DOCSLIB.ORG

Thermodynamics Skeleton Guide

Total Page：16

File Type：pdf, Size：1020Kb

Download full-text PDF Read full-text
Thermodynamics Skeleton Guide Thermodynamics Skeleton Guide Joseph E. Shepherd Division of Engineering and Applied Science California Institute of Technology Pasadena, CA 91125 December 7, 2019 Copyright California Institute of Technology 2001-2007 The Laws of Thermodynamics 1. You can’t win, you can only break even. 2. You can only break even at the absolute zero. 3. You cannot reach absolute zero. Conclusion: You can neither win nor break even. Quoted by Dugdale on the last page of Entropy and its physical meaning. Warning This is not a textbook on thermodynamics or even a set of notes that you can learn from. There are no figures or derivations, nothing about applications, and no examples. Fur- thermore, it is not logically organized. It is a collection of facts and formulas that represent the essential mathematical framework or “skeleton” that I use when teaching thermodynamics. Some of formulas may be wrong and the notation may be inconsistent. The main purpose is to typeset the equations and symbols so that when the students can’t read my terrible handwriting on the chalk board they have something to fall back on. If you need a text, some suggestions are discussed in SectionA. JES, April 1, 2007. Contents 1 Fundamentals1 1.1 Thermodynamic Systems...............................1 1.2 Equilibrium......................................1 1.3 State Variables....................................2 1.4 Energy.........................................2 1.5 Zeroth Law of Thermodynamics...........................2 2 First Law of Thermodynamics3 2.1 Point vs. Path Function................................3 2.2 Work..........................................3 2.3 Enthalpy........................................3 2.4 Specific Properties..................................4 2.5 Heat Capacity and Specific Heat...........................4 3 Cycles 5 3.1 Thermodynamic Efficiency..............................5 3.2 Carnot Cycle.....................................5 3.2.1 Carnot’s Theorem...............................6 3.2.2 Thermodynamic Temperature........................6 4 Second Law of Thermodynamics - Cycle Version6 4.1 Kelvin-Planck.....................................6 4.2 Clausius........................................6 5 Entropy 7 5.1 Entropy as a State Function..............................7 6 Second Law of Thermodynamics - Entropy Version7 7 Open Systems8 7.1 Mass..........................................8 7.2 Energy.........................................8 7.3 Entropy........................................8 7.4 Steady State, Steady Flow..............................9 7.5 Ideal Stagnation Properties..............................9 7.6 Sound speed and Mach number............................ 10 7.7 Efficiency....................................... 10 8 Availability, Maximum Work and Reversibility 11 8.1 Availability of a Closed System............................ 11 8.2 Second Law analysis of flowing systems....................... 11 i 9 Ideal Gas 13 9.1 Ideal Gas Law..................................... 13 9.2 Internal Energy.................................... 13 9.3 Adiabatic Reversible Compression.......................... 14 9.4 Entropy........................................ 15 9.5 Gas Kinetics...................................... 15 9.5.1 Mean Free Path................................ 16 9.5.2 Distribution of Molecular Velocities..................... 17 9.5.3 Distribution of Molecular Energies...................... 20 9.5.4 Ideal Gas Law................................ 21 9.5.5 Specific Heat Capacity and Partition of Energy............... 21 9.5.6 Molecular Flux................................ 23 9.6 Mixtures........................................ 23 9.6.1 Partial Molar Properties........................... 24 10 Relationships 27 10.1 Thermodynamic potentials and fundamental relations................ 27 10.2 Maxwell relations................................... 27 10.3 Calculus identities................................... 27 10.4 Various defined quantities............................... 28 10.5 Specific heat relationships.............................. 28 10.6 Gruneisen¨ Coefficient................................. 28 10.7 Thermal Pressure Coefficient............................. 29 10.8 Enthalpy, Energy and Entropy............................ 29 11 Equation of State 30 11.1 Constructing Equations of State........................... 30 11.2 Critical Points..................................... 31 11.2.1 Law of corresponding states......................... 31 11.3 Compressibility Factor................................ 32 11.4 van der Waals Equation................................ 32 11.5 Throttling and the Joule-Thompson Coefficient................... 32 11.6 Virial Equation.................................... 32 11.7 Ideal Solid....................................... 33 12 Equilibrium Liquid-Vapor Mixtures 34 12.1 Lever Rule....................................... 34 12.2 Humidity....................................... 34 13 Phase Equilibrium 36 13.1 Clapeyron Equation.................................. 36 13.2 Maxwell’s Construction................................ 36 13.3 Multiple Phases.................................... 37 ii 14 Chemical Transformations 38 14.1 Heat of Reaction................................... 38 14.1.1 Enthalpy................................... 38 14.1.2 Heat of formation............................... 39 14.2 Combustion Reactions................................ 39 14.3 Heat of Combustion.................................. 40 14.4 Flame Temperature.................................. 40 14.5 Explosion Pressure and Temperature......................... 41 15 Chemical Equilibrium 41 15.1 Le Chatelier’s Rule.................................. 43 15.1.1 Pressure.................................... 43 15.1.2 Temperature................................. 44 A Textbooks and references 45 A.1 Introductory...................................... 45 A.2 Many others...................................... 46 A.3 Biography and History................................ 46 B Famous Numbers 47 C Fundamental Dimensions 49 D Ideal Gas Properties up to 4000K 50 iii 1 1 Fundamentals At the most basic level, thermodynamics is concerned with energy and the transformation of en- ergy into different forms such as internal energy, work, and heat. Thermodynamics also provides fundamental limitations on the efficiency of energy transformation processes. On a theoretical level, thermodynamics introduces the concept of entropy, a measure of disorder in physical matter. On a more mathematical level, thermodynamics provides a methodology for describing the prop- erties of matter and the relationship between properties such as internal energy, entropy, pressure, temperature and volume. Thermodynamics is a conceptual framework that is based on empirical observations and the- ories about natural processes. It is not a complete theory of nature or method for computing properties of matter but rather a set of ideas for relating properties of matter and governing energy transformation. Thermodynamics can be applied to a fixed or variable quantity of matter that contains a macro- scopic amount of material that can be considered to be an equilibrium state. Macroscopic means that sufficiently large enough numbers of molecules and atoms are in the system that average prop- erties of matter exist and the fluctuations from the average are negligibly small. Equilibrium means that the system has reached a state that is stable, and free from external influences, will not evolve further. 1.1 Thermodynamic Systems The essential unit that we study in thermodynamics is a system. System A quantity of matter or a region in space that we select to study. Systems can be: closed – no exchange of matter with the surroundings open – exchanges matter with the surroundings isolated – closed and no exchange of energy with the surroundings Control boundary or surface – The envelope surrounding and defining the system. Surroundings – Everything other than the system. State – A well-defined condition of a system described by certain observable macroscopic proper- ties. Process – A sequence of states that describe the evolution of a system. 1.2 Equilibrium Condition of a system that has ceased to evolve after a period of time. Isolated systems reach a state of internal equilibrium. Systems that interact with the surroundings or each other reach a state of external or mutual equilibrium. A system in equilibrium is uniquely described by its equilibrium state. 2 1 FUNDAMENTALS 1.3 State Variables A system in internal equilibrium is uniquely defined by a set of thermodynamic parameters or coordinates such as temperature, pressure, volume, composition, etc. Specifying the values of an independent and complete set of these state variables defines a unique equilibrium state of a system. There are two types of state variables: Extensive Properties that are proportional to the amount of substance in the system. Examples are: M mass, V volume, U internal energy, S entropy, quantity – number of molecules N or moles n Intensive Properties that are independent of the amount of substance in the system. Examples are: pressure P , temperature T , specific energy u, composition measured in mole y or mass fraction x of a component or phase. 1.4 Energy The energy of a system consists of the sum of kinetic energy (KE), potential energy (PE) and the internal energy E = KE + PE + U: (1) The KE and PE are due to the motion of the system as a whole. For a mechanical system of mass M moving with velocity v in a gravitational field with acceleration
Load more

Recommended publications
  • Lab: Specific Heat
    Lab: Specific Heat Summary Students relate thermal energy to heat capacity by comparing the heat capacities of different materials and graphing the change in temperature over time for a specific material. Students explore the idea of insulators and conductors in an attempt to apply their knowledge in real world applications, such as those that engineers would. Engineering Connection Engineers must understand the heat capacity of insulators and conductors if they wish to stay competitive in “green” enterprises. Engineers who design passive solar heating systems take advantage of the natural heat capacity characteristics of materials. In areas of cooler climates engineers chose building materials with a low heat capacity such as slate roofs in an attempt to heat the home during the day. In areas of warmer climates tile roofs are popular for their ability to store the sun's heat energy for an extended time and release it slowly after the sun sets, to prevent rapid temperature fluctuations. Engineers also consider heat capacity and thermal energy when they design food containers and household appliances. Just think about your aluminum soda can versus glass bottles! Grade Level: 9-12 Group Size: 4 Time Required: 90 minutes Activity Dependency :None Expendable Cost Per Group : US$ 5 The cost is less if thermometers are available for each group. NYS Science Standards: STANDARD 1 Analysis, Inquiry, and Design STANDARD 4 Performance indicator 2.2 Keywords: conductor, energy, energy storage, heat, specific heat capacity, insulator, thermal energy, thermometer, thermocouple Learning Objectives After this activity, students should be able to: Define heat capacity. Explain how heat capacity determines a material's ability to store thermal energy.
    [Show full text]
  • 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 .
    [Show full text]
  • Chapter 4 Calculation of Standard Thermodynamic Properties of Aqueous Electrolytes and Non-Electrolytes
    Chapter 4 Calculation of Standard Thermodynamic Properties of Aqueous Electrolytes and Non-Electrolytes Vladimir Majer Laboratoire de Thermodynamique des Solutions et des Polymères Université Blaise Pascal Clermont II / CNRS 63177 Aubière, France Josef Sedlbauer Department of Chemistry Technical University Liberec 46117 Liberec, Czech Republic Robert H. Wood Department of Chemistry and Biochemistry University of Delaware Newark, DE 19716, USA 4.1 Introduction Thermodynamic modeling is important for understanding and predicting phase and chemical equilibria in industrial and natural aqueous systems at elevated temperatures and pressures. Such systems contain a variety of organic and inorganic solutes ranging from apolar nonelectrolytes to strong electrolytes; temperature and pressure strongly affect speciation of solutes that are encountered in molecular or ionic forms, or as ion pairs or complexes. Properties related to the Gibbs energy, such as thermodynamic equilibrium constants of hydrothermal reactions and activity coefficients of aqueous species, are required for practical use by geologists, power-cycle chemists and process engineers. Derivative properties (enthalpy, heat capacity and volume), which can be obtained from calorimetric and volumetric experiments, are useful in extrapolations when calculating the Gibbs energy at conditions remote from ambient. They also sensitively indicate evolution in molecular interactions with changing temperature and pressure. In this context, models with a sound theoretical basis are indispensable, describing with a limited number of adjustable parameters all thermodynamic functions of an aqueous system over a wide range of temperature and pressure. In thermodynamics of hydrothermal solutions, the unsymmetric standard-state convention is generally used; in this case, the standard thermodynamic properties (STP) of a solute reflect its interaction with the solvent (water), and the excess properties, related to activity coefficients, correspond to solute-solute interactions.
    [Show full text]
  • Notation for States and Processes, Significance of the Word Standard in Chemical Thermodynamics, and Remarks on Commonly Tabulated Forms of Thermodynamic Functions
    Pure &Appl.Chem.., Vol.54, No.6, pp.1239—1250,1982. 0033—4545/82/061239—12$03.00/0 Printed in Great Britain. Pergamon Press Ltd. ©1982IUPAC INTERNATIONAL UNION OF PURE AND APPLIED CHEMISTRY PHYSICAL CHEMISTRY DIVISION COMMISSION ON THERMODYNAMICS* NOTATION FOR STATES AND PROCESSES, SIGNIFICANCE OF THE WORD STANDARD IN CHEMICAL THERMODYNAMICS, AND REMARKS ON COMMONLY TABULATED FORMS OF THERMODYNAMIC FUNCTIONS (Recommendations 1981) (Appendix No. IV to Manual of Symbols and Terminology for Physicochemical Quantities and Units) Prepared for publication by J. D. COX, National Physical Laboratory, Teddington, UK with the assistance of a Task Group consisting of S. ANGUS, London; G. T. ARMSTRONG, Washington, DC; R. D. FREEMAN, Stiliwater, OK; M. LAFFITTE, Marseille; G. M. SCHNEIDER (Chairman), Bochum; G. SOMSEN, Amsterdam, (from Commission 1.2); and C. B. ALCOCK, Toronto; and P. W. GILLES, Lawrence, KS, (from Commission 11.3) *Membership of the Commission for 1979-81 was as follows: Chairman: M. LAFFITTE (France); Secretary: G. M. SCHNEIDER (FRG); Titular Members: S. ANGUS (UK); G. T. ARMSTRONG (USA); V. A. MEDVEDEV (USSR); Y. TAKAHASHI (Japan); I. WADSO (Sweden); W. ZIELENKIEWICZ (Poland); Associate Members: H. CHIHARA (Japan); J. F. COUNSELL (UK); M. DIAZ-PENA (Spain); P. FRANZOSINI (Italy); R. D. FREEMAN (USA); V. A. LEVITSKII (USSR); 0.SOMSEN (Netherlands); C. E. VANDERZEE (USA); National Representatives: J. PICK (Czechoslovakia); M. T. RATZSCH (GDR). NOTATION FOR STATES AND PROCESSES, SIGNIFICANCE OF THE WORD STANDARD IN CHEMICAL THERMODYNAMICS, AND REMARKS ON COMMONLY TABULATED FORMS OF THERMODYNAMIC FUNCTIONS SECTION 1. INTRODUCTION The main IUPAC Manual of symbols and terminology for physicochemical quantities and units (Ref.
    [Show full text]
  • Compression of an Ideal Gas with Temperature Dependent Specific
    Session 3666 Compression of an Ideal Gas with Temperature-Dependent Specific Heat Capacities Donald W. Mueller, Jr., Hosni I. Abu-Mulaweh Engineering Department Indiana University–Purdue University Fort Wayne Fort Wayne, IN 46805-1499, USA Overview The compression of gas in a steady-state, steady-flow (SSSF) compressor is an important topic that is addressed in virtually all engineering thermodynamics courses. A typical situation encountered is when the gas inlet conditions, temperature and pressure, are known and the compressor dis- charge pressure is specified. The traditional instructional approach is to make certain assumptions about the compression process and about the gas itself. For example, a special case often consid- ered is that the compression process is reversible and adiabatic, i.e. isentropic. The gas is usually ÊÌ considered to be ideal, i.e. ÈÚ applies, with either constant or temperature-dependent spe- cific heat capacities. The constant specific heat capacity assumption allows for direct computation of the discharge temperature, while the temperature-dependent specific heat assumption does not. In this paper, a MATLAB computer model of the compression process is presented. The substance being compressed is air which is considered to be an ideal gas with temperature-dependent specific heat capacities. Two approaches are presented to describe the temperature-dependent properties of air. The first approach is to use the ideal gas table data from Ref. [1] with a look-up interpolation scheme. The second approach is to use a curve fit with the NASA Lewis coefficients [2,3]. The computer model developed makes use of a bracketing–bisection algorithm [4] to determine the temperature of the air after compression.
    [Show full text]
  • Thermodynamic State Variables Gunt
    Fundamentals of thermodynamics 1 Thermodynamic state variables gunt Basic knowledge Thermodynamic state variables Thermodynamic systems and principles Change of state of gases In physics, an idealised model of a real gas was introduced to Equation of state for ideal gases: State variables are the measurable properties of a system. To make it easier to explain the behaviour of gases. This model is a p × V = m × Rs × T describe the state of a system at least two independent state system boundaries highly simplifi ed representation of the real states and is known · m: mass variables must be given. surroundings as an “ideal gas”. Many thermodynamic processes in gases in · Rs: spec. gas constant of the corresponding gas particular can be explained and described mathematically with State variables are e.g.: the help of this model. system • pressure (p) state process • temperature (T) • volume (V) Changes of state of an ideal gas • amount of substance (n) Change of state isochoric isobaric isothermal isentropic Condition V = constant p = constant T = constant S = constant The state functions can be derived from the state variables: Result dV = 0 dp = 0 dT = 0 dS = 0 • internal energy (U): the thermal energy of a static, closed Law p/T = constant V/T = constant p×V = constant p×Vκ = constant system. When external energy is added, processes result κ =isentropic in a change of the internal energy. exponent ∆U = Q+W · Q: thermal energy added to the system · W: mechanical work done on the system that results in an addition of heat An increase in the internal energy of the system using a pressure cooker as an example.
    [Show full text]
  • Schlieren Imaging of Loud Sounds and Weak Shock Waves in Air Near the Limit of Visibility
    Shock Waves DOI 10.1007/s00193-009-0226-6 ORIGINAL ARTICLE Schlieren imaging of loud sounds and weak shock waves in air near the limit of visibility Michael John Hargather · Gary S. Settles · Matthew J. Madalis Received: 27 April 2009 / Accepted: 4 August 2009 © Springer-Verlag 2009 Abstract A large schlieren system with exceptional sensi- Keywords Shock waves · Nonlinear acoustics · Sound · tivity and a high-speed digital camera are used to visualize Noise · Schlieren · High-speed imaging loud sounds and a variety of common phenomena that pro- duce weak shock waves in the atmosphere. Frame rates var- PACS 42.79.Mt · 43.25.+y ied from 10,000 to 30,000frames/s with microsecond frame exposures. Sound waves become visible to this instrumenta- tion at frequencies above 10kHz and sound pressure levels 1 Introduction in the 110dB (6.3Pa) range and above. The density gradient produced by a weak shock wave is examined and found to Visualizing sound-wave motion in air has been a dream of sci- depend upon the profile and thickness of the shock as well as entists and engineers for at least a century and a half, although the density difference across it. Schlieren visualizations of sound waves and weak shock waves were initially confused. weak shock waves from common phenomena include loud August Toepler’s (1836–1912) epitaph, “He was the first to trumpet notes, various impact phenomena that compress a see sound,” actually referred to his schlieren imaging of weak bubble of air, bursting a toy balloon, popping a champagne shock waves from electric sparks [1].
    [Show full text]
  • Gas Kinetics in Galactic Disk. Why We Do Not Need a Dark Matter to Explain Rotation Curves of Spirals? Anton Lipovka
    Gas kinetics in galactic disk. Why we do not need a dark matter to explain rotation curves of spirals? Anton Lipovka To cite this version: Anton Lipovka. Gas kinetics in galactic disk. Why we do not need a dark matter to explain rotation curves of spirals?. 2018. hal-01832309v3 HAL Id: hal-01832309 https://hal.archives-ouvertes.fr/hal-01832309v3 Preprint submitted on 24 Jul 2020 HAL is a multi-disciplinary open access L’archive ouverte pluridisciplinaire HAL, est archive for the deposit and dissemination of sci- destinée au dépôt et à la diffusion de documents entific research documents, whether they are pub- scientifiques de niveau recherche, publiés ou non, lished or not. The documents may come from émanant des établissements d’enseignement et de teaching and research institutions in France or recherche français ou étrangers, des laboratoires abroad, or from public or private research centers. publics ou privés. Gas kinetics in galactic disk. Why we do not need a dark matter to explain rotation curves of spirals? Lipovka A.A. Department of Research for Physics, Sonora University, 83000, Hermosillo, Sonora, México May 27, 2020 Abstract In present paper, we analyze how the physical properties of gas affect the Rotation Curve (RC) of a spiral galaxy. It is shown, that the observed non-Keplerian RCs measured for outer part of disks, and the observed radial gas distribution are closely related by the diffusion equation, which clearly indicates that no additional mass (Dark Matter) is need. It is stressed, that while the inner part of the RC is subject of the Kepler law, for the correct description of the outer part of the RC, the collisional property of the gas should also be taken into account.
    [Show full text]
  • 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).
    [Show full text]
  • Basic Thermodynamics-17ME33.Pdf
    Module -1 Fundamental Concepts & Definitions & Work and Heat MODULE 1 Fundamental Concepts & Definitions Thermodynamics definition and scope, Microscopic and Macroscopic approaches. Some practical applications of engineering thermodynamic Systems, Characteristics of system boundary and control surface, examples. Thermodynamic properties; definition and units, intensive and extensive properties. Thermodynamic state, state point, state diagram, path and process, quasi-static process, cyclic and non-cyclic processes. Thermodynamic equilibrium; definition, mechanical equilibrium; diathermic wall, thermal equilibrium, chemical equilibrium, Zeroth law of thermodynamics, Temperature; concepts, scales, fixed points and measurements. Work and Heat Mechanics, definition of work and its limitations. Thermodynamic definition of work; examples, sign convention. Displacement work; as a part of a system boundary, as a whole of a system boundary, expressions for displacement work in various processes through p-v diagrams. Shaft work; Electrical work. Other types of work. Heat; definition, units and sign convention. 10 Hours 1st Hour Brain storming session on subject topics Thermodynamics definition and scope, Microscopic and Macroscopic approaches. Some practical applications of engineering thermodynamic Systems 2nd Hour Characteristics of system boundary and control surface, examples. Thermodynamic properties; definition and units, intensive and extensive properties. 3rd Hour Thermodynamic state, state point, state diagram, path and process, quasi-static
    [Show full text]
  • Chapter03 Introduction to Thermodynamic Systems
    Chapter03 Introduction to Thermodynamic Systems February 13, 2019 This chapter introduces the concept of thermo- Remark 1.1. In general, we will consider three kinds dynamic systems and digresses on the issue: How of exchange between S and Se through a (possibly ab- complex systems are related to Statistical Thermo- stract) membrane: dynamics. To do so, let us review the concepts of (1) Diathermal (Contrary: Adiabatic) membrane Equilibrium Thermodynamics from the conventional that allows exchange of thermal energy. viewpoint. Let U be the universe. Let a collection of objects (2) Deformable (Contrary: Rigid) membrane that S ⊆ U be defined as the system under certain restric- allows exchange of work done by volume forces tive conditions. The complement of S in U is called or surface forces. the exterior of S and is denoted as Se. (3) Permeable (Contrary: Impermeable) membrane that allows exchange of matter (e.g., in the form 1 Basic Definitions of molecules of chemical species). Definition 1.1. A system S is an idealized body that can be isolated from Se in the sense that changes in Se Definition 1.4. A thermodynamic state variable is a do not have any effects on S. macroscopic entity that is a characteristic of a system S. A thermodynamic state variable can be a scalar, Definition 1.2. A system S is called a thermody- a finite-dimensional vector, or a tensor. Examples: namic system if any possible exchange between S and temperature, or a strain tensor. Se is restricted to one or more of the following: (1) Any form of energy (e.g., thermal, electric, and magnetic) Definition 1.5.
    [Show full text]
  • Thermodynamics the Study of the Transformations of Energy from One Form Into Another
    Thermodynamics the study of the transformations of energy from one form into another First Law: Heat and Work are both forms of Energy. in any process, Energy can be changed from one form to another (including heat and work), but it is never created or distroyed: Conservation of Energy Second Law: Entropy is a measure of disorder; Entropy of an isolated system Increases in any spontaneous process. OR This law also predicts that the entropy of an isolated system always increases with time. Third Law: The entropy of a perfect crystal approaches zero as temperature approaches absolute zero. ©2010, 2008, 2005, 2002 by P. W. Atkins and L. L. Jones ©2010, 2008, 2005, 2002 by P. W. Atkins and L. L. Jones A Molecular Interlude: Internal Energy, U, from translation, rotation, vibration •Utranslation = 3/2 × nRT •Urotation = nRT (for linear molecules) or •Urotation = 3/2 × nRT (for nonlinear molecules) •At room temperature, the vibrational contribution is small (it is of course zero for monatomic gas at any temperature). At some high temperature, it is (3N-5)nR for linear and (3N-6)nR for nolinear molecules (N = number of atoms in the molecule. Enthalpy H = U + PV Enthalpy is a state function and at constant pressure: ∆H = ∆U + P∆V and ∆H = q At constant pressure, the change in enthalpy is equal to the heat released or absorbed by the system. Exothermic: ∆H < 0 Endothermic: ∆H > 0 Thermoneutral: ∆H = 0 Enthalpy of Physical Changes For phase transfers at constant pressure Vaporization: ∆Hvap = Hvapor – Hliquid Melting (fusion): ∆Hfus = Hliquid –
    [Show full text]