DOCSLIB.ORG

Reference St a Tes and Relative Values of Internal Energy, Enthalpy, and Entropy

Total Page：16

File Type：pdf, Size：1020Kb

Download full-text PDF Read full-text
Reference St a Tes and Relative Values of Internal Energy, Enthalpy, and Entropy (eJ ;j pll lecture REFERENCE ST A TES AND RELATIVE VALUES OF INTERNAL ENERGY, ENTHALPY, AND ENTROPY A. G. FREDRICKSON University of Minnesota Minneapolis, MN 55455 MANY PROBLEMS IN chemical engineering ther- modynamics require for their solution the application of the balance equations for moles of various chemical species, (total) energy, and entropy. Fairly general forms of these equations, which are applicable to open, moving and deform­ ing, and unsteady state systems, are (1) A. G. Fredrickson, professor of chemical engineering at the Uni• versity of Minnesota, received his BS and MS at that institution in 1954 and 1956, pnd his PhD from the University of Wisconsin in 1959. He d dt (Ut +Kt+ <I>t) = Q +Wu+ W ex p has been the American editor of Chemical Engineering Science since 1975 and i~ the author of "Principles and Applications of Rheology." (2) + I W q (hq + kq + cpq) His current research area is the dynamics of microbial populations, and q his non-professional interests lie in the fields of natural history, pre­ (3) history, and photography. Here, the energy and entropy transfer rates asso­ action equations must be balanced is expressed by ciated with heat transfer, Q and S, are related to the conqitions the local heat flux vector q and temperature T on the boundary aB of the system B by (4) Q = -f (n·q) and this must be satisfied for all reactions (i) and c)B all elements (k) ; Ej k is the number of atoms of the k t" kind of element in one molecule ( or meric or S = -f i, (n·q) repeating unit) of the j t" chemical species. The oB quantity Wq is the molar flow rate of material at the qt" port of the system; it is positive if material The second law of thermodynamics requires that enters the system at that port but negative if ma­ the entropy generation rate Sa shall be non-nega­ terial leaves the system there. The mole fraction tive, and further, shall be non-negative for every of the j t h chemical species in this stream is de­ subsystem into which B may be divided. The quan­ t h noted by Xq,i• Finally, -Wu and - W ex p are the rates tity a;i is the stoichiometric coefficient of the j at which the system performs useful and expan­ chemical species in the i th reaction, R; is the rate of sion work on the surroundings, and Kt and <I>t de­ the i t" reaction in the system, and the summation note kinetic and potential energy. on i in Eq. (1) is over a set of independent ra­ Eqs. (1-3) are not valid for systems which actions [1]. The fact that all valid chemical re- exchange matter with their surroundings by dif­ fusion across a permeable boundary, but they are © Capyright ChE Division, ASEE, 1983 64 CHEMICAL ENGINEERING EDUCATION easily generalized to include that case also. It can culation of changes of internal energy and entropy. be shown that the results to be deduced here apply The reference quantities do not depend on the tem­ to these more general systems also, but in the perature and pressure of the system, though they interests of simplicity such systems will not be do depend on its composition. Similarly, if we let considered further here. hq rH be the enthalpy of one mole of matter of the The quantities U t and St which appear in Eqs. qt1• process stream when this matter is in the ref­ (2) and (3) are the absolute values of the internal erence state for enthalpy, then we can define a energy and entropy of the system, respectively, relative enthalpy and the quantities hq and Sq which appear in these equations are the absolute values of the enthalpy hq' = hq - hqrH (5c) and entropy of one mole of the q t" process stream, as well as a relative entropy respectively. Thermodynamics provides means for (5d) calculating changes in Ut, St, hq, Sq when the sys­ Sq' = Sq - Sqrs tem and the q n, process stream experience pro­ for the q'·" process stream. It is necessary to place cesses which change their states, but thermody­ the subscript q on the reference state quantities namics does not identify the states in which these hq rH and Sq rs because these quantities depend on quantities are zero. It is sometimes held that the the composition of the q th stream, and this is not in third law of thermodynamics identifies such a general the same as the composition of other pro­ state for the entropy but, within the context of cess streams. However, hq rH and Sqrs do not depend 1 classical thermodynamics at any rate, it is clear on the temperature and pressure of the qt • process that this is not so: the third law, or rather the stream. version of it usually called Nernst's heat theorem, If the relative properties Ut', St', hq', sq' are to asserts only that the entropy changes of certain be useful then they should obey the same balance kinds of systems undergoing certain kinds of equations as do the absolute properties U t, St, hq, isothermal processes approach zero as the tem­ Sq; that is, the relative properties should obey peratures of the processes approach absolute zero [2]. Hence, we do not know how to find the absolute (Ut' +Kt + <I> t) values of U t, St, hq, and Sq, :t However, we need to be able to assign numer­ = Q +Wu + Wexp + I wq (hq' + kq + <pq) (6) ical values to internal energy, entropy, etc. if we q want to tabulate what effects changes of tempera­ dSt' S S "' ' -----at = + G + : Wq Sq (7) ture, pressure, and composition have on them. Hence, reference states for internal energy, where Q, Wu, Wexp, S, and Sa are the same quan­ entropy, and enthalpy are chosen, and values of tities that appear in Eqs. (2) and (3). Clearly, if internal energy, entropy, and enthalpy relative to the relative properties satisfy these balance equa­ the reference states are tabulated. The most fa­ tions they then can be used (correctly) in the cal­ miliar example of this is the steam tables, but the culations of heat and work effects that occur so fre­ utility of enthalpy-composition and related dia­ quently in applied thermodynamics. I have been grams demonstrated in the well-known Hougen, unable to find a recent discussion of the choices of Watson, and Ragatz book [3] make such diagrams reference states which will lead to Eqs. (6) and nearly as familiar as the steam tables. (7), and so provision of such discussion is the ob­ Let Utru be the (absolute) internal energy of jective of this paper. the matter of the system being considered when this matter is in the reference state for internal REFERENCE STATE 1 energy, and let Stt-s be the (absolute) entropy of the matter of the system when this matter is in The Pure Chemical Compounds at Specified Conditions the reference state for entropy. Then the relative of T and p internal energy, Ut', and relative entropy, St', of Although it would be possible to choose refer­ the system are defined by ence states which are solutions we shall not do so Ut' == Ut - U trU (5a) here. Instead, we shall consider only reference states in which only pure substances, unmixed St'= St - StrS (5b) with other substances, are present, and present in and the calculation of Ut' and St' involves only cal- states of aggregation that are at least metastable. SPRING 1983 65 fled by arbitrary choices of the entropies si rs, but If the relative properties ... are if reactions occur, Eq. (10) shows that Eq. (9) to be useful then they should obey the same balance will be satisfied if and only if we chose these en­ equations as do the absolute properties ... tropies such that k ll'. Jj Sj rS = 0 (11) To begin with, we choose the pure substances to be j the pure compounds of which the system and the for each and every independent reaction occurring. process streams are composed. The reference state This shows that if chemical reactions occur, the for internal energy is assumed to involve in the conditions of temperature and pressure for the most general case a different combination of tem­ entropy reference states of the compounds of perature and pressure for each compound, and the which the system is composed cannot be chosen temperature and pressure of the reference state arbitrarily, but must be chosen so that the en­ for internal energy for a given compound are as­ tropies sirs satisfy a number of constraints equal sumed to be different from the temperatur e and to the number of independent reactions which oc­ pressure of the reference state for entropy for that cur. compound. If it is not possible to choose reference Consider now Eq. (8). Let Uiru (hi,n) be the states in this very arbitrary way, we want to find (absolute) molar internal energy (enthalpy) of that out. the pure j th compound when it is in the reference It is easy to show that Eqs. (6) and (7) follow state for internal energy (enthalpy). Then from Eqs. (2) and (3) and the definitions of Eqs. U trU = k NJ UjrU (5) if, and only if, the reference properties satisfy j dUtrU ~ h 0 hqrH = k Xq,j hj rH dt- ~ Wq qrH = (8) j and and so dStrS ~ 0 ~ - ~ Wq Sq rS = (9) dUtrU ~ h ~ ( dNj h ~ ) ---ar- -: Wq qrH = 1 UjrUdt - jrH~ Wq Xq ,J These equations are general; they must be satisfied dN­ for every valid choice of reference states of Ut, H t, = 7(U jrU -hJrn) a{ and St, It might be supposed at first that the time derivatives in these equations are zero, but such is + k R 1 k ll'.
Load more

Recommended publications
  • Internal Energy in an Electric Field
    Internal energy in an electric field In an electric field, if the dipole moment is changed, the change of the energy is, U E P Using Einstein notation dU Ek dP k This is part of the total derivative of U dU TdSij d ij E kK dP H l dM l Make a Legendre transformation to the Gibbs potential G(T, H, E, ) GUTSijij EP kK HM l l SGTE data for pure elements http://www.sciencedirect.com/science/article/pii/036459169190030N Gibbs free energy GUTSijij EP kK HM l l dG dU TdS SdTijij d ij d ij E kk dP P kk dE H l dM l M l dH l dU TdSij d ij E kK dP H l dM l dG SdTij d ij P k dE k M l dH l G G G G total derivative: dG dT d dE dH ij k l T ij EH k l G G ij Pk E ij k G G M l S Hl T Direct and reciprocal effects (Maxwell relations) Useful to check for errors in experiments or calculations Maxwell relations Useful to check for errors in experiments or calculations Point Groups Crystals can have symmetries: rotation, reflection, inversion,... x 1 0 0 x y 0 cos sin y z 0 sin cos z Symmetries can be represented by matrices. All such matrices that bring the crystal into itself form the group of the crystal. AB G for A, B G 32 point groups (one point remains fixed during transformation) 230 space groups Cyclic groups C2 C4 http://en.wikipedia.org/wiki/Cyclic_group 2G Pyroelectricity i Ei T Pyroelectricity is described by a rank 1 tensor Pi i T 1 0 0 x x x 0 1 0 y y y 0 0 1 z z 0 1 0 0 x x 0 0 1 0 y y 0 0 0 1 z z 0 Pyroelectricity example Turmalin: point group 3m Quartz, ZnO, LaTaO 3 for T = 1°C, E ~ 7 ·104 V/m Pyroelectrics have a spontaneous polarization.
    [Show full text]
  • 3. Energy, Heat, and Work
    3. Energy, Heat, and Work 3.1. Energy 3.2. Potential and Kinetic Energy 3.3. Internal Energy 3.4. Relatively Effects 3.5. Heat 3.6. Work 3.7. Notation and Sign Convention In these Lecture Notes we examine the basis of thermodynamics – fundamental definitions and equations for energy, heat, and work. 3-1. Energy. Two of man's earliest observations was that: 1)useful work could be accomplished by exerting a force through a distance and that the product of force and distance was proportional to the expended effort, and 2)heat could be ‘felt’ in when close or in contact with a warm body. There were many explanations for this second observation including that of invisible particles traveling through space1. It was not until the early beginnings of modern science and molecular theory that scientists discovered a true physical understanding of ‘heat flow’. It was later that a few notable individuals, including James Prescott Joule, discovered through experiment that work and heat were the same phenomenon and that this phenomenon was energy: Energy is the capacity, either latent or apparent, to exert a force through a distance. The presence of energy is indicated by the macroscopic characteristics of the physical or chemical structure of matter such as its pressure, density, or temperature - properties of matter. The concept of hot versus cold arose in the distant past as a consequence of man's sense of touch or feel. Observations show that, when a hot and a cold substance are placed together, the hot substance gets colder as the cold substance gets hotter.
    [Show full text]
  • Energy Minimum Principle
    ESCI 341 – Atmospheric Thermodynamics Lesson 12 – The Energy Minimum Principle References: Thermodynamics and an Introduction to Thermostatistics, Callen Physical Chemistry, Levine THE ENTROPY MAXIMUM PRINCIPLE We’ve seen that a reversible process achieves maximum thermodynamic efficiency. Imagine that I am adding heat to a system (dQin), converting some of it to work (dW), and discarding the remaining heat (dQout). We’ve already demonstrated that dQout cannot be zero (this would violate the second law). We also have shown that dQout will be a minimum for a reversible process, since a reversible process is the most efficient. This means that the net heat for the system (dQ = dQin dQout) will be a maximum for a reversible process, dQrev dQirrev . The change in entropy of the system, dS, is defined in terms of reversible heat as dQrev/T. We can thus write the following inequality dQ dQ dS rev irrev , (1) T T Notice that for Eq. (1), if the system is reversible and adiabatic, we get dQ dS 0 irrev , T or dQirrev 0 which illustrates the following: If two states can be connected by a reversible adiabatic process, then any irreversible process connecting the two states must involve the removal of heat from the system. Eq. (1) can be written as dS dQ T (2) The equality will hold if all processes in the system are reversible. The inequality will hold if there are irreversible processes in the system. For an isolated system (dQ = 0) the inequality becomes dS 0 isolated system , which is just a restatement of the second law of thermodynamics.
    [Show full text]
  • Chapter 20 -- Thermodynamics
    ChapterChapter 2020 -- ThermodynamicsThermodynamics AA PowerPointPowerPoint PresentationPresentation byby PaulPaul E.E. TippensTippens,, ProfessorProfessor ofof PhysicsPhysics SouthernSouthern PolytechnicPolytechnic StateState UniversityUniversity © 2007 THERMODYNAMICSTHERMODYNAMICS ThermodynamicsThermodynamics isis thethe studystudy ofof energyenergy relationshipsrelationships thatthat involveinvolve heat,heat, mechanicalmechanical work,work, andand otherother aspectsaspects ofof energyenergy andand heatheat transfer.transfer. Central Heating Objectives:Objectives: AfterAfter finishingfinishing thisthis unit,unit, youyou shouldshould bebe ableable to:to: •• StateState andand applyapply thethe first andand second laws ofof thermodynamics. •• DemonstrateDemonstrate youryour understandingunderstanding ofof adiabatic, isochoric, isothermal, and isobaric processes.processes. •• WriteWrite andand applyapply aa relationshiprelationship forfor determiningdetermining thethe ideal efficiency ofof aa heatheat engine.engine. •• WriteWrite andand applyapply aa relationshiprelationship forfor determiningdetermining coefficient of performance forfor aa refrigeratior.refrigeratior. AA THERMODYNAMICTHERMODYNAMIC SYSTEMSYSTEM •• AA systemsystem isis aa closedclosed environmentenvironment inin whichwhich heatheat transfertransfer cancan taketake place.place. (For(For example,example, thethe gas,gas, walls,walls, andand cylindercylinder ofof anan automobileautomobile engine.)engine.) WorkWork donedone onon gasgas oror workwork donedone byby gasgas INTERNALINTERNAL
    [Show full text]
  • 10.05.05 Fundamental Equations; Equilibrium and the Second Law
    3.012 Fundamentals of Materials Science Fall 2005 Lecture 8: 10.05.05 Fundamental Equations; Equilibrium and the Second Law Today: LAST TIME ................................................................................................................................................................................ 2 THERMODYNAMIC DRIVING FORCES: WRITING A FUNDAMENTAL EQUATION ........................................................................... 3 What goes into internal energy?.......................................................................................................................................... 3 THE FUNDAMENTAL EQUATION FOR THE ENTROPY................................................................................................................... 5 INTRODUCTION TO THE SECOND LAW ....................................................................................................................................... 6 Statements of the second law ............................................................................................................................................... 6 APPLYING THE SECOND LAW .................................................................................................................................................... 8 Heat flows from hot objects to cold objects ......................................................................................................................... 8 Thermal equilibrium ...........................................................................................................................................................
    [Show full text]
  • Forms of Energy: Kinetic Energy, Gravitational Potential Energy, Elastic Potential Energy, Electrical Energy, Chemical Energy, and Thermal Energy
    6/3/14 Objectives Forms of • State a practical definition of energy. energy • Provide or identify an example of each of these forms of energy: kinetic energy, gravitational potential energy, elastic potential energy, electrical energy, chemical energy, and thermal energy. Assessment Assessment 1. Which of the following best illustrates the physics definition of 2. Which statement below provides a correct practical definition of energy? energy? A. “I don’t have the energy to get that done today.” A. Energy is a quantity that can be created or destroyed. B. “Our team needs to be at maximum energy for this game.” B. Energy is a measure of how much money it takes to produce a product. C. “The height of her leaps takes more energy than anyone else’s.” C. The energy of an object can never change. It depends on “ D. That performance was so exhilarating you could feel the energy the size and weight of an object. in the audience!” D. Energy is the quantity that causes matter to change and determines how much change occur. Assessment Physics terms 3. Match each event with the correct form of energy. • energy I. kinetic II. gravitational potential III. elastic potential IV. thermal • gravitational potential energy V. electrical VI. chemical • kinetic energy ___ Ice melts when placed in a cup of warm water. • elastic potential energy ___ Campers use a tank of propane gas on their trip. ___ A car travels down a level road at 25 m/s. • thermal energy ___ A bungee cord causes the jumper to bounce upward. ___ The weightlifter raises the barbell above his head.
    [Show full text]
  • Enthalpy and Internal Energy
    Enthalpy and Internal Energy • H or ΔH is used to symbolize enthalpy. • The mathematical expression of the First Law of Thermodynamics is: ΔE = q + w , where ΔE is the change in internal energy, q is heat and w is work. • Work can be defined in terms of an expanding gas and has the formula: w = -PΔV , where P is pressure in pascals (N/m2) and V is volume in m3. N-23 Enthalpy and Internal Energy • Enthalpy (H) is related to energy. H = E + PV • However, absolute energies and enthalpies are rarely measured. Instead, we measure CHANGES in these quantities. Reconsider the above equations (at constant pressure): ΔH = ΔE + PΔV recall: w = - PΔV therefore: ΔH = ΔE - w substituting: ΔH = q + w - w ΔH = q (at constant pressure) • Therefore, at constant pressure, enthalpy is heat. We will use these words interchangeably. N-24 State Functions • Enthalpy and internal energy are both STATE functions. • A state function is path independent. • Heat and work are both non-state functions. • A non-state function is path dependant. Consider: Location (position) Distance traveled Change in position N-25 Molar Enthalpy of Reactions (ΔHrxn) • Heat (q) is usually used to represent the heat produced (-) or consumed (+) in the reaction of a specific quantity of a material. • For example, q would represent the heat released when 5.95 g of propane is burned. • The “enthalpy (or heat) of reaction” is represented by ΔHreaction (ΔHrxn) and relates to the amount of heat evolved per one mole or a whole # multiple – as in a balanced chemical equation. q molar ΔH = rxn (in units of kJ/mol) rxn moles reacting N-26 € Enthalpy of Reaction • Sometimes, however, knowing the heat evolved or consumed per gram is useful to know: qrxn gram ΔHrxn = (in units of J/g) grams reacting € N-27 Enthalpy of Reaction 7.
    [Show full text]
  • The First Law of Thermodynamics: Closed Systems Heat Transfer
    The First Law of Thermodynamics: Closed Systems The first law of thermodynamics can be simply stated as follows: during an interaction between a system and its surroundings, the amount of energy gained by the system must be exactly equal to the amount of energy lost by the surroundings. A closed system can exchange energy with its surroundings through heat and work transfer. In other words, work and heat are the forms that energy can be transferred across the system boundary. Based on kinetic theory, heat is defined as the energy associated with the random motions of atoms and molecules. Heat Transfer Heat is defined as the form of energy that is transferred between two systems by virtue of a temperature difference. Note: there cannot be any heat transfer between two systems that are at the same temperature. Note: It is the thermal (internal) energy that can be stored in a system. Heat is a form of energy in transition and as a result can only be identified at the system boundary. Heat has energy units kJ (or BTU). Rate of heat transfer is the amount of heat transferred per unit time. Heat is a directional (or vector) quantity; thus, it has magnitude, direction and point of action. Notation: – Q (kJ) amount of heat transfer – Q° (kW) rate of heat transfer (power) – q (kJ/kg) ‐ heat transfer per unit mass – q° (kW/kg) ‐ power per unit mass Sign convention: Heat Transfer to a system is positive, and heat transfer from a system is negative. It means any heat transfer that increases the energy of a system is positive, and heat transfer that decreases the energy of a system is negative.
    [Show full text]
  • LECTURE 6 Properties of Ideal Gases Ideal Gases Are a Very Simple System of Noninteracting Particles
    LECTURE 6 Properties of Ideal Gases Ideal gases are a very simple system of noninteracting particles. The only energy involved is the kinetic energy of the gas particles. There is no potential energy. Let’s study this system as a way to illustrate some of the concepts that we have been discussing such as internal energy, specific heat, etc. First of all, the internal energy of an ideal gas is solely a function of its temperature and is independent of its volume. E = E(T ) independent of V (1) Perhaps this is not surprising since the energy is solely kinetic and hence just depends on the temperature. The energy does not depend on interactions between the particles, so it doesn’t matter how close together the particles are, i.e., the density and volume don’t matter. One can prove that the energy is solely a function of the temperature in 2 different ways. One way is microscopic and uses phase space (Reif section 2.5); the other way is macroscopic and just uses the equation of state pV = νRT (Reif section 5.1). Let’s go over the microscopic proof. Let ri denote the position of the ith particle and let pi be it’s momentum. The number of states Ω(E) lying between the energies E and E + dE is proportional to the volume of phase space contained between the surface in phase space with energy E and the surface with energy E + dE: E+dE 3 3 3 3 Ω(E) ∝ d r1 ... d rN d p1 ..
    [Show full text]
  • Dynamic Model of an Organic Rankine Cycle System Exploiting Low Grade Waste Heat on Board a LNG Carrier
    UNIVERSITÀ DEGLI STUDI DI PADOVA DIPARTIMENTO DI INGEGNERIA INDUSTRIALE Corso di laurea Magistrale in Ingegneria Energetica Tesi di laurea Magistrale in Ingegneria Energetica Dynamic Model of an Organic Rankine Cycle System Exploiting Low Grade Waste Heat on board a LNG Carrier Relatore: Prof. Andrea Lazzaretto Correlatore: Ph.D. Sergio Rech Laureando: Daniele Malandrin ANNO ACCADEMICO 2013 – 2014 1 SOMMARIO Questo lavoro presenta il modello dinamico di off-design per un ciclo Rankine a fluido organico (ORC) che sfrutta il calore di scarto a bassa temperatura rilasciato dall’impianto motore di una reale nave metaniera. Il primo passo del lavoro è stato sviluppare il modello di design di ciascun componente dell’impianto ORC. A tal scopo si sono considerati i cicli termodinamici ottimizzati presentati in un precedente lavoro del gruppo di ricerca. Basandosi sui risultati ottenuti nella fase di dimensionamento preliminare, si è costruito il modello dinamico di ciascun componente. Si è scelto l’approccio di soluzione sequenziale, il quale consente di realizzare una modellazione ad oggetti. Ciò significa che ciascun componente dell’impianto ORC è stato modellizzato come un elemento singolo. Di conseguenza, il modello globale del sistema energetico deriva dall’interconnessione dei singoli blocchi, facenti riferimento ciascuno ad un componente reale dell’impianto. I modelli realizzati seguendo questo approccio possono essere facilmente modificati, ed adattati alla simulazione di sistemi energetici diversi dall’originale. Gli scambiatori di calore, evaporatore e condensatore in primis, influenzano fortemente la risposta dinamica dell’intero sistema. Essi sono stati, quindi, oggetto di un lavoro di modellizzazione particolarmente attento, basato sull’applicazione del metodo dei volumi finiti.
    [Show full text]
  • Energy & Chemical Reactions
    Energy & Chemical Reactions Chapter 6 The Nature of Energy Chemical reactions involve energy changes • Kinetic Energy - energy of motion – macroscale - mechanical energy – nanoscale - thermal energy – movement of electrons through conductor - electrical energy 2 – Ek = (1/2) mv • Potential Energy - stored energy – object held above surface of earth - gravitational energy – energy of charged particles - electrostatic energy – energy of attraction or repulsion among electrons and nuclei - chemical potential energy The Nature of Energy Energy Units • SI unit - joule (J) – amount of energy required to move 2 kg mass at speed of 1 m/s – often use kilojoule (kJ) - 1 kJ = 1000 J • calorie (cal) – amount of energy required to raise the temperature of 1 g of water 1°C – 1 cal = 4.184 J (exactly) – nutritional values given in kilocalories (kcal) First Law of Thermodynamics The First Law of Thermodynamics says that energy is conserved. So energy that is lost by the system must be gained by the surrounding and vice versa. • Internal Energy – sum of all kinetic and potential energy components of the system – Einitial → Efinal – ΔE = Efinal - Einitial – not possible to know the energy of a system but easy to measure energy changes First Law of Thermodynamics • ΔE and heat and work – internal energy changes if system loses or gains heat or if it does work or has work done on it – ΔE = q + w – sign convention to keep track of heat (q > 0) system work (w > 0) – both heat added to system and work done on system increase internal energy First Law of Thermodynamics First Law of Thermodynamics Divide the universe into two parts • system - what we are studying • surroundings - everything else ∆E > 0 system gained energy from surroundings ∆E < 0 system lost energy to surroundings Work and Heat Energy can be transferred in the form of work, heat or a combination of the two.
    [Show full text]
  • An Important Practical Question Is What Happens When a Gas Is Expanded Into Vacuum Or a Very Low Pressure (Against “Zero External Pressure”)
    An important practical question is what happens when a gas is expanded into vacuum or a very low pressure (against “zero external pressure”). We saw already that W=0. And in a fundamental sense, it helps us to further illustrate the (usefulness of the) concept of enthalpy. Does the T decrease, as is typical when it is expanded adiabatically? Should it, if no work is done? (Remember that the adiabatic expansion curve on the P-v diagram is steeper than that of isothermal expansion!) Initial experiments (done by Joule in the 19th century) showed that, when the gas can be considered ideal, heat is neither evolved nor absorbed. Thus both heat and work are zero, which means that the internal energy remains constant: ∂U =0 ∂V T In fact, this condition is a complementary definition of an ideal gas, because Joule and Thomson -- two of the leading 'fathers' of thermodynamics, the latter immortalized as lord Kelvin -- subsequently showed that this is not true in general (for non-ideal or real gases). In fact, the ability to predict the so called Joule-Thomson inversion temperature (see relevant figures in the textbook) is often used as a litmus test for an equation of state. So the concept and the quantification of the Joule-Thomson coefficient is an essential topic in an introductory thermo course: ∂T ≡ μ ∂P H It turns out that the assumption Q=0 is more reasonable than the assumption W=0, because of the need to overcome the attractive (or repulsive!) forces between molecules. In other words, no ‘external’ work is done (by compressing the surroundings), but some ‘internal’ work is done..
    [Show full text]