Chapter 20 -- Thermodynamics

Total Page:16

File Type:pdf, Size:1020Kb

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 ENERGYENERGY OFOF SYSTEMSYSTEM •• TheThe internalinternal energyenergy UU ofof aa systemsystem isis thethe totaltotal ofof allall kindskinds ofof energyenergy possessedpossessed byby thethe particlesparticles thatthat makemake upup thethe system.system. Usually the internal energy consists of the sum of the potential and kinetic energies of the working gas molecules. TWOTWO WAYSWAYS TOTO INCREASEINCREASE THETHE INTERNALINTERNAL ENERGY,ENERGY, U.U. ++UU WORKWORK DONEDONE HEATHEAT PUTPUT INTOINTO ONON AA GASGAS AA SYSTEMSYSTEM (Positive)(Positive) (Positive)(Positive) TWOTWO WAYSWAYS TOTO DECREASEDECREASE THETHE INTERNALINTERNAL ENERGY,ENERGY, U.U. WW outout QQout --UU DecreaseDecrease hot hot WORKWORK DONEDONE BYBY HEATHEAT LEAVESLEAVES AA EXPANDINGEXPANDING GAS:GAS: SYSTEMSYSTEM WW isis positivepositive QQ isis negativenegative THERMODYNAMICTHERMODYNAMIC STATESTATE TheThe STATESTATE ofof aa thermodynamicthermodynamic systemsystem isis determineddetermined byby fourfour factors:factors: •• AbsoluteAbsolute PressurePressure PP inin PascalsPascals •• TemperatureTemperature TT inin KelvinsKelvins •• VolumeVolume VV inin cubiccubic metersmeters •• NumberNumber ofof moles,moles, nn,, ofof workingworking gasgas THERMODYNAMICTHERMODYNAMIC PROCESSPROCESS Increase in Internal Energy, U. WWout QQin Initial State: HeatHeat inputinput Final State: P V T n P V T n 1 1 1 1 WorkWork byby gasgas 2 2 2 2 TheThe ReverseReverse ProcessProcess Decrease in Internal Energy, U. WWin QQout WorkWork onon gasgas Initial State: Final State: P1 V1 T1 n1 LossLoss ofof heatheat P2 V2 T2 n2 THETHE FIRSTFIRST LAWLAW OFOF THERMODYAMICS:THERMODYAMICS: •• TheThe netnet heatheat putput intointo aa systemsystem isis equalequal toto thethe changechange inin internalinternal energyenergy ofof thethe systemsystem plusplus thethe workwork donedone BYBY thethe system.system. Q = U + W final - initial) •• Conversely,Conversely, thethe workwork donedone ONON aa systemsystem isis equalequal toto thethe changechange inin internalinternal energyenergy plusplus thethe heatheat lostlost inin thethe process.process. SIGNSIGN CONVENTIONSCONVENTIONS +W FORFOR FIRSTFIRST LAWLAW +Wout ++QQ in •• HeatHeat QQ inputinput isis positivepositive U • Work BY a gas is positive --WWin • Work ON a gas is negative U •• HeatHeat OUTOUT isis negativenegative --QQout Q = U + W final - initial) APPLICATIONAPPLICATION OFOF FIRSTFIRST LAWLAW OFOF THERMODYNAMICSTHERMODYNAMICS ExampleExample 1:1: InIn thethe figure,figure, thethe gasgas absorbsabsorbs 400400 JJ ofof heatheat andand WW out =120=120 JJ atat thethe samesame timetime doesdoes 120120 JJ ofof workwork onon thethe piston.piston. WhatWhat isis thethe changechange inin internalinternal energyenergy ofof thethe system?system? QQin 400400 JJ Apply First Law: Q = U + W ExampleExample 11 (Cont.):(Cont.): ApplyApply FirstFirst LawLaw Q is positive: +400 J (Heat IN) WWout =120=120 JJ W is positive: +120 J (Work OUT) QQ QQ == UU ++ WW in 400400 JJ UU == QQ -- WW UU == QQ -- WW == (+400(+400 J)J) -- (+120(+120 J)J) U = +280 J == +280+280 JJ ExampleExample 11 (Cont.):(Cont.): ApplyApply FirstFirst LawLaw Energy is conserved: WWout =120=120 JJ TheThe 400400 JJ ofof inputinput thermalthermal energyenergy isis usedused toto performperform QQin 120 J of external work, in 120 J of external work, 400 J increasingincreasing thethe internalinternal 400 J energyenergy ofof thethe systemsystem byby 280280 JJ The increase in internal energy is: U = +280 J FOURFOUR THERMODYNAMICTHERMODYNAMIC PROCESSES:PROCESSES: ••• IsochoricIsochoricIsochoric Process:Process:Process: VVV === 0,0,0, WWW === 000 ••• IsobaricIsobaricIsobaric Process:Process:Process: PPP === 000 ••• IsothermalIsothermalIsothermal Process:Process:Process: TTT === 0,0,0, UUU === 000 ••• AdiabaticAdiabaticAdiabatic Process:Process:Process: QQQ === 000 Q = U + W ISOCHORICISOCHORIC PROCESS:PROCESS: CONSTANTCONSTANT VOLUME,VOLUME, VV == 0,0, WW == 00 0 QQ == UU ++ WW soso thatthat QQ == UU Q QIN QQOUT NoNo WorkWork -U +U DoneDone HEAT IN = INCREASE IN INTERNAL ENERGY HEAT OUT = DECREASE IN INTERNAL ENERGY ISOCHORICISOCHORIC EXAMPLE:EXAMPLE: NoNo ChangeChange inin volume:volume: PP2 BB PP A PP B = TTA TT B PP1 AA VV1 == VV2 400400 JJ HeatHeat inputinput 400400 JJ heatheat inputinput increasesincreases increasesincreases PP internalinternal energyenergy byby 400400 JJ withwith const.const. VV andand zerozero workwork isis done.done. ISOBARICISOBARIC PROCESS:PROCESS: CONSTANTCONSTANT PRESSURE,PRESSURE, PP == 00 QQ == UU ++ WW ButBut WW == PP VV Q QIN QQOUT WorkWork OutOut WorkWork -U +U InIn HEAT IN = Wout + INCREASE IN INTERNAL ENERGY HEAT OUT = Wout + DECREASE IN INTERNAL ENERGY ISOBARICISOBARIC EXAMPLEEXAMPLE ((Constant Pressure): A B P VA VB = TA T B 400 J V1 V2 Heat input 400400 JJ heatheat doesdoes 120120 JJ ofof increases V work,work, increasingincreasing thethe with const. P internalinternal energyenergy byby 280280 JJ. ISOBARICISOBARIC WORKWORK A B P VA VB = TA T B PPA == PPB 400 J V1 V2 Work = Area under PV curve Work P V ISOTHERMALISOTHERMAL PROCESS:PROCESS: CONST.CONST. TEMPERATURE,TEMPERATURE, TT == 0,0, UU == 00 QQ == UU ++ WW ANDAND QQ == WW QQIN QQOUT WorkWork OutOut WorkWork U = 0 U = 0 InIn NETNET HEATHEAT INPUTINPUT == WORKWORK OUTPUTOUTPUT WORKWORK INPUTINPUT == NETNET HEATHEAT OUTOUT ISOTHERMALISOTHERMAL EXAMPLEEXAMPLE (Constant(Constant T):T): A PA B PB UU == TT == 00 V2 V1 Slow compression at constant temperature: P V =PV A A B B ----- NoNo changechange inin UU. ISOTHERMALISOTHERMAL EXPANSIONEXPANSION ((ConstantConstant T)T):: AA PA BB PA VA = PBVB PB T = T V V A B U = T = 0 A B 400 J of energy is absorbed Isothermal Work by gas as 400 J of work is done on gas. V WnRT ln B T = U = 0 VA ADIABATICADIABATIC PROCESS:PROCESS: NONO HEATHEAT EXCHANGE,EXCHANGE, QQ == 00 QQ == UU ++ WW ;; WW == --UU oror UU == --WW W = -U U = -W Work Out Work U +U In Q = 0 Work done at EXPENSE of internal energy INPUT Work INCREASES internal energy ADIABATICADIABATIC EXAMPLE:EXAMPLE: A PP A B PP B VV1 VV2 Insulated ExpandingExpanding gasgas doesdoes Walls: Q = 0 workwork withwith zerozero heatheat loss.loss. WorkWork == --UU ADIABATICADIABATIC EXPANSION:EXPANSION: A PP A B PP AV VA PP BV VB = PP B TT A TT B Q = 0 VVA VVB 400 J of WORK is done, DECREASING the internal energy by 400 J: Net heat PVA ABB PV exchange is ZERO. QQ == 00 MOLARMOLAR HEATHEAT CAPACITYCAPACITY OPTIONAL TREATMENT TheThe molarmolar heatheat capacitycapacity CC isis defineddefined asas thethe heatheat perper unitunit molemole perper CelsiusCelsius degree.degree. CheckCheck withwith youryour instructorinstructor toto seesee ifif thisthis moremore thoroughthorough treatmenttreatment ofof thermodynamicthermodynamic processesprocesses isis required.required. SPECIFICSPECIFIC HEATHEAT CAPACITYCAPACITY RememberRemember thethe definitiondefinition ofof specificspecific heatheat capacitycapacity asas thethe heatheat perper unitunit massmass requiredrequired toto changechange thethe temperature?temperature? Q c mt ForFor example,example, copper:copper: cc == 390390 J/kgJ/kgKK MOLARMOLAR SPECIFICSPECIFIC HEATHEAT CAPACITYCAPACITY TheThe ““molemole”” isis aa betterbetter referencereference forfor gasesgases thanthan isis thethe ““kilogram.kilogram.”” ThusThus thethe molarmolar specificspecific heatheat capacitycapacity isis defineddefined by:by: QQ CC == nn TT ForFor example,example, aa constantconstant volumevolume ofof oxygenoxygen requiresrequires 21.121.1 JJ toto raiseraise thethe temperaturetemperature ofof oneone molemole byby oneone kelvinkelvin degreedegree.. SPECIFICSPECIFIC HEATHEAT CAPACITYCAPACITY CONSTANTCONSTANT VOLUMEVOLUME HowHow muchmuch heatheat isis requiredrequired toto raiseraise thethe temperaturetemperature ofof 22 molesmoles o o ofof OO 2 fromfrom 00 CC toto 100100 C?C? Q = nCv T QQ == (2(2 mol)(21.1mol)(21.1 J/molJ/mol K)(373K)(373 KK -- 273273 K)K) Q = +4220 J SPECIFICSPECIFIC HEATHEAT CAPACITYCAPACITY CONSTANTCONSTANT VOLUMEVOLUME (Cont.)(Cont.) SinceSince thethe volumevolume
Recommended publications
  • 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]
  • 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]
  • Isobaric Expansion Engines: New Opportunities in Energy Conversion for Heat Engines, Pumps and Compressors
    energies Concept Paper Isobaric Expansion Engines: New Opportunities in Energy Conversion for Heat Engines, Pumps and Compressors Maxim Glushenkov 1, Alexander Kronberg 1,*, Torben Knoke 2 and Eugeny Y. Kenig 2,3 1 Encontech B.V. ET/TE, P.O. Box 217, 7500 AE Enschede, The Netherlands; [email protected] 2 Chair of Fluid Process Engineering, Paderborn University, Pohlweg 55, 33098 Paderborn, Germany; [email protected] (T.K.); [email protected] (E.Y.K.) 3 Chair of Thermodynamics and Heat Engines, Gubkin Russian State University of Oil and Gas, Leninsky Prospekt 65, Moscow 119991, Russia * Correspondence: [email protected] or [email protected]; Tel.: +31-53-489-1088 Received: 12 December 2017; Accepted: 4 January 2018; Published: 8 January 2018 Abstract: Isobaric expansion (IE) engines are a very uncommon type of heat-to-mechanical-power converters, radically different from all well-known heat engines. Useful work is extracted during an isobaric expansion process, i.e., without a polytropic gas/vapour expansion accompanied by a pressure decrease typical of state-of-the-art piston engines, turbines, etc. This distinctive feature permits isobaric expansion machines to serve as very simple and inexpensive heat-driven pumps and compressors as well as heat-to-shaft-power converters with desired speed/torque. Commercial application of such machines, however, is scarce, mainly due to a low efficiency. This article aims to revive the long-known concept by proposing important modifications to make IE machines competitive and cost-effective alternatives to state-of-the-art heat conversion technologies. Experimental and theoretical results supporting the isobaric expansion technology are presented and promising potential applications, including emerging power generation methods, are discussed.
    [Show full text]
  • Novel Hot Air Engine and Its Mathematical Model – Experimental Measurements and Numerical Analysis
    POLLACK PERIODICA An International Journal for Engineering and Information Sciences DOI: 10.1556/606.2019.14.1.5 Vol. 14, No. 1, pp. 47–58 (2019) www.akademiai.com NOVEL HOT AIR ENGINE AND ITS MATHEMATICAL MODEL – EXPERIMENTAL MEASUREMENTS AND NUMERICAL ANALYSIS 1 Gyula KRAMER, 2 Gabor SZEPESI *, 3 Zoltán SIMÉNFALVI 1,2,3 Department of Chemical Machinery, Institute of Energy and Chemical Machinery University of Miskolc, Miskolc-Egyetemváros 3515, Hungary e-mail: [email protected], [email protected], [email protected] Received 11 December 2017; accepted 25 June 2018 Abstract: In the relevant literature there are many types of heat engines. One of those is the group of the so called hot air engines. This paper introduces their world, also introduces the new kind of machine that was developed and built at Department of Chemical Machinery, Institute of Energy and Chemical Machinery, University of Miskolc. Emphasizing the novelty of construction and the working principle are explained. Also the mathematical model of this new engine was prepared and compared to the real model of engine. Keywords: Hot, Air, Engine, Mathematical model 1. Introduction There are three types of volumetric heat engines: the internal combustion engines; steam engines; and hot air engines. The first one is well known, because it is on zenith nowadays. The steam machines are also well known, because their time has just passed, even the elder ones could see those in use. But the hot air engines are forgotten. Our aim is to consider that one. The history of hot air engines is 200 years old.
    [Show full text]
  • Section 15-6: Thermodynamic Cycles
    Answer to Essential Question 15.5: The ideal gas law tells us that temperature is proportional to PV. for state 2 in both processes we are considering, so the temperature in state 2 is the same in both cases. , and all three factors on the right-hand side are the same for the two processes, so the change in internal energy is the same (+360 J, in fact). Because the gas does no work in the isochoric process, and a positive amount of work in the isobaric process, the First Law tells us that more heat is required for the isobaric process (+600 J versus +360 J). 15-6 Thermodynamic Cycles Many devices, such as car engines and refrigerators, involve taking a thermodynamic system through a series of processes before returning the system to its initial state. Such a cycle allows the system to do work (e.g., to move a car) or to have work done on it so the system can do something useful (e.g., removing heat from a fridge). Let’s investigate this idea. EXPLORATION 15.6 – Investigate a thermodynamic cycle One cycle of a monatomic ideal gas system is represented by the series of four processes in Figure 15.15. The process taking the system from state 4 to state 1 is an isothermal compression at a temperature of 400 K. Complete Table 15.1 to find Q, W, and for each process, and for the entire cycle. Process Special process? Q (J) W (J) (J) 1 ! 2 No +1360 2 ! 3 Isobaric 3 ! 4 Isochoric 0 4 ! 1 Isothermal 0 Entire Cycle No 0 Table 15.1: Table to be filled in to analyze the cycle.
    [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]
  • Thermodynamics the Goal of Thermodynamics Is to Understand How Heat Can Be Converted to Work
    Thermodynamics The goal of thermodynamics is to understand how heat can be converted to work Main lesson: Not all the heat energy can be converted to mechanical energy This is because heat energy comes with disorder (entropy), and overall disorder cannot decrease Temperature v T Random directions of velocity Higher temperature means higher velocities v Add up energy of all molecules: Internal Energy of gas U Mechanical energy: all atoms move in the same direction 1 Mv2 2 Statistical mechanics For one atom 1 1 1 1 1 1 3 E = mv2 + mv2 + mv2 = kT + kT + kT = kT h i h2 xi h2 yi h2 z i 2 2 2 2 Ideal gas: No Potential energy from attraction between atoms 3 U = NkT h i 2 v T Pressure v Pressure is caused because atoms T bounce off the wall Lx p − x px ∆px =2px 2L ∆t = x vx ∆p 2mv2 mv2 F = x = x = x ∆t 2Lx Lx ∆p 2mv2 mv2 F = x = x = x ∆t 2Lx Lx 1 mv2 =2 kT = kT h xi ⇥ 2 kT F = Lx Pressure v F kT 1 kT A = LyLz P = = = A Lx LyLz V NkT Many particles P = V Lx PV = NkT Volume V = LxLyLz Work Lx ∆V = A ∆Lx v A = LyLz Work done BY the gas ∆W = F ∆Lx We can write this as ∆W =(PA) ∆Lx = P ∆V This is useful because the body could have a generic shape Internal energy of gas decreases U U ∆W ! − Gas expands, work is done BY the gas P dW = P dV Work done is Area under curve V P Gas is pushed in, work is done ON the gas dW = P dV − Work done is negative of Area under curve V By convention, we use POSITIVE sign for work done BY the gas Getting work from Heat Gas expands, work is done BY the gas P dW = P dV V Volume in increases Internal energy decreases ..
    [Show full text]
  • Thermodynamics I - Enthalpy
    CHEM 2880 - Kinetics Thermodynamics I - Enthalpy Tinoco Chapter 2 Secondary Reference: J.B. Fenn, Engines, Energy and Entropy, Global View Publishing, Pittsburgh, 2003. 1 CHEM 2880 - Kinetics Thermodynamics • An essential foundation for understanding physical and biological sciences. • Relationships and interconversions between various forms of energy (mechanical, electrical, chemical, heat, etc) • An understanding of the maximum efficiency with which we can transform one form of energy into another • Preferred direction by which a system evolves, i.e. will a conversion (reaction) go or not • Understanding of equilibrium • It is not based on the ideas of molecules or atoms. A linkage between these and thermo can be achieved using statistical methods. • It does not tell us about the rate of a process (how fast). Domain of kinetics. 2 CHEM 2880 - Kinetics Surroundings, boundaries, system When considering energy relationships it is important to define your point of reference. 3 CHEM 2880 - Kinetics Types of Systems Open: both mass and Closed: energy can be energy may leave and enter exchanged no matter can enter or leave Isolated: neither mass nor energy can enter or leave. 4 CHEM 2880 - Kinetics Energy Transfer Energy can be transferred between the system and the surroundings as heat (q) or work (w). This leads to a change in the internal energy (E or U) of the system. Heat • the energy transfer that occurs when two bodies at different temperatures come in contact with each other - the hotter body tends to cool while the cooler one warms
    [Show full text]
  • Thermal Equilibrium State of the World Oceans
    Thermal equilibrium state of the ocean Rui Xin Huang Department of Physical Oceanography Woods Hole Oceanographic Institution Woods Hole, MA 02543, USA April 24, 2010 Abstract The ocean is in a non-equilibrium state under the external forcing, such as the mechanical energy from wind stress and tidal dissipation, plus the huge amount of thermal energy from the air-sea interface and the freshwater flux associated with evaporation and precipitation. In the study of energetics of the oceanic circulation it is desirable to examine how much energy in the ocean is available. In order to calculate the so-called available energy, a reference state should be defined. One of such reference state is the thermal equilibrium state defined in this study. 1. Introduction Chemical potential is a part of the internal energy. Thermodynamics of a multiple component system can be established from the definition of specific entropy η . Two other crucial variables of a system, including temperature and specific chemical potential, can be defined as follows 1 ⎛⎞∂η ⎛⎞∂η = ⎜⎟, μi =−Tin⎜⎟, = 1,2,..., , (1) Te m ⎝⎠∂ vm, i ⎝⎠∂ i ev, where e is the specific internal energy, v is the specific volume, mi and μi are the mass fraction and chemical potential for the i-th component. For a multiple component system, the change in total chemical potential is the sum of each component, dc , where c is the mass fraction of each component. The ∑i μii i mass fractions satisfy the constraint c 1 . Thus, the mass fraction of water in sea ∑i i = water satisfies dc=− c , and the total chemical potential for sea water is wi∑iw≠ N −1 ∑()μμiwi− dc .
    [Show full text]
  • 25 Kw Low-Temperature Stirling Engine for Heat Recovery, Solar, and Biomass Applications
    25 kW Low-Temperature Stirling Engine for Heat Recovery, Solar, and Biomass Applications Lee SMITHa, Brian NUELa, Samuel P WEAVERa,*, Stefan BERKOWERa, Samuel C WEAVERb, Bill GROSSc aCool Energy, Inc, 5541 Central Avenue, Boulder CO 80301 bProton Power, Inc, 487 Sam Rayburn Parkway, Lenoir City TN 37771 cIdealab, 130 W. Union St, Pasadena CA 91103 *Corresponding author: [email protected] Keywords: Stirling engine, waste heat recovery, concentrating solar power, biomass power generation, low-temperature power generation, distributed generation ABSTRACT This paper covers the design, performance optimization, build, and test of a 25 kW Stirling engine that has demonstrated > 60% of the Carnot limit for thermal to electrical conversion efficiency at test conditions of 329 °C hot side temperature and 19 °C rejection temperature. These results were enabled by an engine design and construction that has minimal pressure drop in the gas flow path, thermal conduction losses that are limited by design, and which employs a novel rotary drive mechanism. Features of this engine design include high-surface- area heat exchangers, nitrogen as the working fluid, a single-acting alpha configuration, and a design target for operation between 150 °C and 400 °C. 1 1. INTRODUCTION Since 2006, Cool Energy, Inc. (CEI) has designed, fabricated, and tested five generations of low-temperature (150 °C to 400 °C) Stirling engines that drive internally integrated electric alternators. The fifth generation of engine built by Cool Energy is rated at 25 kW of electrical power output, and is trade-named the ThermoHeart® Engine. Sources of low-to-medium temperature thermal energy, such as internal combustion engine exhaust, industrial waste heat, flared gas, and small-scale solar heat, have relatively few methods available for conversion into more valuable electrical energy, and the thermal energy is usually wasted.
    [Show full text]
  • 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]
  • The First Law of Thermodynamics Continued Pre-Reading: §19.5 Where We Are
    Lecture 7 The first law of thermodynamics continued Pre-reading: §19.5 Where we are The pressure p, volume V, and temperature T are related by an equation of state. For an ideal gas, pV = nRT = NkT For an ideal gas, the temperature T is is a direct measure of the average kinetic energy of its 3 3 molecules: KE = nRT = NkT tr 2 2 2 3kT 3RT and vrms = (v )av = = r m r M p Where we are We define the internal energy of a system: UKEPE=+∑∑ interaction Random chaotic between atoms motion & molecules For an ideal gas, f UNkT= 2 i.e. the internal energy depends only on its temperature Where we are By considering adding heat to a fixed volume of an ideal gas, we showed f f Q = Nk∆T = nR∆T 2 2 and so, from the definition of heat capacity Q = nC∆T f we have that C = R for any ideal gas. V 2 Change in internal energy: ∆U = nCV ∆T Heat capacity of an ideal gas Now consider adding heat to an ideal gas at constant pressure. By definition, Q = nCp∆T and W = p∆V = nR∆T So from ∆U = Q W − we get nCV ∆T = nCp∆T nR∆T − or Cp = CV + R It takes greater heat input to raise the temperature of a gas a given amount at constant pressure than constant volume YF §19.4 Ratio of heat capacities Look at the ratio of these heat capacities: we have f C = R V 2 and f + 2 C = C + R = R p V 2 so C p γ = > 1 CV 3 For a monatomic gas, CV = R 3 5 2 so Cp = R + R = R 2 2 C 5 R 5 and γ = p = 2 = =1.67 C 3 R 3 YF §19.4 V 2 Problem An ideal gas is enclosed in a cylinder which has a movable piston.
    [Show full text]