Changing States of Matter by Cindy Grigg
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Equation of State for Benzene for Temperatures from the Melting Line up to 725 K with Pressures up to 500 Mpa†
High Temperatures-High Pressures, Vol. 41, pp. 81–97 ©2012 Old City Publishing, Inc. Reprints available directly from the publisher Published by license under the OCP Science imprint, Photocopying permitted by license only a member of the Old City Publishing Group Equation of state for benzene for temperatures from the melting line up to 725 K with pressures up to 500 MPa† MONIKA THOL ,1,2,* ERIC W. Lemm ON 2 AND ROLAND SPAN 1 1Thermodynamics, Ruhr-University Bochum, Universitaetsstrasse 150, 44801 Bochum, Germany 2National Institute of Standards and Technology, 325 Broadway, Boulder, Colorado 80305, USA Received: December 23, 2010. Accepted: April 17, 2011. An equation of state (EOS) is presented for the thermodynamic properties of benzene that is valid from the triple point temperature (278.674 K) to 725 K with pressures up to 500 MPa. The equation is expressed in terms of the Helmholtz energy as a function of temperature and density. This for- mulation can be used for the calculation of all thermodynamic properties. Comparisons to experimental data are given to establish the accuracy of the EOS. The approximate uncertainties (k = 2) of properties calculated with the new equation are 0.1% below T = 350 K and 0.2% above T = 350 K for vapor pressure and liquid density, 1% for saturated vapor density, 0.1% for density up to T = 350 K and p = 100 MPa, 0.1 – 0.5% in density above T = 350 K, 1% for the isobaric and saturated heat capaci- ties, and 0.5% in speed of sound. Deviations in the critical region are higher for all properties except vapor pressure. -
Geometrical Vortex Lattice Pinning and Melting in Ybacuo Submicron Bridges Received: 10 August 2016 G
www.nature.com/scientificreports OPEN Geometrical vortex lattice pinning and melting in YBaCuO submicron bridges Received: 10 August 2016 G. P. Papari1,*, A. Glatz2,3,*, F. Carillo4, D. Stornaiuolo1,5, D. Massarotti5,6, V. Rouco1, Accepted: 11 November 2016 L. Longobardi6,7, F. Beltram2, V. M. Vinokur2 & F. Tafuri5,6 Published: 23 December 2016 Since the discovery of high-temperature superconductors (HTSs), most efforts of researchers have been focused on the fabrication of superconducting devices capable of immobilizing vortices, hence of operating at enhanced temperatures and magnetic fields. Recent findings that geometric restrictions may induce self-arresting hypervortices recovering the dissipation-free state at high fields and temperatures made superconducting strips a mainstream of superconductivity studies. Here we report on the geometrical melting of the vortex lattice in a wide YBCO submicron bridge preceded by magnetoresistance (MR) oscillations fingerprinting the underlying regular vortex structure. Combined magnetoresistance measurements and numerical simulations unambiguously relate the resistance oscillations to the penetration of vortex rows with intermediate geometrical pinning and uncover the details of geometrical melting. Our findings offer a reliable and reproducible pathway for controlling vortices in geometrically restricted nanodevices and introduce a novel technique of geometrical spectroscopy, inferring detailed information of the structure of the vortex system through a combined use of MR curves and large-scale simulations. Superconductors are materials in which below the superconducting transition temperature, Tc, electrons form so-called Cooper pairs, which are bosons, hence occupying the same lowest quantum state1. The wave function of this Cooper condensate has a fixed phase. Hence, by virtue of the uncertainty principle, the number of Cooper pairs in the condensate is undefined. -
Two-Dimensional Vortex Lattice Melting Superconducting Length
Two-Dimensional Vortex Lattice Melting Superconducting Length-Scales and Vortex Lattices Flux Motion Melting Concepts Journal Paper Presentation: “Melting of the Vortex Lattice Through the Hexatic Phase in an MoGe3 Thin Film” 1 Repulsive Interaction Between Vortices Vortex Lattice 2 Vortex Melting in Superconducting Nb 3 (For 3D clean Type II superconductor) Vortex Lattice Expands on Freezing (Like Ice) Jump in the Magnetization 4 Melting Concepts 3D Solid Liquid Lindemann Criterion (∆r)2 ↵a 1st Order Transition ⇡ p 5 6 Journal Presentation Motivation/Context Results Interpretation Questions/Ideas for Future Work (aim for 30-45 mins) Please check the course site about the presentation schedule No class on The April 8, 15 Make-Ups on Ms April 12, 19 (Weekly Discussion to be Rescheduled) 7 First Definitive Observation of the Hexatic Phase in a Superconducting Film (with 8 thanks to Indranil Roy and Pratap Raychaudhuri) Two Dimensional Melting (BKT + HNY theory) 9 10 Hexatics have been observed in 2D colloidal systems Why not in the Melting of the Vortex Phase of Superconducting Films ?? 11 Quest for the Hexatic Liquid Phase in ↵ MoGe − Why Not Before ?? Orientational Coupling Hexatic Glass !! between Atomic and Vortex Lattices Solution: Amorphous Superconductor (no lattice effect) Very Weak Pinning BCS-Type Superconductor 12 Scanning Tunneling Spectroscopy (STS) Magnetotransport 13 14 15 16 17 The Resulting Phase Diagram 18 Summary First Observation of Hexatic Fluid Phase in a 2D Superconducting Film Pinning Significantly Weaker than in Previous Studies STS (imaging) Magnetotransport (“shear”) Questions/Ideas for the Future Size-Dependence of Hexatic Order Parameter ?? Low T limit of the Hexatic Fluid: Quantum Vortex Fluid ?? What happens in Layered Films ?? 19 20. -
Guide to Understanding Condensation
Guide to Understanding Condensation The complete Andersen® Owner-To-Owner™ limited warranty is available at: www.andersenwindows.com. “Andersen” is a registered trademark of Andersen Corporation. All other marks where denoted are marks of Andersen Corporation. © 2007 Andersen Corporation. All rights reserved. 7/07 INTRODUCTION 2 The moisture that suddenly appears in cold weather on the interior We have created this brochure to answer questions you may have or exterior of window and patio door glass can block the view, drip about condensation, indoor humidity and exterior condensation. on the floor or freeze on the glass. It can be an annoying problem. We’ll start with the basics and offer solutions and alternatives While it may seem natural to blame the windows or doors, interior along the way. condensation is really an indication of excess humidity in the home. Exterior condensation, on the other hand, is a form of dew — the Should you run into problems or situations not covered in the glass simply provides a surface on which the moisture can condense. following pages, please contact your Andersen retailer. The important thing to realize is that if excessive humidity is Visit the Andersen website: www.andersenwindows.com causing window condensation, it may also be causing problems elsewhere in your home. Here are some other signs of excess The Andersen customer service toll-free number: 1-888-888-7020. humidity: • A “damp feeling” in the home. • Staining or discoloration of interior surfaces. • Mold or mildew on surfaces or a “musty smell.” • Warped wooden surfaces. • Cracking, peeling or blistering interior or exterior paint. -
Chapter 3 Equations of State
Chapter 3 Equations of State The simplest way to derive the Helmholtz function of a fluid is to directly integrate the equation of state with respect to volume (Sadus, 1992a, 1994). An equation of state can be applied to either vapour-liquid or supercritical phenomena without any conceptual difficulties. Therefore, in addition to liquid-liquid and vapour -liquid properties, it is also possible to determine transitions between these phenomena from the same inputs. All of the physical properties of the fluid except ideal gas are also simultaneously calculated. Many equations of state have been proposed in the literature with either an empirical, semi- empirical or theoretical basis. Comprehensive reviews can be found in the works of Martin (1979), Gubbins (1983), Anderko (1990), Sandler (1994), Economou and Donohue (1996), Wei and Sadus (2000) and Sengers et al. (2000). The van der Waals equation of state (1873) was the first equation to predict vapour-liquid coexistence. Later, the Redlich-Kwong equation of state (Redlich and Kwong, 1949) improved the accuracy of the van der Waals equation by proposing a temperature dependence for the attractive term. Soave (1972) and Peng and Robinson (1976) proposed additional modifications of the Redlich-Kwong equation to more accurately predict the vapour pressure, liquid density, and equilibria ratios. Guggenheim (1965) and Carnahan and Starling (1969) modified the repulsive term of van der Waals equation of state and obtained more accurate expressions for hard sphere systems. Christoforakos and Franck (1986) modified both the attractive and repulsive terms of van der Waals equation of state. Boublik (1981) extended the Carnahan-Starling hard sphere term to obtain an accurate equation for hard convex geometries. -
Chapter 3 Bose-Einstein Condensation of an Ideal
Chapter 3 Bose-Einstein Condensation of An Ideal Gas An ideal gas consisting of non-interacting Bose particles is a ¯ctitious system since every realistic Bose gas shows some level of particle-particle interaction. Nevertheless, such a mathematical model provides the simplest example for the realization of Bose-Einstein condensation. This simple model, ¯rst studied by A. Einstein [1], correctly describes important basic properties of actual non-ideal (interacting) Bose gas. In particular, such basic concepts as BEC critical temperature Tc (or critical particle density nc), condensate fraction N0=N and the dimensionality issue will be obtained. 3.1 The ideal Bose gas in the canonical and grand canonical ensemble Suppose an ideal gas of non-interacting particles with ¯xed particle number N is trapped in a box with a volume V and at equilibrium temperature T . We assume a particle system somehow establishes an equilibrium temperature in spite of the absence of interaction. Such a system can be characterized by the thermodynamic partition function of canonical ensemble X Z = e¡¯ER ; (3.1) R where R stands for a macroscopic state of the gas and is uniquely speci¯ed by the occupa- tion number ni of each single particle state i: fn0; n1; ¢ ¢ ¢ ¢ ¢ ¢g. ¯ = 1=kBT is a temperature parameter. Then, the total energy of a macroscopic state R is given by only the kinetic energy: X ER = "ini; (3.2) i where "i is the eigen-energy of the single particle state i and the occupation number ni satis¯es the normalization condition X N = ni: (3.3) i 1 The probability -
Fish Technology Glossary
Glossary of Fish Technology Terms A Selection of Terms Compiled by Kevin J. Whittle and Peter Howgate Prepared under contract to the Fisheries Industries Division of the Food and Agriculture Organization of the United Nations 6 December 2000 Last updated: February 2002 Kevin J. Whittle 1 GLOSSARY OF FISH TECHNOLOGY TERMS [Words highlighted in bold in the text of an entry refer to another entry. Words in parenthesis are alternatives.] Abnormalities Attributes of the fish that are not found in the great majority of that kind of fish. For example: atypical shapes; overall or patchy discolorations of skin or of fillet; diseased conditions; atypical odours or flavours. Generally, the term should be used for peculiarities present in the fish at the time of capture or harvesting, or developing very soon after; peculiarities arising during processing should be considered as defects. Acetic acid Formal chemical name, ethanoic acid. An organic acid of formula CH3.COOH. It is the main component, 3-6%, other than water, of vinegar. Used in fish technology in preparation of marinades. Acid curing See Marinating Actomyosin A combination of the two main proteins, actin and myosin, present in all muscle tissues. Additive A chemical added to a food to affect its properties. Objectives of including additives in a product include: increased stability during storage; inhibition of growth of microorganisms or production of microbial toxins; prevention or reduction of formation of off-flavours; improved sensory properties, particularly colours and appearance, affecting acceptability to the consumer; improved properties related to preparation and processing of food, for example, ability to create stable foams or emulsions, or to stabilise or thicken sauces. -
Sounds of a Supersolid A
NEWS & VIEWS RESEARCH hypothesis came from extensive population humans, implying possible mosquito exposure long-distance spread of insecticide-resistant time-series analysis from that earlier study5, to malaria parasites and the potential to spread mosquitoes, worsening an already dire situ- which showed beyond reasonable doubt that infection over great distances. ation, given the current spread of insecticide a mosquito vector species called Anopheles However, the authors failed to detect resistance in mosquito populations. This would coluzzii persists locally in the dry season in parasite infections in their aerially sampled be a matter of great concern because insecticides as-yet-undiscovered places. However, the malaria vectors, a result that they assert is to be are the best means of malaria control currently data were not consistent with this outcome for expected given the small sample size and the low available8. However, long-distance migration other malaria vectors in the study area — the parasite-infection rates typical of populations of could facilitate the desirable spread of mosqui- species Anopheles gambiae and Anopheles ara- malaria vectors. A problem with this argument toes for gene-based methods of malaria-vector biensis — leaving wind-powered long-distance is that the typical infection rates they mention control. One thing is certain, Huestis and col- migration as the only remaining possibility to are based on one specific mosquito body part leagues have permanently transformed our explain the data5. (salivary glands), rather than the unknown but understanding of African malaria vectors and Both modelling6 and genetic studies7 undoubtedly much higher infection rates that what it will take to conquer malaria. -
Current Status of Equation of State in Nuclear Matter and Neutron Stars
Open Issues in Understanding Core Collapse Supernovae June 22-24, 2004 Current Status of Equation of State in Nuclear Matter and Neutron Stars J.R.Stone1,2, J.C. Miller1,3 and W.G.Newton1 1 Oxford University, Oxford, UK 2Physics Division, ORNL, Oak Ridge, TN 3 SISSA, Trieste, Italy Outline 1. General properties of EOS in nuclear matter 2. Classification according to models of N-N interaction 3. Examples of EOS – sensitivity to the choice of N-N interaction 4. Consequences for supernova simulations 5. Constraints on EOS 6. High density nuclear matter (HDNM) 7. New developments Equation of State is derived from a known dependence of energy per particle of a system on particle number density: EA/(==En) or F/AF(n) I. E ( or Boltzman free energy F = E-TS for system at finite temperature) is constructed in a form of effective energy functional (Hamiltonian, Lagrangian, DFT/EFT functional or an empirical form) II. An equilibrium state of matter is found at each density n by minimization of E (n) or F (n) III. All other related quantities like e.g. pressure P, incompressibility K or entropy s are calculated as derivatives of E or F at equilibrium: 2 ∂E ()n ∂F ()n Pn()= n sn()=− | ∂n ∂T nY, p ∂∂P()nnEE() ∂2 ()n Kn()==9 18n +9n2 ∂∂nn∂n2 IV. Use as input for model simulations (Very) schematic sequence of equilibrium phases of nuclear matter as a function of density: <~2x10-4fm-3 ~2x10-4 fm-3 ~0.06 fm-3 Nuclei in Nuclei in Neutron electron gas + ‘Pasta phase’ Electron gas ~0.1 fm-3 0.3-0.5 fm-3 >0.5 fm-3 Nucleons + n,p,e,µ heavy baryons Quarks ??? -
Liquid-Vapor Equilibrium in a Binary System
Liquid-Vapor Equilibria in Binary Systems1 Purpose The purpose of this experiment is to study a binary liquid-vapor equilibrium of chloroform and acetone. Measurements of liquid and vapor compositions will be made by refractometry. The data will be treated according to equilibrium thermodynamic considerations, which are developed in the theory section. Theory Consider a liquid-gas equilibrium involving more than one species. By definition, an ideal solution is one in which the vapor pressure of a particular component is proportional to the mole fraction of that component in the liquid phase over the entire range of mole fractions. Note that no distinction is made between solute and solvent. The proportionality constant is the vapor pressure of the pure material. Empirically it has been found that in very dilute solutions the vapor pressure of solvent (major component) is proportional to the mole fraction X of the solvent. The proportionality constant is the vapor pressure, po, of the pure solvent. This rule is called Raoult's law: o (1) psolvent = p solvent Xsolvent for Xsolvent = 1 For a truly ideal solution, this law should apply over the entire range of compositions. However, as Xsolvent decreases, a point will generally be reached where the vapor pressure no longer follows the ideal relationship. Similarly, if we consider the solute in an ideal solution, then Eq.(1) should be valid. Experimentally, it is generally found that for dilute real solutions the following relationship is obeyed: psolute=K Xsolute for Xsolute<< 1 (2) where K is a constant but not equal to the vapor pressure of pure solute. -
Pressure Vs Temperature (Boiling Point)
Boiling Points and Vapor Pressure Background Boiling Points and Vapor Pressure Background: Definitions Vapor Pressure: The equilibrium pressure of a vapor above its liquid; the pressure of the vapor resulting from the evaporation of a liquid above a sample of the liquid in a closed container. Boiling Point: The temperature at which the vapor pressure of a liquid is equal to the atmospheric (or applied) pressure. As the temperature of the liquid increases, the vapor pressure will increase, as seen below: https://www.chem.purdue.edu/gchelp/liquids/vpress.html Vapor pressure is interpreted in terms of molecules of liquid converting to the gaseous phase and escaping into the empty space above the liquid. In order for the molecules to escape, the intermolecular forces (Van der Waals, dipole- dipole, and hydrogen bonding) have to be overcome, which requires energy. This energy can come in the form of heat, aka increase in temperature. Due to this relationship between vapor pressure and temperature, the boiling point of a liquid decreases as the atmospheric pressure decreases since there is more room above the liquid for molecules to escape into at lower pressure. The graph below illustrates this relationship using common solvents and some terpenes: Pressure vs Temperature (boiling point) Ethanol Heptane Isopropyl Alcohol B-myrcene 290.0 B-caryophyllene d-Limonene Linalool Pulegone 270.0 250.0 1,8-cineole (eucalyptol) a-pinene a-terpineol terpineol-4-ol 230.0 p-cymene 210.0 190.0 170.0 150.0 130.0 110.0 90.0 Temperature (˚C) Temperature 70.0 50.0 30.0 10 20 30 40 50 60 70 80 90 100 200 300 400 500 600 760 10.0 -10.0 -30.0 Pressure (torr) 1 Boiling Points and Vapor Pressure Background As a very general rule of thumb, the boiling point of many liquids will drop about 0.5˚C for a 10mmHg decrease in pressure when operating in the region of 760 mmHg (atmospheric pressure). -
Δtb = M × Kb, Δtf = M × Kf
8.1HW Colligative Properties.doc Colligative Properties of Solvents Use the Equations given in your notes to solve the Colligative Property Questions. ΔTb = m × Kb, ΔTf = m × Kf Freezing Boiling K K Solvent Formula Point f b Point (°C) (°C/m) (°C/m) (°C) Water H2O 0.000 100.000 1.858 0.521 Acetic acid HC2H3O2 16.60 118.5 3.59 3.08 Benzene C6H6 5.455 80.2 5.065 2.61 Camphor C10H16O 179.5 ... 40 ... Carbon disulfide CS2 ... 46.3 ... 2.40 Cyclohexane C6H12 6.55 80.74 20.0 2.79 Ethanol C2H5OH ... 78.3 ... 1.07 1. Which solvent’s freezing point is depressed the most by the addition of a solute? This is determined by the Freezing Point Depression constant, Kf. The substance with the highest value for Kf will be affected the most. This would be Camphor with a constant of 40. 2. Which solvent’s freezing point is depressed the least by the addition of a solute? By the same logic as above, the substance with the lowest value for Kf will be affected the least. This is water. Certainly the case could be made that Carbon disulfide and Ethanol are affected the least as they do not have a constant. 3. Which solvent’s boiling point is elevated the least by the addition of a solute? Water 4. Which solvent’s boiling point is elevated the most by the addition of a solute? Acetic Acid 5. How does Kf relate to Kb? Kf > Kb (fill in the blank) The freezing point constant is always greater.