal Expansion, Ideal Gas Law 17.1-17.10 2. Oct 7 Kinetic Theory of Gases, Changes of Phase 18.1-18.5 3. Oct 14 Mean Free Path, Internal Energy of Gases 18.6-19.3 4. Oct 21 Heat and the 1st Law of Thermodynamics 19.4-19.9 5. Oct 28 Heat Transfer; Heat Engines, Carnot Cycle 19.10-20.2 6. Nov 4 Midterm Exam (in class, one page of notes allowed) 7. Nov 18 The 2nd Law of Thermodynamics, Heat Pumps 20.3-20.5 8. Nov 25 Entropy, Disorder, Statistical Interpretation of 2nd Law 20.6-20.10 9. Dec 2 Thermodynamics of Earth and Cosmos; Overview of the Course 10. Dec 11 Final Exam (5-8 pm, in class, two pages of notes allowed) Copyright © 2009 Pearson Education, Inc. Monday, September 30, 13 Website for homeworks: http://physics.ucsc.edu/~joel/Phys5D TextCopyright Text © 2009 Text Pearson Text Education, Inc. Monday, September 30, 13 Giancoli - Chapter 17 Temperature, Thermal Expansion, and the Ideal Gas Law Copyright © 2009 Pearson Education, Inc. Monday, September 30, 13 17-1 Atomic Theory of Matter Atomic and molecular masses are measured in unified atomic mass units (u).
    [Show full text]
  • Creativity, Science Cooperation, Progress and Responsibility
    ANNALS OF THE FACULTY OF ENGINEERING HUNEDOARA 2006, Tome IV, Fascicole 1, (ISSN 1584 – 2665) FACULTY OF ENGINEERING HUNEDOARA, 5, REVOLUTIEI, 331128, HUNEDOARA EDUCATIONAL SOFTWARE FOR PRESENTATION OF THE IDEAL GAS LAWS IORDAN Anca Elena, PĂNOIU Manuela POLITEHNICA UNIVERSITY OF TIMIŞOARA, ENGINEERING FACULTY OF HUNEDOARA ABSTRACT: The informative society needs important changes in educational programs. The informational techniques needs a reconsideration of the learning process, of the programs, manuals structures, a reconsideration of the methods and organization forms of the didactic activities, taking into account the computer assisted instruction and self instruction. This paper presents a software package, which can be used as educational software. KEYWORDS: Educational software, ideal gas, graphical interface 1. INTRODUCTION Today, it is use the computer in many areas, including in education, from the elementary school to the universities, by following some purposes. Between these purposes it can be cite the necessity to prepare the young people for a future where the computer science is a dominant area. This purpose can be realized by using new didactical teaching methods based on educational software that is programs useful in teaching-learning process [1][2]. The CBL type systems (Computer Based Learning) are used in universities from the entire world. For instance, at Dundee University, Scotland, UK [2] a CBL system is integrated part in the courses from the first two years in computers field. These courses present the students
    [Show full text]
  • Topic 2: Gases and the Atmosphere
    TOPIC 2: GASES AND THE ATMOSPHERE Topic 2: Gases and the Atmosphere C11-2-01 Identify the abundances of the naturally occurring gases in the atmosphere and examine how these abundances have changed over geologic time. Include: oxygenation of Earth’s atmosphere, the role of biota in oxygenation, changes in carbon dioxide content over time C11-2-02 Research Canadian and global initiatives to improve air quality. C11-2-03 Examine the historical development of the measurement of pressure. Examples: the contributions of Galileo Galilei, Evangelista Torricelli, Otto von Guericke, Blaise Pascal, Christiaan Huygens, John Dalton, Joseph Louis Gay-Lussac, Amadeo Avogadro… C11-2-04 Describe the various units used to measure pressure. Include: atmospheres (atm), kilopascals (kPa), millimetres of mercury (mmHg), millibars (mb) C11-2-05 Experiment to develop the relationship between the pressure and volume of a gas using visual, numeric, and graphical representations. Include: historical contributions of Robert Boyle C11-2-06 Experiment to develop the relationship between the volume and temperature of a gas using visual, numeric, and graphical representations. Include: historical contributions of Jacques Charles, the determination of absolute zero, the Kelvin temperature scale C11-2-07 Experiment to develop the relationship between the pressure and temperature of a gas using visual, numeric, and graphical representations. Include: historical contributions of Joseph Louis Gay-Lussac C11-2-08 Solve quantitative problems involving the relationships among
    [Show full text]