Class Note for ECE 449 at UA 3
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Date Created: 02/06/15
A I we 449549 Giantinnons System mutualitth Chemical Thermodynamics I 0 In this lecture we shall talk about chemical thermodynamics and shall attempt a bondgraphic interpretation thereof 0 In the previous lecture we only considered the mass ows associated with chemical reaction systems However these masses also cany volume and heat 0 Chemical reactions are different from convective flows because the reaction occurs in a mixture ie masses do not get moved around macroscopically November 10 2003 start Presentation I we 449549 Glontinnnns System mutualitth Chemical Thermodynamics II 0 Yet some reactions change the overall volume or pressure of the reactants such as in eXplosive materials others occur either exothennically or endothennically It is obviously necessary to keep track of these changes 0 Furthennore we chose to represent substances in a mixture by separate CFelements If we wish to continue with this approach volume and heat flows indeed do occur between these capacitive fields November 10 2003 start Presentation A I we 449549 ontinnons System mmml Table of Contents I Chemical thermodynamics Causality in chemical bond graphs Conversion between mass and molar ow rates Stoichiome Periodic table of elements Eguation of state Isothermal and isobaric reactions Gibbs eguation Chemical reactor model November 10 2003 Start Presentation ltIJEIgt I we 449549 Glontinnnns System mutualingl Table of Contents II Mass balance Energy balance Volume ow Entropy ow Improved chemical reactor model Vectorbusbonds Chemical multiport transformers Chemical resistive fields November 10 2003 Start Presentation ltnrgt A I we 449549 ontinnons System mutualitth Causality in Chemical Bond Graphs Let us look once more at the generic chemical reaction bond graph Since the Nmatrix cannot be inverted the causality of the chemical M T F element is xed November 10 2003 start Presentation EA I we 449549 Gluntinnons System mutualitth Conversion Between Mass Flow Rate and Molar Flow Rate 0 The molar ow rate is proportional to the mass ow rate Thus we are dealing here With a regular transformer The transformation constant m depends on the substance For example since 1 kg of H2 correspond to 500 moles mHz 0 002 The entropy ow and heat ow don t change November 10 2003 start Presentation 1A3 l cote 449549 continuous system mammal The TFchElement Hence it makes sense to create the following chemical transformation element ulnllg hllylvhl m name p M 0Y 390 TF v w 0h m1 32 all Y halnldsund h Fi u v deu lanui nn Eajg g x an s ntErfacEs wDFDrL Parameter Rea m1 quotBnndgraphm Transformatzlnn Canstantquot A f 1 N b 10 2003 ovem er A 39 l eclarat39i39uns o class A l we 449549 toutinunus Mutant Whaling Stoichiometric Coef cients As we saw in the previous lecture the generic chemical reaction bond graph can be decomposed into a detailed bond graph showing individual ows between reactants and reactions In such a bond graph the stoichiometric coefficients are represented by transformers However since the mass ow rate truly changes in such a transformer this is not merely a conversion of units the entropy and heat ows must change along with it November 10 2003 Wrought tfld39l39fluwilnm Staquot Presentation g l 93M 449549 tantamount system attitudinal The TFst Element Hence it makes sense to create the following stoichiometric transformation element u at ailment94 1 TVF name TF 6YV Yo o o m St m1 m m A l gt 7 are Del 4 November 102003 SEX S 2 Ex S 1 ALI lgAL l we 449549 Ginn nuous 93mm Minimal Periodic Table of Elements We can consult the geriodic table of elements Name Bromine Symbol Bi Atomic Number 35 Atomic Mass 79904 amu Melting Point 12 0C 265 95 K 19 94 Pl Boiling Point 5878 lSl804 Fl Number of Protonsl lectrons 35 Number of Neutron 45 Classi cation 1 mole 80 g Crystal Structure Onhorhombic Density 293 K Si 19 glcrn3 Color Red November 10 2003 Start Presentation A we 449549 ontinnons System whalingl k Br2 4 2Br CthI VkE kl MBr m VBr Br ZHBr39 CS 239 TF 239 0 a 1 393 Brz BLT l lialr2 T Vkll le1 November 10 2003 Start Presentation I we 449549 Glontinnnns System whalingl The Equation of State 0 Chemical substances satisfy a socalled equation of state that relates the three domains to each other For ideal gases the equation of state can be written as follows E 83121 116 mole l The equation of state can be written either for partial pressures Dalton s law or for partial volumes Avogadro s law Dalton s law Avagadra s law November 10 2003 Start Presentation IA l we 449549 Summons system mmml Isothermal and Isobaric Reactions I If both pressure and temperature can be assumed approximately constant the equation of state can be conveniently differentiated as follows using Avogudro s law This equation can be used to compute the volume ow from the mass ow November 10 2003 start Presentation Al I it 449549 un nuonx System mutualitml Isothermal and Isobaric Reactions II This relationship holds for all ows in the hydrogen bromine reaction thus describe the corresponding partial pressures start Presentation November 10 2003 Eh I we 449549 Summons system mmml The Gibbs Equation 0 Chemical substances also satisfy the socalled Gibbs equation which can be written as Since we already know Vi and qi we can use this equation to compute Si 0 The entropy ow accompanies the mass ow and the volume ow 0 Due to linearity T p constant 3 u constant the entropy ow can be superposed to the mass and volume ows November 10 2003 start Presentation 1A5 I it 449549 un nuonx System mutualitml Isothermal and Isobaric Reactions III Entropy ows for the hydrogenbromine reaction Neither the partial entropies nor the V physically extremely dubious partial temperatures are used anywhere except for de ning the corresponding power flows describe the corresponding partial temperatures November 10 2003 start Presentation A was 449549 ontinnous System whalingl Br2 1 2Br39 CthI VkHkI 1V1Br2 m VBr2 Brz 2MBrquot m Br39 Br39 m gBr39 CSBr2 E 0 1 1 If E If 0 If TF CSBr g3r2 mm LLB Vkl Vkl quote zvkl Br m MBr39 CthI qkagkl qBr PB 2pmquot m p p CSBr 95239 2 quot 39 a TF 39 34 quot2 cs 2 pBr O qul l 1 lqkl ma lzqk 0 qur39 Br November 1039 2003 start Presentation was 449549 Glontinnnns System mutualitth k1 Br2 gt 2Br CthI VkEEJkI CS Mgrzl W Van 13er ZIHBr39 m lu Br IHBr39 m lgBr S Br gBrlzemTwii BIr2 0 szll 1 I Oak lick O Ivalgr39 131 Brquot CthI S T 2T T T Br2 Br Br N Br Br CS 9539 f 39 3 39m 3997 CS r2 TBr O Saki 1 ngl lzsk 0 SEE Br Navember 10 2003 start Presentation A we 449549 Summons system mmml Br2 1 2Br39 We are now ready to sketch the combined model r TFDM CFBrzi 0 K m al TF5 mm mxn n 0 H9LEH CFBE This mm the standard gape eld as it mid been nira the smxsion of the convective November 10 2003 Start Presentation lt2JEIgt A I it 449549 un nuonx System mutualitml The Chemical Reactor Model I We already know that the chemical reactor needs to compute the three ows We already have the equations for this model 4 reaction rate equation 4 equation of state 4 Gibbs equation We still need to verify though that no balance equations are being Violated November 10 2003 Start Presentation ltnrgt 10 A we 449549 ontinnons System mutualitth Mass Balance 0 The mass balance is embedded in the stoichiometric coefficients Whatever gets removed from one reactant gets added back to another Hence the total reaction mass will not change 0 This is true for each step reaction separately since each step reaction must satisfy the stoichiometric constraints November 10 2003 start Presentation I we 449549 Glontinnnns System mutualitth Energy Balance I 0 The way the equations were set up we already know that November 10 2003 start Presentation ll A I we 449549 ontinnons System mutualitth Energy Balance II 0 The above equation holds true under all operating conditions ie the topology of the chemical reaction network is independent of the conditions under which the chemical reaction is perfonned The isothermal and isobaric conditions assumed before only in uence the CFfield ie the way in which the three potentials are being computed and possibly the RFfield ie the way in which the three flows are being computed we shall discuss in the next class whether this is indeed true or not November 10 2003 start Presentation EAE E I we 449549 Glontinnnns System mutualitth Volume Flow I 0 Under isothermal and isobaric conditions we can write 3 Eran Hymn Vk1 quotR 39 Ehtbbquot November 10 2003 start Presentation A l we 449549 ontinnnu system mmml Volume Flow 11 0 However under isobaric conditions we can also write November 10 2003 Start Presentation ALE I it 449549 un nuonx System mnamgl Entropy Flow I 0 Let us now discuss the entropy ow We are certainly allowed to apply the Gibbs equation to the substances 0 Under isothermal and isobll rk conditions November 10 2003 Start Presentation l3 AL I we 449549 Marianna 52mm Whalingl Entropy Flow II Therefore Thus the Gibbs equation can also be applied to reactions November 10 2003 Start Presentation ZAL lace 449549 outinunns 52mm mammal The Chemical Reactor Model 11 We are now ready to program the chemical reactor model 5 it 5121312141 131 IV T slgnall c Slgnalrl 1 Cth1 November 10 2003 Start Presentation 14 A I we 449549 ontinnons System whalingl The Chemical Reactor Model III Consequently mm T7er mm CFBrz ei39wTF39 E 0 A 1 TF 0 i 39TFH CFBr Mealsq T ms W I Effort State sensor sensor November 10 2003 Start Presentation Z113 I we 449549 Glontinnnns System whalingl The Vector Bus Bond The only clean solution is to create a new bond graph library the ChemBondLib Which operates on vector bus bonds ie vectors of bus bonds that group all the ows together Special blue vectorbus0juncti0ns Will be needed that have on the one side a group of red busbond connectors on the other side one blue vectorbusbond connector The individual CFelements can be connected to the red side Whereas the MT Felement is connected to the blue side November 10 2003 Start Presentation 15 A l we 449549 cantian system mnhelingl The MTFElement The MTFelement is specific to each reaction since it contains the Nmatrix Which is used six times inside the M T F element November 10 2003 start Presentation 2A5 I 449549 toutinuoux System mnamgl The RFElement The RFelement is also specific to each reaction and it may furthermore be specific to the operating conditions eg isobaric and isothermal In the isobaric and isothermal case it could contain the vector equations November 10 2003 start Presentation ltIgt A we 449549 untinnons System whalingl Conclusions I 0 In my Continuous Svstem Modeling book I had concentrated on the modeling the reaction rates ie on the mass ow equations I treated the volume and heat flows as global properties disassociating them from the individual flows 0 In this new presentation I recognized that mass flows cannot occur without simultaneous volume and heat flows which led to an improved and thennodynamically more appealing treatment November 10 2003 Start Presentation ltIJEgt I we 449549 Glontinnnns System whalingl Conclusions 11 0 Although I had already recognized in my book the N matrix relating reaction ow rates and substance ow rates to each other and although I had seen already then that the relationship between the substance chemical potentials and the reaction chemical potentials was the transposed matrix M N I had not yet recognized the chemical reaction network as a bondgraphic Multiport Transformer the M T F element 0 Although I had recognized the CSelement as a capacitive storage element I had not recognized the ChRelement as a reactive element November 10 2003 Start Presentation ltnrgt 17 A I we 449549 Giantinnons System mutualitth Conclusions 111 When I wrote my modeling book I started out with the known reaction rate equations and tried to come up with a consistent bondgraphic interpretation thereof I took the known equations and t them into boxes wherever they t best and in all honesty I didn t goof up very much doing so because there aren t many ways using the bondgraphic technique that would lead to a complete and consistent ie contradictionfree set of equations and yet be incorrect November 10 2003 Start Presentation ltIJEgt A I we 449549 Glontinnnns System mutualitth Conclusions IV However the bondgraphic approach to modeling physical systems is much more powerful than that In this lecture I showed you how this approach can lead to a clean and consistent thenno dynamically appealing description of chemical reaction systems We shall continue with this approach during one more class where I shall teach you a yet improved way of looking at these equations November 10 2003 Start Presentation ltnrgt 18 A we 449549 untinnons System mmml References Cellier FE 1991 Continuous System Modeling SpringerVerlag New York Chapter 9 November 10 2003 Start Presentation ltIJEIgt 19
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