Thermodynamica 2. Lecture 1. November 9, 2010

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1 hermodynamica hijs J.H. lugt Piero Colonna Lecture 1 Noember 9, 010 1

2 hermodynamica Studiehandleiding op blackboard Boek Moran&Shapiro (5e/6e editie) + extra materiaal blackboard oorkennis: hermodynamica 1 en wiskunde (integreren, differentiëren) entamen Open ragen Gesloten boek Formuleblad zal worden uitgereikt op het tentamen Uitgewerkte opgaen op blackboard College 1 tm 9.J.H. lugt (oornamelijk H11) College 10 tm 14 P. Colonna (zie studiehandleiding) Begin op tijd met de oorbereiding an het tentamen! Is iets niet duidelijk, neem (op tijd) contact op met de docenten!! Noember 9, 010

3 Inhoud college 1 tm 9 Eenwichten (b loeistof / damp) Relaties tussen thermodynamische grootheden eranderingen an thermodynamische grootheden Wat te doen met systemen anders dan een ideaal gas Breng papier en pen mee naar het college Print het formuleblad uit Noember 9, 010 3

4 andaag: samenatting hermoi 1e hoofdwet oor open en gesloten systemen.1-.5, Warmte en arbeid, toestandsgrootheid en procesgrootheid.1-.5 Enthalpie 3.3. e hoofdwet oor open en gesloten systemen Fasediagram an zuiere componenten Ideale gaswet, toestandsergelijkingen Afwijkingen an ideaal gasgedrag 3.4, 11.1 Homework: make the following exercises: Noember 9, 010 4

5 he 1 st law of hermodynamics closed systems open systems du Q W de dt c Q c W c m i hi i gz i m e h e e gz e hermodynamics I: applied e.g. to combustion cycle processes (modified) Otto cycle hermodynamics I: applied e.g. to compressors etc. in Brayton cycle Q x Q4 y combust Qx 3 adiabaat cool Qy 1 polytroop n=1. adiabaat Noember 9, isobaar

6 Quantities and concepts in hermodynamics first law 1 State property (toestandsgrootheid), A( 1, N ) with differential operator 1 (total differential) A does not depend on process path, but only on ariables ( 1, N ) for state properties for example U(,), p(,), (p,), (,p), for state properties Process quantities (procesgrootheid) with differential operator (inexact differential) process quantities depend on the process path for example heat Q du Q W da 0 '' 1 U du U 1, '1' '' 1 Q '1', U Q not equal to Q" state " Q" state1" Noember 9, process coordinate

7 olume-work F A F pressure p A z work 1 W Fds p Adz p d( Az) p d work through olume change 1 W 1 pd W>0 W<0 work is done by the system work is done on the system Noember 9, 010 7

8 Energy transfer by heat energy transfer of heat is due to a temperature-difference (temp.-gradient) the energy transfer is in the direction of decreasing temperature wind z Q Q erwarm erlies energy transfer by heat conduction follows the Fourier s law outside air Q erlies inside air isolation layer, i wall (brick), w with w > i z d Q A dz heat-conductiity coefficient (warmtegeleidingscoëfficiënt) surface area an energy-package of heat is defined as 1 Noember 9, Q depends on the process path, it is a process quantity (no state property) Q Qdt is an inexact differential 1 Q t t Qdt

9 1 st Law of hermodynamics Each closed system has a property U, the internal energy, for which: (neglect differences in KE and PE) the change in U for an adiabatic process is equal to the work W by the system; the added heat Q for a non-adiabatic process is gien by Q U U W 1 heat & work are process quantities; internal energy U is a state quantity Q>0 heat is transferred to the system Q<0 heat is transferred from the system W>0 work is done by the system W<0 work is done on the system Noember 9, 010 9

10 1 st Law of hermodynamics Q U U W 1 Adiabatic process: Q=0 Q>0 heat is transferred to the system Q<0 heat is transferred from the system W>0 work is done by the system W<0 work is done on the system Noember 9,

11 he Enthalpy H U p h u p dh du d p du pd dp Noember 9,

12 Adding heat while keeping the pressure constant Recall the first law: Enthalpy: H U p First law in terms of enthalpy: du q w q pd h u p dq d p = constant +d dh q dp Adding heat at constant pressure dh q Definition of heat capacity at constant pressure: (here: in units of [J mol -1 K -1 ]) c p h p Noember 9, 010 1

13 Noember 9, Energy balance for an open system e e e e i i i i c c c gz h m gz h m W Q dt de c d gz u E with

14 hrottle (Smoorklep) p i i p e <p i e 1 st law for stationary open system W adiabatic process (Q c =0kW) and with W c =0kW and g(z i -z e ) << (h i -h e ) h i c Q c m 1 i he 1 e i e h h gz z i e when the kinetic energy is negligible, i.e. low compared to c p (,p) 1 i e i e hi h e for ideal gases h(,p) is only h() i = e for ideal gases ONLY 1 kj/(kg K) =1000 (m /s )K -1 order of magnitude Noember 9,

15 urbine i h i W c 1 st law for stationary open system W c Q c m i e h h gz z i e i e e h e heating/cooling is often not realized, so that the process is adiabatic (Q c =0kW) and with g(z i -z e ) << (h i -h e ) and 1/( i - e ) << (h i -h e ) we get W c m h i h e to be checked caution: this is not applicable for liquid systems, say in hydro-power plants as a result of the work obtained from the system, the enthalpy of the working-fluid is reduced (and therewith the working-fluids temperature e < i ) Noember 9,

16 he second law of hermodynamics the nd law for closed systems in differential form ds Q 0 (closed system) 0 0 entropy production for reersible processes entropy production of non-reersible processes (due to irreersibilities) he entropy S is a state property. he entropy production is a process quantity, NO a state property he entropy production 0 is the lost work of the system, i.e. the nonutilized work potential For a close-to-ideal process (close to reersible), approaches zero (but in practice does not reach zero) Noember 9,

17 Second law for open systems For closed systems we hae ds Q entropy production 0 =0 for reersible processes >0 for irreersible processes For open systems (control olume) there is also entropy carried with mass entering and entropy carried by mass leaing, so that ds dt c Q c ms i i mo so c with c 0 trans temperature at which the heat transport Q coccurs Noember 9,

18 Phase diagram G apor L liquid S solid S L p p c S S + L c C L L+G S+G G c p solid S G critical point liquid L G apor/gas triple point Noember 9,

19 Equation of state of Ideal Gases p nr p R n R J mol K p pressure [Pa] olume [m 3 ] temperature [K ] n amount of substance [mol] 1 mol contains N A = molecules Noember 9,

20 he iso -diagrams for ideal gases he relation between of the 3 properties {p,,} can be isualized in state diagrams p p p isotherm, =const. isobar, p=const. isochor, =const. Noember 9, 010 0

21 Dealing with real gases compressibility factor: Z p R ideal gas limit: lim Z 1 p0 reduced pressure and reduced temperature: p R p p c, R c Noember 9, 010 1

22 Noember 9, 010

23 Examples of equations of state Ideal gas equation of state Z p R 1 irial equation of state (for non-ideal gasses) p Z B pc p D p R 3 1 ( ) ( ) ( )... an der Waals equation of state (for non-ideal gasses) na p nbnr Noember 9, 010 3

24 Isothermal expansion of an ideal gas p 1 first law isotherm, =const. adiabatic, Q=0 du Q W 0 pd because u() and =const. 1 1Q 1W pd nr d nr ln p nr 1 1 p Q W ideal gas law note: an isothermal process requires proiding energy in form of heat during expansion, otherwise the temperature would decrease 1 Noember 9, 010 4

25 Adiabatic expansion of an ideal gas (c = constant) du q pd pd Rd cd d d c R c c d 1 1 ln R 1 1 after some math... p d Rln cp constant (with ) c Noember 9, 010 5

26 Adiabatic Expansion p constant p constant c c p Noember 9, 010 6

27 Homework 1e hoofdwet oor open en gesloten systemen.1-.5, Warmte en arbeid, toestandsgrootheid en procesgrootheid.1-.5 Enthalpie 3.3. e hoofdwet oor open en gesloten systemen Fasediagram an zuiere componenten Ideale gaswet, toestandsergelijkingen Afwijkingen an ideaal gasgedrag 3.4, 11.1 Breng papier en pen mee naar het college Print het formuleblad uit Maak de olgende sommetjes: Noember 9, 010 7