DOCSLIB.ORG

The Superheating Field of Niobium: Theory and Experiment

Total Page：16

File Type：pdf, Size：1020Kb

Download full-text PDF Read full-text
The Superheating Field of Niobium: Theory and Experiment Proceedings of SRF2011, Chicago, IL USA TUIOA05 THE SUPERHEATING FIELD OF NIOBIUM: THEORY AND EXPERIMENT N. Valles† and M. Liepe, Cornell University, CLASSE, Ithaca, NY 14853, USA Abstract new research being done at Cornell to probe this phenom- ena. Finally, the implications of the work presented here This study discusses the superheating field of Niobium, are discussed and regions for further study are explored. a metastable state, which sets the upper limit of sustainable magnetic fields on the surface of a superconductors before flux starts to penetrate into the material. Current models Critical Fields of Superconductors for the superheating field are discussed, and experimental When a superconductor in a constant magnetic field is results are presented for niobium obtained through pulsed, cooled below its critical temperature, it expels the mag- high power measurements performed at Cornell. Material netic field from the bulk of the superconductor. This is preparation is also shown to be an important parameter in accomplished by superconducting electrons establishing a exploring other regions of the superheating field, and fun- magnetization cancelling the applied field in the bulk of damental limits are presented based upon these experimen- the material. The magnetic is field limited to a small region tal and theoretical results. close to the surface, characterized by a penetration depth λ, which is the region in which supercurrents flow. Another INTRODUCTION important length scale in superconductors is the coherence length, ξ0 which is related to the spatial variation of the An important property of superconductors that has posed superconducting electron density. The ratio of these char- both theoretical and experimental challenges is the mag- acteristic length scales yields the Ginsburg-Landau (GL) netic superheating field, a metastable state wherein the ma- parameter, κ ≡ λ/ξ. terial remains fully superconducting above the respective Pippard improved upon the superconductor model that critical fields in steady state. Obtaining accurate measure- only assumed local electron interaction to take into account ments of this metastable state is essential to expand the the- non-local effects. He argued that superconducting wave- oretical understanding of this phenomena and determine functions should have a characteristic dimension ξ 0. If only the ultimate limit of radio-frequency superconductors. In electrons around kB Tc of the Fermi energy can be involved this study, niobium is used to probe this limiting field. in the dynamics around the critical temperature, and they Studying the superheating field is important on sev- have a momentum range Δp ≈ kBTc/vF , where vF is eral counts. First, current theoretical models can imme- the Fermi velocity, then the approximate coherence length diately be tested against measurements. Second, the re- should, by the uncertainty principle be gions in which empirical methods accurately describe the field tend to be in limiting cases, such as the low- or high-κ ¯h ¯hvF Δx ∼ → ξ0 ∼ . (1) limit,[1, 2] or in small temperature ranges around the criti- Δp kBTc cal temperature.[3] Measuring the superheating field in the intermediate range, where κ ∼ 1, provides an important re- Assuming a pure material has a coherence length ξ 0, Pi- sult that can guide development of new models covering the pard showed that if impurities introduce scattering centers entire range of κ. Third, most models are based upon a phe- giving an electron mean free path of , then the coherence nomenological model of the superheating field, only valid length of the impure material, ξ, is modified to be near Tc, and so say nothing about the behaviour as a func- 1 1 1 tion of temperature. Newer, non-phenomenological calcu- = + , (2) lations taking temperature dependence into account need ξ ξ0 accurate data to test against. Finally, the accurate determi- and the penetration depth becomes nation of the superheating field also is of particular interest T in application. While theory and experiment agree near c, ξ niobium microwave cavities for particle accelerators oper- λ = λ 1+ 0 , L (3) ate at temperatures <Tc/4, where theory and experiment are disparate, so measurements can set stringent upper lim- where λL is the mean free-path of the material with no scat- its for what is possible with these cavities. tering sites.[4] This paper begins with a brief review of the the criti- These expressions can be used to give κ as a function of cal fields of superconductors, discusses the current state mean free path: of knowledge on the superheating field and then presents 3/2 ∗ Work supported by DOE award ER41628 λL ξ0 + † κ()= . (4) *[email protected] ξ0 04 Material studies 293 TUIOA05 Proceedings of SRF2011, Chicago, IL USA The ratio κ separates superconductors√ into two broad the behaviour near the surfaces must be taken into account. categories; those with κ<1/ 2 are√ called Type-I super- For fields parallel to a superconducting surface, above H c2 conductors and those with κ>1/ 2 are called Type-II superconductivity can nucleate at a metal-insulator inter- superconductors. The implications of this categorization faces, though the bulk remains normal conducting. will be elaborated upon later in this paper. Both theory and experiment have shown that for fields of The superconducting state is more ordered than the nor- magnitude mal conducting state because of the Cooper pairing of elec- Hc3 =1.695Hc2 (11) trons near the Fermi energy. Subjecting a material to a a superconducting surface sheath of thickness ξ persists, DC magnetic field causes supercurrents to flow in the layer while the bulk is normal conducting. This field dominates a within a penetration depth of the superconducting surface different type of phenomena compared with the other crit- to cancel out interior fields, which raises the free-energy of ical fields, because of the depth dependence of the state. the superconductor, Fs, which depends on the applied field. The other fields have constant depth profiles, either being When Fs is equal to the free energy of the normal conduct- in the Meissner state or normal conducting state, where as ing state, Fn, flux enters the superconductor, of volume V s, Hc3 transitions from superconducting to normal as depth and a phase transition occurs. increases. Finally, the field orientation for the other fields Mathematically, one can write an expression for the crit- is normal to the surface, whereas for Hc3 the field is paral- ical field that causes this phase transition, Hc, lel to the surface. Hc Fn = Fs(H =0)+μ0Vs HdH, (5) Metastability So far, these critical fields mentioned 0 are in equilibrium conditions. Before a transition takes which is applicable for Type-I superconductors in steady- place, there is an energy cost to nucleate a fluxoid, which state conditions. leaves open the possibility of a metastable state in which Supposing the energy density of superconductors is sup- the energetically favorable transition has not occurred due pressed over a coherence length ξ0, the free energy per unit to the activation energy barrier. This barrier vanishes at the area would be increased by superheating field, Hsh. Both Type-I and Type-II superconductors can persist in μ0 2 H ξ . the Meissner state above Hc1. The precise relationship be- 2 c 0 (6) tween Hsh and Hc is still a field of active experimental and If magnetic field, He is admitted to penetrate the material a theoretical research, but a phenomenological result shows distance λ, the free energy is lowered by that near Tc μ 2 0 2 T − He λ, (7) 2 Hsh = c(κ)Hc 1 − , (12) Tc giving a net boundary energy per unit area of c(κ) μ where is the ratio of the superheating field and the 0 ξ H2 − λH2 2 0 c e (8) thermodynamic critical field. The determination of this fac- tor is one of the central focuses of this work. Type-II superconductors, (having ξ 0 <λ) can benefit from a negative surface energy gain by allowing flux tubes SURVEY OF PREVIOUS WORK into the bulk of a superconductor at a field H c1, which by definition is below the field Hc. The superconductor is then Theoretical Survey in a mixed state having normal conducting regions inter- The superheating field has been studied in sev- H penetrating the bulk material, up to a field c2 when the eral regimes, mostly with phenomenological treatments entire material transitions into the normal state. through Ginzburg-Landau theory and is a challenging field H H An expression relating c1 and c, was given by to determine theoretically. Because it has been the most Merrill[5] as frequently used tools to study superconductivity, here we 0.08 outline the basic tenets of the GL Model. Hc1 = ln κ + √ Hc (9) Ginzburg and Landau approached superconductivity 2κ λ phenomenologically by introducing a parameter κ = ξ , The thermodynamic critical field and Hc2 are related ac- that is the ratio of the two characteristic lengths in a super- cording to conductor which can be used to broadly characterize su- 1 Hc2 perconductors into two classes, Type-I, with κ< √ and Hc = √ . (10) 2 2κ √1 <κ Type-II having 2 . There is one more type of critical field, denoted H c3 The basic postulate of GL theory is that if ψ, a pseudo- that is a surface effect first predicted by Saint-James and wavefunction that is the order parameter corresponding to de Gennes. Because real superconductors are finite in size, the number of superconducting electrons, varies slowly in 294 04 Material studies Proceedings of SRF2011, Chicago, IL USA TUIOA05 space then the free energy density f can be expanded in a superheating field as a function of temperature. Eliash- series of the form berg theory[7] requires the full information about the elec- tronic structure of the superconductor and is very difficult 2 2 2 β 4 1 ¯h ∗ μ0h to solve.
Load more

Recommended publications
  • Parallel-Powered Hybrid Cycle with Superheating “Partially” by Gas
    Parallel-Powered Hybrid Cycle with Superheating “Partially” by Gas Turbine Exhaust Milad Ghasemi, Hassan Hammodi, Homan Moosavi Sigaroodi ETA800 Final Thesis Project Division of Heat and Power Technology Department of Energy Technology Royal Institute of Technology Stockholm, Sweden [This page is left intentionally blank for the purposes of printing] Abstract It is of great importance to acquire methods that has a sustainable solution for treatment and disposal of municipal solid waste (MSW). The volumes are constantly increasing and improper waste management, like open dumping and landfilling, causes environmental impacts such as groundwater contamination and greenhouse gas emissions. The rationalization of developing a sustainable solution implies in an improved way of utilizing waste resources as an energy source with highest possible efficiency. MSW incineration is by far the best available way to dispose the waste. One drawback of conventional MSW incineration plants is that when the energy recovery occurs in the steam power cycle configuration, the reachable efficiency is limited due to steam parameters. The corrosive problem limits the temperature of the superheated steam from the boiler which lowers the efficiency of the system. A suitable and relatively cheap option for improving the efficiency of the steam power cycle is the implementation of a hybrid dual-fuel cycle. This paper aims to assess the integration of an MSW incineration with a high quality fuel conversion device, in this case natural gas (NG) combustion cycle, in a hybrid cycle. The aforementioned hybrid dual-fuel configuration combines a gas turbine topping cycle (TC) and a steam turbine bottoming cycle (BC). The TC utilizes the high quality fuel NG, while the BC uses the lower quality fuel, MSW, and reaches a total power output of 50 MW.
    [Show full text]
  • 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.
    [Show full text]
  • Thermodynamics of Air-Vapour Mixtures Module A
    roJuclear Reactor Containment Design Chapter 4: Thermodynamics ofAir-Vapour Mixtures Dr. Johanna Daams page 4A - 1 Module A: Introduction to Modelling CHAPTER 4: THERMODYNAMICS OF AIR-VAPOUR MIXTURES MODULE A: INTRODUCTION TO MODELLING MODULE OBJECTIVES: At the end of this module, you will be able to describe: 1. The three types of modelling, required for nuclear stations 2. The differences between safety code, training simulator code and engineering code ,... --, Vuclear Reector Conte/nment Design Chapter 4: Thermodynamics ofAir-Vapour Mixtures ". Johanna Daams page 4A-2 Module A: Introduction to Modelling 1.0 TYPES OF MODELLING CODE n the discussion of mathematical modelling of containment that follows, I will often say that certain !pproxlmatlons are allowable for simple simulations, and that safety analysis require more elaborate :alculations. Must therefore understand requirements for different types of simulation. 1.1 Simulation for engineering (design and post-construction design changes): • Purpose: Initially confirm system is within design parameters • limited scope - only parts of plant, few scenarios - and detail; • Simplified representation of overall plant or of a system to design feedback loops 1.2 Simulation for safety analysis: • Purpose: confirm that the nuclear station's design and operation during normal and emergency conditions will not lead to unacceptable excursions in physical parameters leading to equipment failure and risk to the public. Necessary to license plant design and operating mode. • Scope: all situations that may cause unsafe conditions. All systems that may cause such conditions. • Very complex representation of components and physical processes that could lead to public risk • Multiple independent programs for different systems, e.g.
    [Show full text]
  • Thermodynamic and Gasdynamic Aspects of a Boiling Liquid Expanding Vapour Explosion
    Thermodynamic and Gasdynamic Aspects of a Boiling Liquid Expanding Vapour Explosion Thermodynamic and Gasdynamic Aspects of a Boiling Liquid Expanding Vapour Explosion Proefschrift ter verkrijging van de graad van doctor aan de Technische Universiteit Delft, op gezag van de Rector Magnificus Prof. ir. K.C.A.M. Luyben, voorzitter van het College voor Promoties, in het openbaar te verdedigen op donderdag 29 augustus 2013 om 15:00 uur door Mengmeng XIE Master of Science in Computational and Experimental Turbulence Chalmers University of Technology, Sweden geboren te Shandong, China P.R. Dit proefschrift is goedgekeurd door de promotor: Prof. dr. D.J.E.M. Roekaerts Samenstelling promotiecommissie: Rector Magnificus, voorzitter Prof. dr. D.J.E.M. Roekaerts, Technische Universiteit Delft, promotor Prof. dr. ir. T.J.H. Vlugt, Technische Universiteit Delft Prof. dr. ir. C. Vuik, Technische Universiteit Delft Prof. dr. R.F.Mudde, Technische Universiteit Delft Prof. dr. ir. B. Koren, Technische Universiteit Eindhoven Prof. dr. D. Bedeaux, Norwegian University of Science and Technology Dr. ir. J. Weerheijm, TNO ⃝c 2013, Mengmeng Xie All rights reserved. No part of this book may be reproduced, stored in a retrieval system, or transmitted, in any form or by any means, without prior permission from the copyright owner. ISBN 978-90-8891-674-8 Keywords: BLEVE, Tunnel Safety, Shock, PLG, Non-equilibrium thermodynamics The research described in this thesis was performed in the section Reactive Flows and Explosions, of the department Multi-Scale Physics (MSP), of Delft University of Technology, Delft, The Netherlands. Printed by: Proefschriftmaken.nl || Uitgeverij BOXPress Published by: Uitgeverij BOXPress, ’s-Hertogenbosch, The Netherlands Dedicated to my family and in memory of Zhengchuan Su Financial support This project was financially supported by the Delft Cluster (www.delftcluster.nl), project Bijzondere Belastingen : Ondiep Bouwen.
    [Show full text]
  • Chemistry and Corrosion Issues in Supercritical Water Reactors
    IAEA-CN-164-5S12 Chemistry and Corrosion Issues in Supercritical Water Reactors V.A. Yurmanov, V. N.Belous, V. N.Vasina, E.V. Yurmanov N.A.Dollezhal Research and Development Institute of Power Engineering, Moscow, Russia Abstract. At the United Nations Millennium Summit, the President of the Russian Federation presented the initiative regarding energy supply for sustained development of mankind, radical solution of problems posed by proliferation of nuclear weapons, and global environmental improvement. Over the past years, Russia together with other countries of the world has seen nuclear renaissance. It is noteworthy that besides mass-scale construction of new nuclear plants some promising innovative projects are being developed by leading nuclear companies worldwide. Russia could significantly contribute to this process by sharing its huge experience and results of investigations. Russia has marked 45 year anniversary of commercial nuclear power industry. It was 45 years ago that a well known VVER reactor and a channel type reactor were put into operation at Novovoronezh NPP and at Beloyarsk NPP, respectively. Beloyarsk NPP’s experience with channel type reactor operation could be of special interest for the development of new generation supercritical water reactors. It is because already 45 years ago superheated nuclear steam was successfully used at AMB-100 and AMB-200 channel-type boiling reactors. Water chemistry for supercritical water reactors is vital. Optimum selection of structural materials and chemistry controls are two important issues. Despite multiple studies chemistry for supercritical water reactors is not clearly determined. Unlike thermodynamics or thermo-hydraulics, chemistry cannot be based solely on theoretical calculations.
    [Show full text]
  • Lecture 5: 09.21.05 Heat Storage and Release in Phase Transitions
    3.012 Fundamentals of Materials Science Fall 2005 Lecture 5: 09.21.05 Heat storage and release in phase transitions Today: LAST TIME .........................................................................................................................................................................................2 Calculation of internal energy changes .....................................................................................................................................3 HEAT STORED AND RELEASED DURING PHASE CHANGES................................................................................................................4 Adding heat to materials .............................................................................................................................................................4 Adding heat to material… at a phase transition ........................................................................................................................5 ACCOUNTING FOR THERMAL ENERGY IN A MATERAL: ENTHALPY1 ................................................................................................6 A new thermodynamic function to help us analyze the heat storage/release in phase transitions.........................................6 Enthalpies, phase fraction, and heat capacities at first-order phase transitions ....................................................................8 Phase fractions during a transformation.......................................................................................................................................................9
    [Show full text]
  • An Integrated Study of Flue Gas Flow and Superheating Process in Recovery Boiler Using Computational Fluid Dynamics and 1D-Process Modelling
    An Integrated Study of Flue Gas Flow and Superheating Process in Recovery Boiler using Computational Fluid Dynamics and 1D-Process Modelling Kunal Kumar Andritz Oy, Viljami Maakala Andritz Oy and Ville Vuorinen Aalto University ABSTRACT Superheaters are the last heat exchangers on the steam side in recovery boilers. They are typically made of expensive materials due to the high steam temperature and risks associated with ash-induced corrosion. Therefore, detailed knowledge about the steam properties and material temperature distribution is essential for improving the energy efficiency, cost efficiency and safety of recovery boilers. In this work, for the first time, a comprehensive 1D-process model (1D-PM) for superheated steam cycle is developed and linked with a full-scale 3D CFD (computational fluid dynamics) model of the superheater region flue gas flow. The results indicate that first; the geometries of headers and superheater platens affect platen-wise steam distribution. Second, the CFD solution of the 3D flue gas flow field and platen heat flux distribution coupled with the 1D-PM affect the generated superheated steam properties and material temperature distribution. These new observations clearly demonstrate the value of the present integrated CFD/1D-PM modelling approach. It is advantageous for trouble shooting, optimizing the performance of superheaters and selecting their design margins for the future. The developed integrated modelling approach could also be relevant for other large-scale energy production units such as biomass-fired boilers. 1 INTRODUCTION Recovery boilers are used to combust black liquor for chemical recovery and producing high-pressure superheated steam. The generated steam is utilized for self-sustainable pulp mill operations and electricity generation.
    [Show full text]
  • Experimental Superheating of Water and Aqueous Solutions Kirill Shmulovich, Lionel Mercury, Régis Thiery, Claire Ramboz, Mouna El Mekki
    Experimental superheating of water and aqueous solutions Kirill Shmulovich, Lionel Mercury, Régis Thiery, Claire Ramboz, Mouna El Mekki To cite this version: Kirill Shmulovich, Lionel Mercury, Régis Thiery, Claire Ramboz, Mouna El Mekki. Experimental superheating of water and aqueous solutions. Geochimica et Cosmochimica Acta, Elsevier, 2009, 73, pp.2457-2470. 10.1016/j.gca.2009.02.006. insu-00371852 HAL Id: insu-00371852 https://hal-insu.archives-ouvertes.fr/insu-00371852 Submitted on 30 Mar 2009 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. Experimental superheating of water and aqueous solutions Kirill I. Shmulovicha Lionel Mercury b, c, Régis Thiéryd Claire Rambozb and Mouna El Mekkib aInstitute of Experimental Mineralogy, Russian Academy of Science, 142432 Chernogolovka, Russia bInstitut des Sciences de la Terre d’Orléans, UMR 6113 CNRS/Universités Orléans-Tours, 1A rue de la Férollerie, 45071 Orléans Cedex, France cUMR-CNRS 8148 “IDES”, Université Paris-Sud, bat. 504, 91405 Orsay, France dLaboratoire Magmas et Volcans, UMR 6524, CNRS/Clermont Université, 5 rue Kessler, 63038 Clermont-Ferrand Cedex, France Abstract The metastable superheated solutions are liquids in transitory thermodynamic equilibrium inside the stability domain of their vapor (whatever the temperature is).
    [Show full text]
  • Vapor Power Cycles Ideal Rankine Cycle
    Vapor Power Cycles We know that the Carnot cycle is most efficient cycle operating between two specified temperature limits. However; the Carnot cycle is not a suitable model for steam power cycle since: The turbine has to handle steam with low quality which will cause erosion and wear in turbine blades. It is impractical to design a compressor that handles two phase. It is difficult to control the condensation process that precisely as to end up with the desired at point 4. T 1 2 1 2 4 3 4 3 s s Fig. 1: T-s diagram for two Carnot vapor cycle. Other issues include: isentropic compression to extremely high pressure and isothermal heat transfer at variable pressures. Thus, the Carnot cycle cannot be approximated in actual devices and is not a realistic model for vapor power cycles. Ideal Rankine Cycle The Rankine cycle is the ideal cycle for vapor power plants; it includes the following four reversible processes: 1-2: Isentropic compression Water enters the pump as state 1 as saturated liquid and is compressed isentropically to the operating pressure of the boiler. 2-3: Const P heat addition Saturated water enters the boiler and leaves it as superheated vapor at state 3 3-4: Isentropic expansion Superheated vapor expands isentropically in turbine and produces work. 4-1: Const P heat rejection High quality steam is condensed in the condenser M. Bahrami ENSC 461 (S 11) Vapor Power Cycles 1 Boiler T 3 Turbine Wout Q in Qin 2 Wout Pump Win 4 Win 1 Qout Condenser Qout s Fig.
    [Show full text]
  • Extreme Liquid Superheating and Homogeneous Bubble Nucleation in a Solid State Nanopore
    Extreme Liquid Superheating and Homogeneous Bubble Nucleation in a Solid State Nanopore The Harvard community has made this article openly available. Please share how this access benefits you. Your story matters Citation Levine, Edlyn Victoria. 2016. Extreme Liquid Superheating and Homogeneous Bubble Nucleation in a Solid State Nanopore. Doctoral dissertation, Harvard University, Graduate School of Arts & Sciences. Citable link http://nrs.harvard.edu/urn-3:HUL.InstRepos:33493497 Terms of Use This article was downloaded from Harvard University’s DASH repository, and is made available under the terms and conditions applicable to Other Posted Material, as set forth at http:// nrs.harvard.edu/urn-3:HUL.InstRepos:dash.current.terms-of- use#LAA Extreme Liquid Superheating and Homogeneous Bubble Nucleation in a Solid State Nanopore a dissertation presented by Edlyn Victoria Levine to The School of Engineering and Applied Sciences in partial fulfillment of the requirements for the degree of Doctor of Philosophy in the subject of Applied Physics Harvard University Cambridge, Massachusetts April 2016 ©2016 – Edlyn Victoria Levine all rights reserved. Thesis advisor: Professor Jene A. Golovchenko Author: Edlyn Victoria Levine Extreme Liquid Superheating and Homogeneous Bubble Nucleation in a Solid State Nanopore Abstract This thesis explains how extreme superheating and single bubble nucleation can be achieved in an electrolytic solution within a solid state nanopore. A highly focused ionic current, induced to flow through the pore by modest voltage biases, leads to rapid Joule heating of the electrolyte in the nanopore. At sufficiently high current densities, temperatures near the thermodynamic limit of superheat are achieved, ultimately leading to nucleation of a vapor bubble within the nanopore.
    [Show full text]
  • Ability of the Generalized Van Der Waals and Berthelot Equations of State to Determine the Thermodynamic Stability of Liquid Lead
    Volume 20, issue 4, pages 132–138 31 December 2020 https://doi.org/10.33493/scivis.20.04.01 RESEARCH ARTICLE Ability of the generalized van der Waals and Berthelot equations of state to determine the thermodynamic stability of liquid lead Ramesh Arumugam, Balasubramanian Ramasamy* Department of Physics, Arignar Anna Government Arts College, Namakkal 637 002, Tamilnadu, India The known van der Waals and Berthelot equations of state do-not precisely Received 3 August 2020 Accepted 10 December 2020 describe the thermodynamic properties of fluids. To improve its accuracy, the attractive term of the van der Waals equation of state has been modified in six *For correspondence: [email protected] different ways. These generalized equations of state have been employed to determine the spinodal (thermodynamic stability boundary) and the Contact us: [email protected] thermodynamic limit of superheat of liquid lead. The equations of state are rewritten in reduced form, from which follows the law of corresponding states. The appropriate modification of the attractive term of the equation of state yielding the value of thermodynamic limit of superheat agreeing with the experimental value for lead has been established. It has been established that liquid lead can be superheated, under rapid heating, up to a temperature 4565 K. That is, liquid lead can be superheated to 2544 K above the normal boiling temperature. At the thermodynamic limit of superheat, the volume of the liquid lead is 4.0095 × 10-5 m3 mol-1. This fact is to be taken into account when liquid lead is subjected to rapid heating. Keywords: Corresponding states, critical point, equation of state, lead, spinodal, thermodynamic limit of superheating.
    [Show full text]
  • Thermodynamics of Water Superheated in the Microwave Oven Ben H
    CORE Metadata, citation and similar papers at core.ac.uk Provided by Sacred Heart University: DigitalCommons@SHU Sacred Heart University DigitalCommons@SHU Chemistry & Physics Faculty Publications Chemistry and Physics 10-2000 Thermodynamics of Water Superheated in the Microwave Oven Ben H. Erné Penny A. Snetsinger Sacred Heart University, [email protected] Follow this and additional works at: http://digitalcommons.sacredheart.edu/chem_fac Part of the Chemistry Commons Recommended Citation Erné, B.H. & Snetsinger, P. (2000). Thermodynamics of water superheated in the microwave oven. Journal of Chemical Education 77(10), 1309-1310. doi: 10.1021/ed077p1309 This Article is brought to you for free and open access by the Chemistry and Physics at DigitalCommons@SHU. It has been accepted for inclusion in Chemistry & Physics Faculty Publications by an authorized administrator of DigitalCommons@SHU. For more information, please contact [email protected], [email protected]. In the Classroom edited by Tested Demonstrations Ed Vitz Kutztown University Thermodynamics of Water Superheated Kutztown, PA 19530 in the Microwave Oven submitted by: B. H. Erné Institut Lavoisier (IREM, UMR CNRS C8637), Université de Versailles St-Quentin-en-Yvelines, 45 Avenue des Etats-Unis, 78035 Versailles, France; [email protected] checked by: Penny Snetsinger Department of Chemistry and Physics, Sacred Heart University, Fairfield, CT 06432 The beauty of classical thermodynamics is that heat a microwave oven allows one to superheat water relatively homo- transfers can be accounted for without a detailed description geneously throughout the entire volume, as opposed to using a of the physical systems considered, but the concepts are rather stove or a Bunsen burner, in which case superheating is highest abstract and concrete examples are welcome.
    [Show full text]