A Theoretical Analysis on Enthalpy of Vaporization: Temperature-Dependence and Singularity at the Critical State
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Physical Model for Vaporization
Physical model for vaporization Jozsef Garai Department of Mechanical and Materials Engineering, Florida International University, University Park, VH 183, Miami, FL 33199 Abstract Based on two assumptions, the surface layer is flexible, and the internal energy of the latent heat of vaporization is completely utilized by the atoms for overcoming on the surface resistance of the liquid, the enthalpy of vaporization was calculated for 45 elements. The theoretical values were tested against experiments with positive result. 1. Introduction The enthalpy of vaporization is an extremely important physical process with many applications to physics, chemistry, and biology. Thermodynamic defines the enthalpy of vaporization ()∆ v H as the energy that has to be supplied to the system in order to complete the liquid-vapor phase transformation. The energy is absorbed at constant pressure and temperature. The absorbed energy not only increases the internal energy of the system (U) but also used for the external work of the expansion (w). The enthalpy of vaporization is then ∆ v H = ∆ v U + ∆ v w (1) The work of the expansion at vaporization is ∆ vw = P ()VV − VL (2) where p is the pressure, VV is the volume of the vapor, and VL is the volume of the liquid. Several empirical and semi-empirical relationships are known for calculating the enthalpy of vaporization [1-16]. Even though there is no consensus on the exact physics, there is a general agreement that the surface energy must be an important part of the enthalpy of vaporization. The vaporization diminishes the surface energy of the liquid; thus this energy must be supplied to the system. -
Thermodynamics Notes
Thermodynamics Notes Steven K. Krueger Department of Atmospheric Sciences, University of Utah August 2020 Contents 1 Introduction 1 1.1 What is thermodynamics? . .1 1.2 The atmosphere . .1 2 The Equation of State 1 2.1 State variables . .1 2.2 Charles' Law and absolute temperature . .2 2.3 Boyle's Law . .3 2.4 Equation of state of an ideal gas . .3 2.5 Mixtures of gases . .4 2.6 Ideal gas law: molecular viewpoint . .6 3 Conservation of Energy 8 3.1 Conservation of energy in mechanics . .8 3.2 Conservation of energy: A system of point masses . .8 3.3 Kinetic energy exchange in molecular collisions . .9 3.4 Working and Heating . .9 4 The Principles of Thermodynamics 11 4.1 Conservation of energy and the first law of thermodynamics . 11 4.1.1 Conservation of energy . 11 4.1.2 The first law of thermodynamics . 11 4.1.3 Work . 12 4.1.4 Energy transferred by heating . 13 4.2 Quantity of energy transferred by heating . 14 4.3 The first law of thermodynamics for an ideal gas . 15 4.4 Applications of the first law . 16 4.4.1 Isothermal process . 16 4.4.2 Isobaric process . 17 4.4.3 Isosteric process . 18 4.5 Adiabatic processes . 18 5 The Thermodynamics of Water Vapor and Moist Air 21 5.1 Thermal properties of water substance . 21 5.2 Equation of state of moist air . 21 5.3 Mixing ratio . 22 5.4 Moisture variables . 22 5.5 Changes of phase and latent heats . -
Vapour Absorption Refrigeration Systems Based on Ammonia- Water Pair
Lesson 17 Vapour Absorption Refrigeration Systems Based On Ammonia- Water Pair Version 1 ME, IIT Kharagpur 1 The specific objectives of this lesson are to: 1. Introduce ammonia-water systems (Section 17.1) 2. Explain the working principle of vapour absorption refrigeration systems based on ammonia-water (Section 17.2) 3. Explain the principle of rectification column and dephlegmator (Section 17.3) 4. Present the steady flow analysis of ammonia-water systems (Section 17.4) 5. Discuss the working principle of pumpless absorption refrigeration systems (Section 17.5) 6. Discuss briefly solar energy based sorption refrigeration systems (Section 17.6) 7. Compare compression systems with absorption systems (Section 17.7) At the end of the lecture, the student should be able to: 1. Draw the schematic of a ammonia-water based vapour absorption refrigeration system and explain its working principle 2. Explain the principle of rectification column and dephlegmator using temperature-concentration diagrams 3. Carry out steady flow analysis of absorption systems based on ammonia- water 4. Explain the working principle of Platen-Munter’s system 5. List solar energy driven sorption refrigeration systems 6. Compare vapour compression systems with vapour absorption systems 17.1. Introduction Vapour absorption refrigeration system based on ammonia-water is one of the oldest refrigeration systems. As mentioned earlier, in this system ammonia is used as refrigerant and water is used as absorbent. Since the boiling point temperature difference between ammonia and water is not very high, both ammonia and water are generated from the solution in the generator. Since presence of large amount of water in refrigerant circuit is detrimental to system performance, rectification of the generated vapour is carried out using a rectification column and a dephlegmator. -
Chapter 8 and 9 – Energy Balances
CBE2124, Levicky Chapter 8 and 9 – Energy Balances Reference States . Recall that enthalpy and internal energy are always defined relative to a reference state (Chapter 7). When solving energy balance problems, it is therefore necessary to define a reference state for each chemical species in the energy balance (the reference state may be predefined if a tabulated set of data is used such as the steam tables). Example . Suppose water vapor at 300 oC and 5 bar is chosen as a reference state at which Hˆ is defined to be zero. Relative to this state, what is the specific enthalpy of liquid water at 75 oC and 1 bar? What is the specific internal energy of liquid water at 75 oC and 1 bar? (Use Table B. 7). Calculating changes in enthalpy and internal energy. Hˆ and Uˆ are state functions , meaning that their values only depend on the state of the system, and not on the path taken to arrive at that state. IMPORTANT : Given a state A (as characterized by a set of variables such as pressure, temperature, composition) and a state B, the change in enthalpy of the system as it passes from A to B can be calculated along any path that leads from A to B, whether or not the path is the one actually followed. Example . 18 g of liquid water freezes to 18 g of ice while the temperature is held constant at 0 oC and the pressure is held constant at 1 atm. The enthalpy change for the process is measured to be ∆ Hˆ = - 6.01 kJ. -
A Comparative Energy and Economic Analysis Between a Low Enthalpy Geothermal Design and Gas, Diesel and Biomass Technologies for a HVAC System Installed in an Office Building
energies Article A Comparative Energy and Economic Analysis between a Low Enthalpy Geothermal Design and Gas, Diesel and Biomass Technologies for a HVAC System Installed in an Office Building José Ignacio Villarino 1, Alberto Villarino 1,* , I. de Arteaga 2 , Roberto Quinteros 2 and Alejandro Alañón 1 1 Department of Construction and Agronomy, Construction Engineering Area, High Polytechnic School of Ávila, University of Salamanca, Hornos Caleros, 50, 05003 Ávila, Spain; [email protected] (J.I.V.); [email protected] (A.A.) 2 Facultad de Ingeniería, Escuela de Ingeniería Mecánica, Pontificia Universidad Católica de Valparaíso, Av. Los Carrera 01567, Quilpué 2430000, Chile; [email protected] (I.d.A.); [email protected] (R.Q.) * Correspondence: [email protected]; Tel.: +34-920-353-500; Fax: +34-920-353-501 Received: 3 January 2019; Accepted: 25 February 2019; Published: 6 March 2019 Abstract: This paper presents an analysis of economic and energy between a ground-coupled heat pump system and other available technologies, such as natural gas, biomass, and diesel, providing heating, ventilation, and air conditioning to an office building. All the proposed systems are capable of reaching temperatures of 22 ◦C/25 ◦C in heating and cooling modes. EnergyPlus software was used to develop a simulation model and carry out the validation process. The first objective of the paper is the validation of the numerical model developed in EnergyPlus with the experimental results collected from the monitored building to evaluate the system in other operating conditions and to compare it with other available technologies. The second aim of the study is the assessment of the position of the low enthalpy geothermal system proposed versus the rest of the systems, from energy, economic, and environmental aspects. -
A Comprehensive Review of Thermal Energy Storage
sustainability Review A Comprehensive Review of Thermal Energy Storage Ioan Sarbu * ID and Calin Sebarchievici Department of Building Services Engineering, Polytechnic University of Timisoara, Piata Victoriei, No. 2A, 300006 Timisoara, Romania; [email protected] * Correspondence: [email protected]; Tel.: +40-256-403-991; Fax: +40-256-403-987 Received: 7 December 2017; Accepted: 10 January 2018; Published: 14 January 2018 Abstract: Thermal energy storage (TES) is a technology that stocks thermal energy by heating or cooling a storage medium so that the stored energy can be used at a later time for heating and cooling applications and power generation. TES systems are used particularly in buildings and in industrial processes. This paper is focused on TES technologies that provide a way of valorizing solar heat and reducing the energy demand of buildings. The principles of several energy storage methods and calculation of storage capacities are described. Sensible heat storage technologies, including water tank, underground, and packed-bed storage methods, are briefly reviewed. Additionally, latent-heat storage systems associated with phase-change materials for use in solar heating/cooling of buildings, solar water heating, heat-pump systems, and concentrating solar power plants as well as thermo-chemical storage are discussed. Finally, cool thermal energy storage is also briefly reviewed and outstanding information on the performance and costs of TES systems are included. Keywords: storage system; phase-change materials; chemical storage; cold storage; performance 1. Introduction Recent projections predict that the primary energy consumption will rise by 48% in 2040 [1]. On the other hand, the depletion of fossil resources in addition to their negative impact on the environment has accelerated the shift toward sustainable energy sources. -
Cryogenicscryogenics Forfor Particleparticle Acceleratorsaccelerators Ph
CryogenicsCryogenics forfor particleparticle acceleratorsaccelerators Ph. Lebrun CAS Course in General Accelerator Physics Divonne-les-Bains, 23-27 February 2009 Contents • Low temperatures and liquefied gases • Cryogenics in accelerators • Properties of fluids • Heat transfer & thermal insulation • Cryogenic distribution & cooling schemes • Refrigeration & liquefaction Contents • Low temperatures and liquefied gases ••• CryogenicsCryogenicsCryogenics ininin acceleratorsacceleratorsaccelerators ••• PropertiesPropertiesProperties ofofof fluidsfluidsfluids ••• HeatHeatHeat transfertransfertransfer &&& thermalthermalthermal insulationinsulationinsulation ••• CryogenicCryogenicCryogenic distributiondistributiondistribution &&& coolingcoolingcooling schemesschemesschemes ••• RefrigerationRefrigerationRefrigeration &&& liquefactionliquefactionliquefaction • cryogenics, that branch of physics which deals with the production of very low temperatures and their effects on matter Oxford English Dictionary 2nd edition, Oxford University Press (1989) • cryogenics, the science and technology of temperatures below 120 K New International Dictionary of Refrigeration 3rd edition, IIF-IIR Paris (1975) Characteristic temperatures of cryogens Triple point Normal boiling Critical Cryogen [K] point [K] point [K] Methane 90.7 111.6 190.5 Oxygen 54.4 90.2 154.6 Argon 83.8 87.3 150.9 Nitrogen 63.1 77.3 126.2 Neon 24.6 27.1 44.4 Hydrogen 13.8 20.4 33.2 Helium 2.2 (*) 4.2 5.2 (*): λ Point Densification, liquefaction & separation of gases LNG Rocket fuels LIN & LOX 130 000 m3 LNG carrier with double hull Ariane 5 25 t LHY, 130 t LOX Air separation by cryogenic distillation Up to 4500 t/day LOX What is a low temperature? • The entropy of a thermodynamical system in a macrostate corresponding to a multiplicity W of microstates is S = kB ln W • Adding reversibly heat dQ to the system results in a change of its entropy dS with a proportionality factor T T = dQ/dS ⇒ high temperature: heating produces small entropy change ⇒ low temperature: heating produces large entropy change L. -
Thermodynamics
ME346A Introduction to Statistical Mechanics { Wei Cai { Stanford University { Win 2011 Handout 6. Thermodynamics January 26, 2011 Contents 1 Laws of thermodynamics 2 1.1 The zeroth law . .3 1.2 The first law . .4 1.3 The second law . .5 1.3.1 Efficiency of Carnot engine . .5 1.3.2 Alternative statements of the second law . .7 1.4 The third law . .8 2 Mathematics of thermodynamics 9 2.1 Equation of state . .9 2.2 Gibbs-Duhem relation . 11 2.2.1 Homogeneous function . 11 2.2.2 Virial theorem / Euler theorem . 12 2.3 Maxwell relations . 13 2.4 Legendre transform . 15 2.5 Thermodynamic potentials . 16 3 Worked examples 21 3.1 Thermodynamic potentials and Maxwell's relation . 21 3.2 Properties of ideal gas . 24 3.3 Gas expansion . 28 4 Irreversible processes 32 4.1 Entropy and irreversibility . 32 4.2 Variational statement of second law . 32 1 In the 1st lecture, we will discuss the concepts of thermodynamics, namely its 4 laws. The most important concepts are the second law and the notion of Entropy. (reading assignment: Reif x 3.10, 3.11) In the 2nd lecture, We will discuss the mathematics of thermodynamics, i.e. the machinery to make quantitative predictions. We will deal with partial derivatives and Legendre transforms. (reading assignment: Reif x 4.1-4.7, 5.1-5.12) 1 Laws of thermodynamics Thermodynamics is a branch of science connected with the nature of heat and its conver- sion to mechanical, electrical and chemical energy. (The Webster pocket dictionary defines, Thermodynamics: physics of heat.) Historically, it grew out of efforts to construct more efficient heat engines | devices for ex- tracting useful work from expanding hot gases (http://www.answers.com/thermodynamics). -
International Centre for Theoretical Physics
REFi IC/90/116 INTERNATIONAL CENTRE FOR THEORETICAL PHYSICS FIXED SCALE TRANSFORMATION FOR ISING AND POTTS CLUSTERS A. Erzan and L. Pietronero INTERNATIONAL ATOMIC ENERGY AGENCY UNITED NATIONS EDUCATIONAL, SCIENTIFIC AND CULTURAL ORGANIZATION 1990 MIRAMARE- TRIESTE IC/90/116 International Atomic Energy Agency and United Nations Educational Scientific and Cultural Organization INTERNATIONAL CENTRE FOR THEORETICAL PHYSICS FIXED SCALE TRANSFORMATION FOR ISING AND POTTS CLUSTERS A. Erzan International Centre for Theoretical Physics, Trieste, Italy and L. Pietronero Dipartimento di Fisica, Universita di Roma, Piazzale Aldo Moro, 00185 Roma, Italy. ABSTRACT The fractal dimension of Ising and Potts clusters are determined via the Fixed Scale Trans- formation approach, which exploits both the self-similarity and the dynamical invariance of these systems at criticality. The results are easily extended to droplets. A discussion of inter-relations be- tween the present approach and renormalization group methods as well as Glauber—type dynamics is provided. MIRAMARE - TRIESTE May 1990 To be submitted for publication. T 1. INTRODUCTION The Fixed Scale Transformation, a novel technique introduced 1)i2) for computing the fractal dimension of Laplacian growth clusters, is applied here to the equilibrium problem of Ising clusters at criticality, in two dimensions. The method yields veiy good quantitative agreement with the known exact results. The same method has also recendy been applied to the problem of percolation clusters 3* and to invasion percolation 4), also with very good results. The fractal dimension D of the Ising clusters, i.e., the connected clusters of sites with identical spins, has been a controversial issue for a long time ^ (see extensive references in Refs.5 and 6). -
A Critical Review on Thermal Energy Storage Materials and Systems for Solar Applications
AIMS Energy, 7(4): 507–526. DOI: 10.3934/energy.2019.4.507 Received: 05 July 2019 Accepted: 14 August 2019 Published: 23 August 2019 http://www.aimspress.com/journal/energy Review A critical review on thermal energy storage materials and systems for solar applications D.M. Reddy Prasad1,*, R. Senthilkumar2, Govindarajan Lakshmanarao2, Saravanakumar Krishnan2 and B.S. Naveen Prasad3 1 Petroleum and Chemical Engineering Programme area, Faculty of Engineering, Universiti Teknologi Brunei, Gadong, Brunei Darussalam 2 Department of Engineering, College of Applied Sciences, Sohar, Sultanate of Oman 3 Sathyabama Institute of Science and Technology, Chennai, India * Correspondence: Email: [email protected]; [email protected]. Abstract: Due to advances in its effectiveness and efficiency, solar thermal energy is becoming increasingly attractive as a renewal energy source. Efficient energy storage, however, is a key limiting factor on its further development and adoption. Storage is essential to smooth out energy fluctuations throughout the day and has a major influence on the cost-effectiveness of solar energy systems. This review paper will present the most recent advances in these storage systems. The manuscript aims to review and discuss the various types of storage that have been developed, specifically thermochemical storage (TCS), latent heat storage (LHS), and sensible heat storage (SHS). Among these storage types, SHS is the most developed and commercialized, whereas TCS is still in development stages. The merits and demerits of each storage types are discussed in this review. Some of the important organic and inorganic phase change materials focused in recent years have been summarized. The key contributions of this review article include summarizing the inherent benefits and weaknesses, properties, and design criteria of materials used for storing solar thermal energy, as well as discussion of recent investigations into the dynamic performance of solar energy storage systems. -
Corollary from the Exact Expression for Enthalpy of Vaporization
Hindawi Publishing Corporation Journal of Thermodynamics Volume 2011, Article ID 945047, 7 pages doi:10.1155/2011/945047 Research Article Corollary from the Exact Expression for Enthalpy of Vaporization A. A. Sobko Department of Physics and Chemistry of New Materials, A. M. Prokhorov Academy of Engineering Sciences, 19 Presnensky Val, Moscow 123557, Russia Correspondence should be addressed to A. A. Sobko, [email protected] Received 14 November 2010; Revised 9 March 2011; Accepted 16 March 2011 Academic Editor: K. A. Antonopoulos Copyright © 2011 A. A. Sobko. This is an open access article distributed under the Creative Commons Attribution License, which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly cited. A problem on determining effective volumes for atoms and molecules becomes actual due to rapidly developing nanotechnologies. In the present study an exact expression for enthalpy of vaporization is obtained, from which an exact expression is derived for effective volumes of atoms and molecules, and under certain assumptions on the form of an atom (molecule) it is possible to find their linear dimensions. The accuracy is only determined by the accuracy of measurements of thermodynamic parameters at the critical point. 1. Introduction 1938 [2] with the edition from 1976 [3], we may find them actually similar. we may come to the same conclusion if In the present study, the relationship is obtained that we compare [2] with recent monograph by Prigogine and combines the enthalpy of vaporization with other thermody- Kondepudi “Modern Thermodynamics” [4]. The chapters namic evaporation parameters from the general expression devoted to first-order phase transitions in both monographs for the heat of first-order phase transformations. -
Liquid Equilibrium Measurements in Binary Polar Systems
DIPLOMA THESIS VAPOR – LIQUID EQUILIBRIUM MEASUREMENTS IN BINARY POLAR SYSTEMS Supervisors: Univ. Prof. Dipl.-Ing. Dr. Anton Friedl Associate Prof. Epaminondas Voutsas Antonia Ilia Vienna 2016 Acknowledgements First of all I wish to thank Doctor Walter Wukovits for his guidance through the whole project, great assistance and valuable suggestions for my work. I have completed this thesis with his patience, persistence and encouragement. Secondly, I would like to thank Professor Anton Friedl for giving me the opportunity to work in TU Wien and collaborate with him and his group for this project. I am thankful for his trust from the beginning until the end and his support during all this period. Also, I wish to thank for his readiness to help and support Professor Epaminondas Voutsas, who gave me the opportunity to carry out this thesis in TU Wien, and his valuable suggestions and recommendations all along the experimental work and calculations. Additionally, I would like to thank everybody at the office and laboratory at TU Wien for their comprehension and selfless help for everything I needed. Furthermore, I wish to thank Mersiha Gozid and all the students of Chemical Engineering Summer School for their contribution of data, notices, questions and solutions during my experimental work. And finally, I would like to thank my family and friends for their endless support and for the inspiration and encouragement to pursue my goals and dreams. Abstract An experimental study was conducted in order to investigate the vapor – liquid equilibrium of binary mixtures of Ethanol – Butan-2-ol, Methanol – Ethanol, Methanol – Butan-2-ol, Ethanol – Water, Methanol – Water, Acetone – Ethanol and Acetone – Butan-2-ol at ambient pressure using the dynamic apparatus Labodest VLE 602.