Triple Point of Water
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Lecture Notes: BCS Theory of Superconductivity
Lecture Notes: BCS theory of superconductivity Prof. Rafael M. Fernandes Here we will discuss a new ground state of the interacting electron gas: the superconducting state. In this macroscopic quantum state, the electrons form coherent bound states called Cooper pairs, which dramatically change the macroscopic properties of the system, giving rise to perfect conductivity and perfect diamagnetism. We will mostly focus on conventional superconductors, where the Cooper pairs originate from a small attractive electron-electron interaction mediated by phonons. However, in the so- called unconventional superconductors - a topic of intense research in current solid state physics - the pairing can originate even from purely repulsive interactions. 1 Phenomenology Superconductivity was discovered by Kamerlingh-Onnes in 1911, when he was studying the transport properties of Hg (mercury) at low temperatures. He found that below the liquifying temperature of helium, at around 4:2 K, the resistivity of Hg would suddenly drop to zero. Although at the time there was not a well established model for the low-temperature behavior of transport in metals, the result was quite surprising, as the expectations were that the resistivity would either go to zero or diverge at T = 0, but not vanish at a finite temperature. In a metal the resistivity at low temperatures has a constant contribution from impurity scattering, a T 2 contribution from electron-electron scattering, and a T 5 contribution from phonon scattering. Thus, the vanishing of the resistivity at low temperatures is a clear indication of a new ground state. Another key property of the superconductor was discovered in 1933 by Meissner. -
Supercritical Fluid Extraction of Positron-Emitting Radioisotopes from Solid Target Matrices
XA0101188 11. United States of America Supercritical Fluid Extraction of Positron-Emitting Radioisotopes From Solid Target Matrices D. Schlyer, Brookhaven National Laboratory, Chemistry Department, Upton, Bldg. 901, New York 11973-5000, USA Project Description Supercritical fluids are attractive as media for both chemical reactions, as well as process extraction since their physical properties can be manipulated by small changes in pressure and temperature near the critical point of the fluid. What is a supercritical fluid? Above a certain temperature, a vapor can no longer be liquefied regardless of pressure critical temperature - Tc supercritical fluid r«gi on solid a u & temperature Fig. 1. Phase diagram depicting regions of solid, liquid, gas and supercritical fluid behavior. The critical point is defined by a critical pressure (Pc) and critical temperature (Tc) for a particular substance. Such changes can result in drastic effects on density-dependent properties such as solubility, refractive index, dielectric constant, viscosity and diffusivity of the fluid[l,2,3]. This suggests that pressure tuning of a pure supercritical fluid may be a useful means to manipulate chemical reactions on the basis of a thermodynamic solvent effect. It also means that the solvation properties of the fluid can be precisely controlled to enable selective component extraction from a matrix. In recent years there has been a growing interest in applying supercritical fluid extraction to the selective removal of trace metals from solid samples [4-10]. Much of the work has been done on simple systems comprised of inert matrices such as silica or cellulose. Recently, this process as been expanded to environmental samples as well [11,12]. -
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. -
Determination of the Identity of an Unknown Liquid Group # My Name the Date My Period Partner #1 Name Partner #2 Name
Determination of the Identity of an unknown liquid Group # My Name The date My period Partner #1 name Partner #2 name Purpose: The purpose of this lab is to determine the identity of an unknown liquid by measuring its density, melting point, boiling point, and solubility in both water and alcohol, and then comparing the results to the values for known substances. Procedure: 1) Density determination Obtain a 10mL sample of the unknown liquid using a graduated cylinder Determine the mass of the 10mL sample Save the sample for further use 2) Melting point determination Set up an ice bath using a 600mL beaker Obtain a ~5mL sample of the unknown liquid in a clean dry test tube Place a thermometer in the test tube with the sample Place the test tube in the ice water bath Watch for signs of crystallization, noting the temperature of the sample when it occurs Save the sample for further use 3) Boiling point determination Set up a hot water bath using a 250mL beaker Begin heating the water in the beaker Obtain a ~10mL sample of the unknown in a clean, dry test tube Add a boiling stone to the test tube with the unknown Open the computer interface software, using a graph and digit display Place the temperature sensor in the test tube so it is in the unknown liquid Record the temperature of the sample in the test tube using the computer interface Watch for signs of boiling, noting the temperature of the unknown Dispose of the sample in the assigned waste container 4) Solubility determination Obtain two small (~1mL) samples of the unknown in two small test tubes Add an equal amount of deionized into one of the samples Add an equal amount of ethanol into the other Mix both samples thoroughly Compare the samples for solubility Dispose of the samples in the assigned waste container Observations: The unknown is a clear, colorless liquid. -
Equation of State and Phase Transitions in the Nuclear
National Academy of Sciences of Ukraine Bogolyubov Institute for Theoretical Physics Has the rights of a manuscript Bugaev Kyrill Alekseevich UDC: 532.51; 533.77; 539.125/126; 544.586.6 Equation of State and Phase Transitions in the Nuclear and Hadronic Systems Speciality 01.04.02 - theoretical physics DISSERTATION to receive a scientific degree of the Doctor of Science in physics and mathematics arXiv:1012.3400v1 [nucl-th] 15 Dec 2010 Kiev - 2009 2 Abstract An investigation of strongly interacting matter equation of state remains one of the major tasks of modern high energy nuclear physics for almost a quarter of century. The present work is my doctor of science thesis which contains my contribution (42 works) to this field made between 1993 and 2008. Inhere I mainly discuss the common physical and mathematical features of several exactly solvable statistical models which describe the nuclear liquid-gas phase transition and the deconfinement phase transition. Luckily, in some cases it was possible to rigorously extend the solutions found in thermodynamic limit to finite volumes and to formulate the finite volume analogs of phases directly from the grand canonical partition. It turns out that finite volume (surface) of a system generates also the temporal constraints, i.e. the finite formation/decay time of possible states in this finite system. Among other results I would like to mention the calculation of upper and lower bounds for the surface entropy of physical clusters within the Hills and Dales model; evaluation of the second virial coefficient which accounts for the Lorentz contraction of the hard core repulsing potential between hadrons; inclusion of large width of heavy quark-gluon bags into statistical description. -
Physics, Chapter 17: the Phases of Matter
University of Nebraska - Lincoln DigitalCommons@University of Nebraska - Lincoln Robert Katz Publications Research Papers in Physics and Astronomy 1-1958 Physics, Chapter 17: The Phases of Matter Henry Semat City College of New York Robert Katz University of Nebraska-Lincoln, [email protected] Follow this and additional works at: https://digitalcommons.unl.edu/physicskatz Part of the Physics Commons Semat, Henry and Katz, Robert, "Physics, Chapter 17: The Phases of Matter" (1958). Robert Katz Publications. 165. https://digitalcommons.unl.edu/physicskatz/165 This Article is brought to you for free and open access by the Research Papers in Physics and Astronomy at DigitalCommons@University of Nebraska - Lincoln. It has been accepted for inclusion in Robert Katz Publications by an authorized administrator of DigitalCommons@University of Nebraska - Lincoln. 17 The Phases of Matter 17-1 Phases of a Substance A substance which has a definite chemical composition can exist in one or more phases, such as the vapor phase, the liquid phase, or the solid phase. When two or more such phases are in equilibrium at any given temperature and pressure, there are always surfaces of separation between the two phases. In the solid phase a pure substance generally exhibits a well-defined crystal structure in which the atoms or molecules of the substance are arranged in a repetitive lattice. Many substances are known to exist in several different solid phases at different conditions of temperature and pressure. These solid phases differ in their crystal structure. Thus ice is known to have six different solid phases, while sulphur has four different solid phases. -
Ionic Liquid and Supercritical Fluid Hyphenated Techniques for Dissolution and Separation of Lanthanides, Actinides, and Fission Products
Project No. 09-805 Ionic Liquid and Supercritical Fluid Hyphenated Techniques for Dissolution and Separation of Lanthanides, Actinides, and Fission Products ItIntegrat tdUied Universit itPy Programs Dr. Chien Wai University of Idaho In collaboration with: Idaho National Laboratory Jack Law, Technical POC James Bresee, Federal POC 1 Ionic Liquid and Supercritical Fluid Hyphenated Techniques For Dissolution and Separation of Lanthanides and Actinides DOE-NEUP Project (TO 00058) Final Technical Report Principal Investigator: Chien M. Wai Department of Chemistry, University of Idaho, Moscow, Idaho 83844 Date: December 1, 2012 2 Table of Contents Project Summary 3 Publications Derived from the Project 5 Chapter I. Introduction 6 Chapter II. Uranium Dioxide in Ionic Liquid with a TP-HNO3 Complex – Dissolution and Coordination Environment 9 1. Dissolution of UO2 in Ionic Liquid with TBP(HNO3)1.8(H2O)0.6 2. Raman Spectra of Dissolved Uranyl Species in IL 13 3. Transferring Uranium from IL Phase to sc-CO2 15 Chapter III. Kinetic Study on Dissolution of Uranium Dioxide and Neodymium Sesquioxide in Ionic Liquid 19 1. Rate of Dissolution of UO2 and Nd2O3 in RTIL 19 2. Temperature Effect on Dissolution of UO2 and Nd2O3 24 3. Viscosity Effect on Dissolution of UO2 in IL with TBP(HNO3)1.8(H2O)0.6 Chapter IV. Separation of UO2(NO3)2(TBP)2 and Nd(NO3)3(TBP)3 in Ionic Liquid Using Diglycolamide and Supercritical CO2 Extraction 30 1. Complexation of Uranyl with Diglycolamide TBDGA in Ionic Liquid 31 2. Complexation of Neodymium(III) with TBDGA in Ionic Liquid 35 3. Solubility and Distribution Ratio of UO2(NO3)2(TBP)2 and Nd(NO3)3(TBP)3 in Supercritical CO2 Phase 38 4. -
The Basics of Vapor-Liquid Equilibrium (Or Why the Tripoli L2 Tech Question #30 Is Wrong)
The Basics of Vapor-Liquid Equilibrium (Or why the Tripoli L2 tech question #30 is wrong) A question on the Tripoli L2 exam has the wrong answer? Yes, it does. What is this errant question? 30.Above what temperature does pressurized nitrous oxide change to a gas? a. 97°F b. 75°F c. 37°F The correct answer is: d. all of the above. The answer that is considered correct, however, is: a. 97ºF. This is the critical temperature above which N2O is neither a gas nor a liquid; it is a supercritical fluid. To understand what this means and why the correct answer is “all of the above” you have to know a little about the behavior of liquids and gases. Most people know that water boils at 212ºF. Most people also know that when you’re, for instance, boiling an egg in the mountains, you have to boil it longer to fully cook it. The reason for this has to do with the vapor pressure of water. Every liquid wants to vaporize to some extent. The measure of this tendency is known as the vapor pressure and varies as a function of temperature. When the vapor pressure of a liquid reaches the pressure above it, it boils. Until then, it evaporates until the fraction of vapor in the mixture above it is equal to the ratio of the vapor pressure to the total pressure. At that point it is said to be in equilibrium and no further liquid will evaporate. The vapor pressure of water at 212ºF is 14.696 psi – the atmospheric pressure at sea level. -
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). -
Application of Supercritical Fluids Review Yoshiaki Fukushima
1 Application of Supercritical Fluids Review Yoshiaki Fukushima Abstract Many advantages of supercritical fluids come Supercritical water is expected to be useful in from their interesting or unusual properties which waste treatment. Although they show high liquid solvents and gas carriers do not possess. solubility solutes and molecular catalyses, solvent Such properties and possible applications of molecules under supercritical conditions gently supercritical fluids are reviewed. As these fluids solvate solute molecules and have little influence never condense at above their critical on the activities of the solutes and catalysts. This temperatures, supercritical drying is useful to property would be attributed to the local density prepare dry-gel. The solubility and other fluctuations around each molecule due to high important parameters as a solvent can be adjusted molecular mobility. The fluctuations in the continuously. Supercritical fluids show supercritical fluids would produce heterogeneity advantages as solvents for extraction, coating or that would provide novel chemical reactions with chemical reactions thanks to these properties. molecular catalyses, heterogenous solid catalyses, Supercritical water shows a high organic matter enzymes or solid adsorbents. solubility and a strong hydrolyzing ability. Supercritical fluid, Supercritical water, Solubility, Solvation, Waste treatment, Keywords Coating, Organic reaction applications development reached the initial peak 1. Introduction during the period from the second half of the 1960s There has been rising concern in recent years over to the 1970s followed by the secondary peak about supercritical fluids for organic waste treatment and 15 years later. The initial peak was for the other applications. The discovery of the presence of separation and extraction technique as represented 1) critical point dates back to 1822. -
Glossary of Terms
GLOSSARY OF TERMS For the purpose of this Handbook, the following definitions and abbreviations shall apply. Although all of the definitions and abbreviations listed below may have not been used in this Handbook, the additional terminology is provided to assist the user of Handbook in understanding technical terminology associated with Drainage Improvement Projects and the associated regulations. Program-specific terms have been defined separately for each program and are contained in pertinent sub-sections of Section 2 of this handbook. ACRONYMS ASTM American Society for Testing Materials CBBEL Christopher B. Burke Engineering, Ltd. COE United States Army Corps of Engineers EPA Environmental Protection Agency IDEM Indiana Department of Environmental Management IDNR Indiana Department of Natural Resources NRCS USDA-Natural Resources Conservation Service SWCD Soil and Water Conservation District USDA United States Department of Agriculture USFWS United States Fish and Wildlife Service DEFINITIONS AASHTO Classification. The official classification of soil materials and soil aggregate mixtures for highway construction used by the American Association of State Highway and Transportation Officials. Abutment. The sloping sides of a valley that supports the ends of a dam. Acre-Foot. The volume of water that will cover 1 acre to a depth of 1 ft. Aggregate. (1) The sand and gravel portion of concrete (65 to 75% by volume), the rest being cement and water. Fine aggregate contains particles ranging from 1/4 in. down to that retained on a 200-mesh screen. Coarse aggregate ranges from 1/4 in. up to l½ in. (2) That which is installed for the purpose of changing drainage characteristics.