Cmbustin Chemistry Hai Wang Stanfrd University 2015 Princetn-CEFRC Summer Schl On Cmbustin Curse Length: 3 hrs June 22 26, 2015 Cpyright 2015 by Hai Wang This material is nt t be sld, reprduced r distributed withut prir written permissin f the wner, Hai Wang.
Lecture 1 1. THERMOCHEMISTRY Thermdynamics is the fundatin f a large range f physical science prblems. It prvides us with a basic understanding abut the driving frce f a physical prcess and the limits f such a prcess. The develpment f thermdynamic thery was intimately related t cmbustin. In particular, the secnd law f thermdynamics was cnceived largely t prve that it is impssible t perate a perpetual mtin machine. 1.1 Thermdynamic First Law The first law f thermdynamics states that the energy is cnserved when this energy is transfrmed frm ne frm t anther. In the cntext f cmbustin analysis, we state that fr a cntrl mass (r the wrking fluid), Q W = ΔU (1.1) where Q (kj r kcal) is the heat transferred frm the wrking fluid t the surrunding, W (kj r kcal) is the wrk dne by the wrking fluid t the surrunding, and U (kj r kcal) is the internal energy f the wrking fluid. It is imprtant t mentin that energy transfrmatin always invlves a prcess that has a initial state (1) and a final state (2). ΔU = U 2 U 1 is therefre the change f internal energy f the wrking fluid frm the initial state t the final state. Thermdynamic analysis fllw the cnventin that if the wrking fluid gives ff heat t the surrunding, Q < 0, and if the wrking fluid receives heat frm the surrunding, Q is psitive. Fr example, in a simple cling prcess, a fluid lses its internal energy t the surrunding (i.e., lwering its temperature) and thus ΔU < 0. Assuming that n wrk is dne (W = 0), then Q < 0. Likewise, if the wrking fluid des net wrk t the surrunding, W is psitive, and if the surrunding des net wrk t the wrking fluid, W < 0 (e.g., fr adiabatic cmpressin (Q = 0), the wrk dne by the surrunding t the wrking fluid serves t raise the internal energy f the wrking fluid, since W = ΔU > 0. The symbl U designates the internal energy f a given mass f a substance. Internal energy is a measure f the ttal energy f the cntrl mass. Fr example, excluding nuclear energy the internal energy f air is a sum f the kinetic energy f each atm. Therefre, the internal energy can be made a material prperty if it is defined as the internal energy per mass, an intensive prperty, dented here as u (kj/kg) r u (kj/kml). In this curse, we shall fllw the ntatin that intensive prperties are expressed in lwer cases. Assuming that we are running a thermdynamic prcess that the nly wrk dne during the prcess is that assciated with bundary wrk under a cnstant pressure P 1 = P 2 = P (e.g., a pistn wrk), the wrk dne may be calculated frm 1-1
Stanfrd University Versin 1.2 Putting Eq. (1.2) int Eq. (1.1), we have 2 2 1 1 W = PdV = P( V V ). (1.2) Q = ( U 2 + P 2 V 2 ) ( U 1 + P 1 V 1 ), (1.3) where V is the vlume f the wrking fluid. In this case, the heat transferred during the prcess crrespnds t a net change f the cntrlled mass in the quantity U + PV between the initial and final states. We find it cnvenient t define a new thermdynamic prperty, the enthalpy H = U + PV, (1.4a) h = u + Pv, (1.4b) h = u + Pv. (1.4c) Here v and v are the specific vlumes, having the units (m 3 /kg) and (m 3 /kml) respectively. Clearly, these specific vlumes are related t the mass density ρ and mlar density (r cncentratin) c, respectively, i.e., v = 1/ρ and v = 1/c. In general, the internal energy u and enthalpy h depend n nly tw independent prperties that specifying the thermdynamic state, e.g., (T, P), (T, v), r (P, v). Fr a lw-density gas like air r cmbustin gases, T, P, and v are related by the ideal gas law r the equatin f state, Pv = R ' T, (1.5a) Pv = R u T, (1.5b) where R u is the universal gas cnstant (8.314 kj/kml-k), R is the specific gas cnstant and equal t R u/mw, and MW is the mlecular weight f the substance. Fr a lw-density gas, the internal energy is primarily a functin f T, i.e., u u( T ). This relatinship may be expressed by defining a cnstant-vlume specific heat c v (kj/kml-k) c v u = T v. (1.6) Fr an ideal gas we have du = c v dt. Likewise, the relatinship between enthalpy and temperature may be established by defining a cnstant-pressure specific heat c p (kj/kml-k) " c p = h % $ ' # T & p, (1.7) 1-2
Stanfrd University Versin 1.2 and dh = c p dt. In ther wrds, the tw specific heats defined abve characterize the heat required t raise the temperature f a substance by 1 K. Since fr an ideal gas dh = du + d( pv ) = du + RudT and u u( T ), we see that h and c p are als functin f temperature nly. The relatin between dh and du als yields cp = cv + R u. Here it is imprtant t nte that the enthalpy discussed thus far invlves nly the heating r cling a substance. This type f enthalpy is knwn as the sensible enthalpy r sensible heat. Later, we will intrduce tw ther types f enthalpy, ne f which is critical t cmbustin prblems. The first law f thermdynamics is quite insufficient t describe energy cnversin. Equatin (1.1) states that it is pssible t cl a substance f a given mass spntaneusly (i.e., lwering its internal energy U), and transfer this energy t the surrunding. In ther wrds, within the first law f thermdynamics, it is pssible t transfrm heat frm a lwtemperature bdy t a high temperature bdy. We knw that this cannt be true. The secnd law f thermdynamics, t be discussed belw, will address this prblem. 1.2 Thermdynamic Secnd Law and Entrpy In cntrast t the first law f thermdynamics, the secnd law is mre difficult t understand. The Kelvin-Planck statement f this law is It is impssible t cnstruct a device that will perate in a cycle and prduce n effect ther than the raising f a weight and the exchange f heat with a single reservir. In ther wrds, it is impssible t cnstruct a heat engine that (a) receives heat cntinuusly frm a heat reservir, (b) turns the heat transferred entirely t wrk, (c) withut having t leave any marks n the surrunding. Withut diverging int a lengthy discussin f the secnd law f thermdynamics, let us define entrpy S (kj/k) as δ Q S = T int rev. (1.8) where (δq) int rev is the heat a cntrl mass received during an infinitesimal, internally reversible prcess. Based n an analysis f thermdynamic cycles, it may be shwn that fr a spntaneus prcess t ccur, the entrpy f the cntrl mass must be equal t r greater than zer, ΔS = S 2 S 1 0. (1.9) Neither the Kelvin-Planck statement nr Eq. (1.8) really tells us what entrpy is. An understanding f entrpy will have t cme smetime later when we intrduce statistical thermdynamics. Here let us place sme discussin abut entrpy in a nn-rigrus fashin. Entrpy is a measure f mlecular randmness. This randmness may be measured by the predictability f the psitins f atms in a substance. A crystal material wuld have a small entrpy because atms are mre r less lcked int the crystal lattice. In fact, the third law f thermdynamics states that the entrpy f a pure crystalline substance at abslute 1-3
Stanfrd University Versin 1.2 zer temperature is zer. In ther wrds, the atms in a pure crystal are frzen (n scillatin) at 0 K. Therefre, their spatial psitin is cmpletely predictive. In cntrast, a gas wuld have a large entrpy because mlecules that make up the gas cnstantly mve abut in the space, resulting in small predictability regarding their psitins. Mrever, an increase in temperature f the gas leads an increase in the speed f mlecular mtin and smaller predictability f the mlecular psitins. In ther wrds, entrpy increases with an increase in temperature. In cntrast, an increase in pressure leads t clser spacing amng mlecules. As a result, the mlecules becme mre cnfined spatially and the entrpy is smaller at higher pressures. The dissciatin f a chemical substance int gaseus fragments always leads t an increase in entrpy since it is harder t predict the spatial psitins f the fragments than the mlecules f their parent substance. The inequality expressed by Eq. (1.9) basically says that fr a spntaneus prcess t ccur, the entrpy f the cntrl vlume must increase, i.e., natural prcesses favr mre randmness than rderness. Cnceptually this makes sense since ur experience tells us that a building can spntaneusly cllapse int a pile f rubble, but a pile f rubble wuld nt spntaneusly transfrm int a building (nt withut ur interventin). Tw different gases, say, N 2 and O 2, wuld always mix and they never spntaneusly separate spatially, leading t better predictability f their psitins. The cncept f entrpy is als deeply rted in ur life. Take the life f a wrkahlic as an example, the first law f thermdynamics states that it is pssible fr him/her t receive heat Q in the frm f fd and hpefully withut gaining weight (ΔU = 0), t transfrm this heat entirely t wrk W. The secnd law says that he/she really cannt d this. That is, my ffice always gets messier ver time and I will need t clean it (i.e., nt all the heat ges t useful wrk) as time ges by. Because entrpy is a measure f randmness, which in turn, is determined by T and P, it is als a material prperty. It fllws that we can define and dente the entrpy f a substance by s (kj/kg-k) r s (kj/kml-k). Althugh we d nt knw fr the time being hw t directly measure entrpy, we may develp sme relatinships that can help us t determine the entrpy value. Here we apply the first law t a cnstant T and P, internally reversible prcess (e.g., cmpress a vlume immersed in a temperature bath by a pistn very slwly), but since δ Qint rev = TdS and δ Wint rev = r δq δw = du (1.10) int rev int rev, PdV, we have TdS = du + PdV (1.11) ds = + = c dt v + T T T T. (1.12) 1-4
Stanfrd University Versin 1.2 Replacing u by h Ts and rearranging, we btain ds = dh vdp = c dt p vdp T T T T. (1.13) Applying the ideal gas law, we may rewrite equatins (12) and (13) as One may integrate the abve equatins t shw that dt dv ds = cv + Ru, (1.14) T v dt dp ds = cp Ru T P. (1.15) dt Δ s = s2 s1 = cv + R 1 T 2 2 u ln v1 v, (1.16) Δ = = 2 dt P2 s s2 s1 cp Ru ln 1 T P. (1.17) Equatin (1.17) states that if c p is a cnstant, an increase f temperature by ΔT frm T causes the entrpy t increase by cp ln( 1+ΔT T ) and an increase f pressure by ΔP frm P leads t the entrpy t decrease by Ru ln( 1+ΔP P ). Given the third law f thermdynamics, which establish the abslute zer fr entrpy, the entrpy f an ideal gas at a given thermdynamic state (i.e., knwn T and P) can be easily determined if c p is knwn. Equatin (1.17) als states that unlike enthalpy and internal energy, the entrpy f an ideal gas is a functin f bth temperature and pressure. In applicatin, we define the standard entrpy s as 1 2 dt T2 dt T 1 dt Δ s = s2 s1 = cp = cp Ru ln( P ) cp Ru ln( P ) 1 T 0 0 T T, (1.18) r where T dt s = cp Ru ln P 0 T P is the standard pressure f 1 atm. Hence, ( ), (1.19a) Δ s = T 0 c p dt T, (1.19b) 1-5
Stanfrd University Versin 1.2 By tabulating this standard entrpy, we may easily determine the entrpy change f an ideal gas under an arbitrary cnditin by 1.3 Chemical Reactins P s ( T, P) = s ( T) Ru ln P. (1.20) Befre we apply the abve thermdynamic principles t cmbustin analysis, we need t take a mment t review a few aspects f chemical reactins. Frm a prcess pint f view, a chemical reactin may be viewed as the cnversin f reactants that enter int a reactr (the initial state) t prducts that leaves the reactr (the final state). Fr example, methane (CH 4) flws int a reactr with air (21%O 2 and 79% N 2). Suppse the mlar rati f xygen t methane is 2-t-1. We may write that t burn 1 mle f methane, CH 4 + 2 O 2 + (2 79/21) N 2 Reactr CO 2 + 2H 2O + (2 79/21) N 2. Here the prducts include 1 mle CO 2, 2 mles f H 2O and (2 79/21) mles f N 2. Of curse, in writing the abve prcess reactin, we may neglect the bx and simply write CH 4 + 2 O 2 + (2 79/21) N 2 CO 2 + 2H 2O + (2 79/21) N 2. (1.21) The abve reactin is knwn as the cmplete cmbustin reactin as all the carbn in the fuel is xidized t CO 2 and all the hydrgen is cnverted t H 2O. These cmpunds are called the cmplete cmbustin prducts. If there is n excess xygen (i.e., all xygen is cnsumed in the xidatin prcess), the characteristic fuel-t-xygen mlar rati is knwn as the stichimetric rati (equal t ½ fr methane). The stichimetric rati fr an arbitrary fuel C mh n may be readily determined by writing ut the cmplete, stichimetric reactin, C mh n + (m+ n 4 ) O 2 + (m+ n 4 ) (79/21) N2 m CO 2 + which gives the stichimetric rati equal t 1/(m+ n 4 ). n H 2 2O + (m+ n 4 ) (79/21) N2. (1.22) In a practical cmbustin prcess, hwever, the fuel-t-xygen mlar rati needs nt t be the stichimetric rati. Fr example, a gasline engine ften runs slightly abve the stichimetric rati at the cld start, fr reasns t be discussed later. T characterize fuelt-xygen rati in a practical cmbustin prcess, we intrduce the equivalence rati, defined as the mlar rati f fuel-t-xygen fr an actual cmbustin prcess by that f stichimetric cmbustin: φ = ( mles f fuel mles f xygen ) ( mles f fuel mles f xygen ) act. sti.. (1.23) 1-6
Stanfrd University Versin 1.2 Of curse, it may be shwn that the equivalence rati may be calculated using the mlar rati f fuel-t-air r the mass rati f fuel-t-xygen r fuel-t-air. By examining the equivalence rati, we can quickly tell the nature f the fuel/air mixture. That is, if φ = 1, we have stichimetric reactin; if φ < 1 we have excess xygen that is nt cmpletely used in a reactin prcess and the cmbustin is called fuel-lean cmbustin; if φ > 1 we have excess fuel and the cmbustin is called fuel-rich cmbustin. < 1 fuel lean φ = 1 stichimetric > 1 fuel rich Under the fuel rich cmbustin, the cmbustin reactin inherently yields incmplete cmbustin prducts, like CO, H 2 etc. 1.4 Enthalpy f Frmatin, Enthalpy f Cmbustin As we discussed in sectin 1.1, there are 3 types f enthalpy. The first type is assciated with heating r cling f a substance. The secnd type is latent enthalpy (r heat). This is the enthalpy assciated with the phase change f a substance. Fr example, the latent heat f evapratin f H 2O, h lg, is hlg = hg h l, (1.24) where h g and h l are the enthalpy f water in its vapr and liquid states, respectively. What is perhaps mre imprtant t cmbustin analysis is the reactin enthalpy. Fr example, reactin (21) releases an amunt f heat due t chemical bnd rearrangements. Cmbining Eqs (1.3) and (1.4a), we have Q = H2 H 1. Since state 1 crrespnds t the reactants, and state 2 crrespnds the prducts, the abve equatin states that (a) in a nn-adiabatic reactr, the heat released frm the reactr is equal t the ttal enthalpy f the cmbustin prducts subtracted by the ttal enthalpy f the reactant, and (b) since fr a cmbustin prcess Q < 0, H 2 < H 1, i.e., the ttal enthalpy f the prducts is lwer than that f the reactants. The nature f reactin enthalpy is very different frm the sensible enthalpy, as the frmer is due t re-arranging chemical bnds and the latter is simply due t heat and cling withut changing the chemical nature f the substance. T calculate the exact amunt f reactin enthalpy and therefre the amunt f heat release, we need t first understand the cncept and applicatin f enthalpy f frmatin. 1-7
Stanfrd University Versin 1.2 The enthalpy f frmatin h f at a given temperature is defined as the heat released frm prducing 1 mle f a substance frm its elements at that temperature. By this definitin, the enthalpy f frmatin is zer fr the reference elements. These elements are, fr example, graphite [dented by C(S) hereafter), mlecular hydrgen H 2, mlecular xygen (O 2), mlecular nitrgen (N 2), and mlecular chlrine (Cl 2). The enthalpy f frmatin f CO 2, say at 298 K, may be cnceptually measured by reacting 1 mle f graphite and 1 mle f O 2 at 298 K, prducing 1 mle f CO 2 at the same temperature: C(S) + O 2 CO 2 + Q, where Q is the heat released frm the abve prcess (Q = 393.522 kj). Using Eq. (1.24), we have ( CO ) ( ) ( ) ( ) Q = -393.522 (kj)= H H = 1 hf K CO 1 hf K C(S) + hf K O = h f,298k 2 2 1,298 2,298,298 2. The enthalpy f frmatin f CO 2 is therefre h f = 393.522 kj/ml at 298 K. Likewise the enthalpy f frmatin f CO is determined by measuring the heat release frm and C(S) + ½ O 2 CO + Q ( 110.53 kj at 298 K), (1.25) h f (CO) = 110.53 kj/ml at 298 K. The cnceptual definitin uses the same temperature fr the reactr, reactants, and prducts, and this cnditin is knwn as the standard cnditin. Fr this reasn, we use a superscript, i.e., h f, t designate this standard cnditin and the crrespnding enthalpy f frmatin is termed as the standard enthalpy f frmatin. Obviusly if reactin (25) is carried ut at a different temperature under the standard cnditin, we d nt necessarily get the same heat release. In ther wrds, the enthalpy f frmatin is dependent n temperature, yet this temperature dependence is related t sensible heat. T illustrate the relatinship f enthalpy f frmatin f a substance at tw different temperatures, we sketch the fllwing diagram: 1-8
Stanfrd University Versin 1.2 elements Δ H = H ( T ) H ( 298 ) elements = h ( T ) h ( 298 ) + h ( T ) h ( 298 ) C(S) O 2 1 h, 2 f T 1 2 h f,298 K Elements Substance (1 mle C(s) + 1 mle O 2 ) (1 mle CO 2 ) T Δ H = ( ) ( ) h T h 298 2 CO CO 2 298 K Recgnizing that enthalpy is a state functin, i.e., fr an ideal gas the enthalpy f a substance is fully defined if the temperature is knwn, and the change f enthalpy fr a prcess is independent f the path, we may write H 2' H 1 = H 2' H 2 + H 2 H 1 It fllws that ( ) = " h ( T ) h (298) = H 2' H 1' + ( H 1' H 1 ) = h f,t # ( CO 2 ) + " # h T ( ) $ % + h CO2 f,298 CO 2 ( ) h (298) $ % + " h T C(S) # ( ) h (298). $ % O2 h f,t ( CO 2 ) = h f,298 ( CO 2 ) + " # h ( T ) h (298) $ % CO2 " # h ( T ) h (298) $ % + " h T C(S) # ( ) h (298) $ { % O2 }, which may be generalized t ( ) ν ( ) h, = h,298 + h T h(298) h T h (298) substance, (1.25a) f T f i i elements where ν i is the stichimetric cefficients f the i th elements in the reactin that frms the substance. Therefre if the specific heat r sensible enthalpy f a substance is knwn, we nly need t knw the value f enthalpy f frmatin at a particular temperature, and in general this temperature is equal t 298 K. In cmbustin analysis, we ften grup the first and secnd term f Eq. (1.25a) by defining a ttal enthalpy as and h T h f,298 + # $ h T ( ) h(298) % &, substance (1.25b) h f,t ( ) h(298) = h T ν " i # h T $. (1.25c) elements % i Table 1.2 lists the enthalpy f frmatin f sme imprtant species fr cmbustin analysis. 1-9
Stanfrd University Versin 1.2 Table 1.2 Standard enthalpy f frmatin f key cmbustin species in the vapr state Species Name h (kj/ml) f,298 H 2O Water -241.8 CO Carbn mnxide -110.5 CO 2 Carbn dixide -393.5 CH 4 Methane -74.9 C 2H 6 Ethane -84.8 C 3H 8 Prpane -104.7 C 4H 10 Butane -125.6 C 8H 18 Octane -208.4 C 2H 4 Ethylene 52.5 C 2H 2 Acetylene 226.7 CH 3OH Methanl -201.0 C 6H 6 Benzene 82.9 H Hydrgen atm 218.0 O Oxygen atm 248.2 OH Hydrxyl radical 39.0 The standard enthalpy f cmbustin h c (kj/ml-fuel) is defined as the heat released frm the cmplete cmbustin f 1 mle f fuel at 298 K. Cnsider the cmplete cmbustin f methane (Eq. 1.21). We will again utilize the path independent prperty t illustrate that hc may be determined by the sum f enthalpy f frmatin f the prducts (multiplied by the mlar rati f the prduct-t-fuel) subtracted by the sum f enthalpy f frmatin f the reactants: h c CH 4 + 2O 2 + 2 79/21 N 2 CO 2 + 2H 2 O + 2 79/21 N 2 Δ H 1 Δ H 2 C(S) + 2H 2 + 2O 2 + 2 79/21 N 2 ( ) ( ) ( ) h (kj/kml-fuel) =Δ H +Δ H = 1 h CH + 1 h CO + 2 h H O. c 1 2 f,298 4 f,298 2 f,298 2 Fr an arbitrary fuel (C mh n) underging cmbustin (1.22), we determine its enthalpy f cmbustin as 1-10
Stanfrd University Versin 1.2 h = ( ) + ( ) c(kj/kml-fuel) m h,298 CO n f 2 hf,298 H2 O h f,298 ( CmHn). 2 In additin, fr an arbitrary reactin given by ' νiai ν ' A ', (1.26) i i react. prd. ' where A and i A are the i i th reactants and prducts, respectively, and ν i are termed as the stichimetric cefficients, we determine the enthalpy f reactin at an arbitrary temperature T by ( ) ν ( ) Δ H = ν h A h A rt, i' T i' i T i prd. react. = νi' hf,298( Ai' ) νihf,298( Ai) + νi' h ( T) h(298) ν ( ) (298) ' i h T h i i prd. react. prd. react. =Δ Hr,298 + νi' h ( T) h(298) ν ( ) (298) i' i h T h i prd. react. Since the ttal numbers f the elements in the reactants and prducts are identical, the sensible enthalpy terms fr the elements in Eq. (1.25c) are canceled ut. If ΔH rt, is psitive, the reactin absrbs heat. This type f reactins is knwn t be endrthermic. If ΔH rt, < 0, the reactin releases heat as it prceeds t cmpletin. This type f reactins is knwn t be exthermic. Cnversely, If ΔH rt, > 0, the reactin requires heat t achieve cmpletin. This type f reactins is knwn t be endthermic. 1.5 Chemical Equilibrium The cmplete cmbustin reactins given by Eqs. (1.21) and (1.22) essentially crrespnd t maximum heat release. That is, if prducts ther than CO 2 and H 2O are frmed, the enthalpy f reactin will be decidedly lwer. In practical cmbustin prcesses, a cmbustin reactin can never reach cmpletin. Rather the prducts f cmbustin will acquire the state f chemical equilibrium. Althugh ften than nt the prducts will be dminated by the cmplete cmbustin prducts, incmplete cmbustin prducts (CO, H 2, st, NO etc) are inherent t a cmbustin prcess. Our experience tells us that a prcess r reactin wuld be spntaneus if it releases heat. Fr example, the cmbustin f methane spntaneusly prduces CO 2 and H 2O ( ΔH r,298 <0), but a mixture f CO 2 and H 2O wuld nt spntaneusly react and prduce methane and O 2. On the ther hand, the entrpy f 1 mle f CO 2 is decidedly smaller than the entrpy fr a mixture made f 1 mle f CO and 0.5 mle f O 2. Likewise the entrpy f 1 1-11
Stanfrd University Versin 1.2 mle f H 2O is smaller than the entrpy fr a mixture made f 1 mle f H 2 and 0.5 mle f O 2. Therefre it may be said that reactin (1.21) CH 4 + 2 O 2 + (2 79/21) N 2 CO 2 + 2H 2O + (2 79/21) N 2. (1.21) prduces the largest heat but with a smaller entrpy change, whereas reactin (1.27) prduces less heat but with a larger change f entrpy upn reactin: CH 4 + 2 O 2 + (2 79/21) N 2 CO + 2H 2 + O 2 + (2 79/21) N 2. (1.27) We learned frm the secnd law f thermdynamics that withut heat release r absrptin, a spntaneus prcess will prceed in the directin t increase entrpy. Therefre a cmprmise between enthalpy and entrpy Figure 1.1. releases Variatin must f be the made. enthalpy, entrpy, and Gibbs This cmprmise is respnsible fr functin chemical fr equilibrium. an exthermic It reactin. may be quantified by the Gibbs functin r Gibbs free energy, G(T,P) = H(T) - TS(T,P) G(T,P) H(T) -TS(T,P) 0 Equilibrium 1 100% Reactants 100% Prducts Reactin Prgress, ε G H TS, (1.28a) g h Ts, (1.28b) g h Ts, (1.28c) Figure 1.1 shws a pssible scenari fr variatin f the enthalpy, entrpy times temperature, Gibbs functin fr an exthermic reactin as it prgresses t cmpletin at a given T and P. We define here a reactin prgress variable ε, such that ε = 0 fr pure reactants and ε = 1 fr pure prducts. If the reactin is exthermic, the ttal enthalpy f the reacting gases (reactants and prducts) decreases as ε increases. Here the spntaneus release f chemical energy is driving the reactin twards cmpletin. If the reactin is accmpanied by a decrease in the entrpy (e.g., H 2 + 1/2O 2 H 2O), the TS(T,P) functin wuld mntnically increase as reactin prgresses. This entrpy reductin gives resistance twards the cmpletin f reactin. Overall the Gibbs functin must decrease initially, but because f the rise f the TS term, it eventually will have t g 1-12
Stanfrd University Versin 1.2 up as ε increases. In ther wrds, the Gibbs functin must reach a minimum at sme pint. The definitin f chemical equilibrium is therefre r simply (, ) dg T P dε = 0, (1.29a) dg( T, P ) = 0. (1.29b) Again, the abve equilibrium criterin represents a cmprmise f H and ST, since bth f them prefer t minimize themselves. Therefre, the driving frce f chemical reactin lies in the minimizatin f the Gibbs functin. Nw let us cnsider an arbitrary reactin given by Eq. (1.26). The Gibbs functin f the reacting gas may be written as i i i' i' (, ) = (, ) + (, ) GTP ng TP ng TP, (1.30) react. where n i is the mlar number f the i th species. Putting Eq. (1.30) int (1.29a), we btain, fr cnstant T and P, (, ) Cnservatin f mass requires that prd. dg T P dni dni' = gi ( T, P) + gi' ( T, P) = 0, (1.31) dε dε dε react. prd. 1 dn 1 dn 1 dn 1 = 2 N 1 dn 1 dn 1 dn = = 1' = 2' N... = ' = γ ( ε), (1.32) ν dε ν dε ν dε ν dε ν dε ν dε 1 2 n 1' 2' n' where N and N are the ttal numbers f reactants and prducts, respectively, and γ( ε ) is a functin that depends nly n ε. Cmbining equatins (1.31) and (1.32), we btain γ( ε) νigi ( T, P) + νi' gi' ( T, P ) = 0. (1.33) react. prd. Since γ( ε) 0, we see that equilibrium state is given by i i i' i' ( ) ν ( ) ν g T, P + g T, P = 0. (1.34) react. The functin g i is the Gibbs functin f species i, which may be expressed by prd. 1-13
Stanfrd University Versin 1.2 P gi( T, P) = hf ( T) Tsi ( T) = hf ( T) T si ( T) Ru ln. (1.35) P We nw define a standard Gibbs functin (, = 1 atm) and re-write Eq. (1.35) as g T P as ( ) = ( ) ( ) g T h T Ts T, (1.36) f i Putting Eq. (1.37) int (1.34) and rearranging, we have P gi ( T, P) = g ( T) + RuT ln. (1.37) P P P i νi i νi i u νi νi ln, (1.38) P P i' ' g '( T) g ( T) = R T ' ln prd. react. prd. react. where P i is the partial pressure f species i, and f curse, P = 1 atm. The left-hand side f the abve equatin may be defined as the standard Gibbs functin change f reactin, ( ) ν ( ) ν ( ) ΔG T g T g T (1.39) r i' i' i i prd. react. The right-hand side f Eq. (1.38) may be re-arranged t yield r K p ν i ' i ' prd. Δ Gr ( T) = RuT ln ν i Pi react. ( T) P νi ' Pi ' prd. ΔGr = exp ν i Pi RuT react. ( T). (1.40). (1.41) where K p(t) is the equilibrium cnstant f the reactin. Nte that by neglecting (1.40) and (1.41), we have frced P i t take the unit f atm. P in Eqs. The equilibrium cnstant may als be defined by the cncentratins f the reactants and prducts, 1-14
Stanfrd University Versin 1.2 c ν i' i' P ν i' i' prd. prd. Δν ( ) = ( ) = ( )( ) K T R T K T R T c νi ν u p u i ci Pi react. react. Δν, (1.42) where Δ ν = v v. i' prd. react. There are several imprtant facts abut the equilibrium cnstant. (a) While K p is defined as the pressure rati f the prducts and reactants (Eq. 1.41), this equilibrium cnstant is a functin f temperature nly. i (b) Cnsider the reactin H 2O = H 2 + ½ O 2. (1.43f) The equilibrium cnstant fr the frward directin f the reactin is K p, f P P 12 H2 O2 ( T) = P HO 2. We may als write the reactin in the back directin, H 2 + ½ O 2 = H 2O, (1.43b) and its equilibrium cnstant K P 2 ( T) = HO pb, 12 PH P 2 O2. Obviusly, K p, f ( T) (c) Reactin (43f) may be written alternatively as 1 = K T. pb, ( ) 2H 2O = 2H 2 + O 2, (1.43f ) with its equilibrium cnstant K P P 2 ' p, f 2 PHO 2 H2 O2 ( T) =. 1-15
Stanfrd University Versin 1.2 Cmparing the equilibrium cnstants fr the tw frward reactins, we see that (d) Cnsider the fllwing tw reactins ( ) ( ) ' 2 K T = K T. p, f p, f H 2 = 2 H. H 2O = H + OH (1.44f) (1.45f) (where the dentes that the species is a free radical). We have K p,44 f P P 2 H ( T) = H2 K P P = P H OH and ( ) p,45 f T HO 2. A linear cmbinatin f reactins (43f-45f) yield H 2O = ½ H 2 + OH. (1.46f) A little algebra tells us that (e) While K p is nt a functin f pressure, K c generally is dependent n pressure s lng as Δν 0. On the ther hand, if Δ ν =0, K c(t) = K p(t). (f) The equilibrium cnstant f a given reactin may be determined if the enthalpy f frmatin and the entrpy f reactants and prducts are knwn thrugh Eqs. (1.36), (1.39) and (1.41). (g) The definitin f K p tells us that the reactin wuld be mre cmplete if K p is larger. A larger K p may be accmplished with a larger, negative ΔG r ( T ). Cmbining Eqs. (1.36) and (39), we see that ΔGr ( T) νi' hf, i' ( T) νihf, i ( T) T νi' si' ( T) νisi ( T) prd. react. prd. react., (1.47) where Δ r ( ) ΔH r ( ) S ( ) ( ) ( ) =ΔH T TΔS T r r S T is termed as the entrpy f reactin. Therefre a large, negative T (reactin being highly exthermic) favrs a large K p, whereas a large, psitive Δ r T (reactin creating a large amunt f entrpy) als favrs a large K p r prmtes the cmpletin f the reactin. 1-16
Stanfrd University Versin 1.2 1.6 Adiabatic Flame Temperature With the cncepts f chemical equilibrium understd, we may nw try t calculate the equilibrium cmpsitin f a cmbustin reactin. In ding s, we wish t define the adiabatic flame temperature. Cnsider an adiabatic cmbustin prcess whereby the reactants enters int a cmbustr at temperature T 0, and prducts exit the cmbustr at the adiabatic flame temperature T ad. Since the prcess is adiabatic (Q = 0 ), we have ( ) ( ) Hprd. Tad Hreact. T 0 = 0. (1.48) We nw expand Eq. (1.48) using the ttal enthalpy equatin fr each species (Eq. 1.25b), ν h ν h = ν h ν h + ν h ( T ) h ( 298) ad 0.(1.49) i' T, i' i T, i i' f,298, i' i f,298, i i' ad i ' prd. react. prd. react. prd. ( ) h ( ) ν i h T0 298 = 0 react. Obviusly the first term n the right-hand side f Eq. (1.49) is the standard enthalpy f reactin ΔH r,298. The secnd term determines the sensible heat needed t heat the prducts frm 298 K t the adiabatic flame temperature T ad. T simplify ur analysis, we shall assume that the reactants enter int the reactr at T 0 = 298 K s the third term becmes 0. Rearranging Eq. (1.49), we see that ( ) ( 298) i Δ H = ν h T h. (1.50) r,298 i' ad i ' prd. In ther wrds, the adiabatic flame temperature is btained when all the heat released frm a cmbustin reactin is used t raise the prduct temperature frm 298 t T ad. The existence f chemical equilibrium makes the calculatin f this adiabatic flame temperature a bit mre invlved. Specifically, while the values f ν i are always well defined, is nt since it is dependent n the equilibrium cmpsitin f the prducts. ν ' i Cnsider the cmbustin f 1 mle f carbn (graphite) in 1 mle f xygen at a pressure f 1 atm. 1 mle C(S) + 1 mle O 2 x CO 2 + yco + zo 2. (1.51) The reactant temperature is 298 K. The principle f chemical equilibrium states that the prducts cannt be entirely CO 2. Rather, a small amunt f CO (y mles) must be prduced alng with z mles f O 2 unused. These prducts are in equilibrium at the adiabatic flame temperature amng themselves thrugh 1-17
Stanfrd University Versin 1.2 with its equilibrium cnstant given by CO 2 = CO + ½ O 2, (1.52) 1 2 K p ( T ad ) = P P CO O 2 = yz 1 2 P P CO2 x x + y + z 1 2 0 = exp( ΔG r R u T ad ). (1.53) (We need t recgnize that the prducts f a cmbustin prcess cannt be in equilibrium with the reactants f the prcess. Rather it is the prducts that are in equilibrium amng themselves.) Since there are fur unknwns in Eq. (1.53) (i.e., x, y, z and T ad), we need t prvide three mre equatins t slve this prblem. Tw f these equatins cme frm mass cnservatin: Carbn: x+ y =1 ml, (1.54) Oxygen: 2x+ y+ 2z = 2 ml. (1.55) The last equatin is given by Eq. (1.50), which may be expanded t give ( CO ) ( CO) ( ) ( 298) xh + f yh f = x h Tad h,298 2,298 CO2 ( ) ( 298) ( ) ( 298) + y h Tad h + z h Tad h CO O2.(1.56) Clearly the cupled Eqs (1.53-1.56) cannt be slved analytically. We shall defer t sectin 1.8 and use Excel t slve the equatin. Any mre realistic cmbustin equilibrium prblems will have t be slved numerically by a cmputer a tpic we will discuss als in sectin 1.8. Figure 1.2 shws the variatin f the adiabatic flame temperature as a functin f equivalence rati fr the cmbustin f methane, prpane, ethylene and benzene in air at 1 atm pressure. As expected, the flame temperature peaks at an equivalence rati arund unity, slightly n the fuel rich side. The decrease f T ad twards smaller φ is caused by dilutin f unused xygen as well as the greater amunt f nitrgen brught int the cmbustr with xygen. The decrease f the flame temperature twards larger φ is because f xygen deficiency, which des nt allw the fuel t be fully xidized. Figure 1.3 shws the effect f pressure n the adiabatic flame temperature. It is seen that as pressure increases, (a) the adiabatic flame temperature becmes higher and (b) the peak shifts twards φ = 1. Here it may be nted that the pressure serves t reduce the extent f dissciatin f CO 2 and H 2O, and in ding s, frce the reactin twards better cmpletin. T explain the variatin f Tad as a functin f pressure, we plt in Figure 1.4 the equilibrium cmpsitin at φ = 1. It is seen that as pressure decreases, the extent f CO 2 and H 2O dissciatin int H 2, O 2, CO, and even highly unstable free radical species, including H, O, and OH becmes mre and mre significant. 1-18
Stanfrd University Versin 1.2 2500 Adiabatic Flame Temperature, T ad (K) 2000 1500 Figure 1.3. Adiabatic Figure flame temperature f Figure 1.4. prpane 1.2. Mle cmbustin Adiabatic fractins in flame f air equilibrium temperature prducts cmputed fr at several pressures. f methane, prpane prpane, cmbustin ethylene in and air (φ=1). benzene at 1 atm pressure. ethylene benzene prpane methane 1000 0.0 0.5 1.0 1.5 2.0 2.5 3.0 Equivalence Rati, φ Adiabatic Flame Temperature, T ad (K) 100 atm 10 atm 2300 1 atm 2200 0.1 atm 2100 0.85 0.90 0.95 1.00 1.05 1.10 1.15 1.20 Equivalence Rati, φ H 2 O 10-1 CO 2 Mle Fractin 10-2 10-3 CO O 2 H 2 H OH O 10-4 10-5 0.1 1 10 100 Pressure, P (atm) 1-19
Stanfrd University Versin 1.2 1.7 Tabulatin and Mathematical Parameterizatin f Thermchemical Prperties Key thermdynamic r thermchemical prperties discussed s far include the cnstantpressure specific heat, sensible enthalpy, enthalpy f frmatin, and entrpy under the standard cnditin. It is imprtant t recgnize that under the ideal gas cnditin, c p is nt a functin f pressure, but it is a functin f temperature. A cmmn methd is t tabulate, amng thers, ( ) p c T, s ( T ), h(t) h(298) and h ( ) f T as a functin f temperature. Such table is knwn as the JANAF table. 1 Appendix 1.A gives a truncated versin f these tables fr species listed in Table 1.2. In research publicatins, these tables are usually cndensed t smething that lks like Table 1.3. Table 1.3. Thermchemical prperties f selected species in the vapr state. h f ( 298K) s ( 298K) cp ( ) T (J/ml-K) Species (kj/ml) (J/ml-K) 298 500 1000 1500 2000 2500 C(S) 0 5.730 8.523 14.596 21.624 23.857 25.167 25.976 H 2 0 130.663 28.834 29.297 30.163 32.358 34.194 35.737 O 2 0 205.127 29.377 31.082 34.881 36.505 37.855 38.999 H 2O -241.8 188.810 33.587 35.214 41.294 47.333 51.678 54.731 CO -110.5 197.640 29.140 29.811 33.163 35.132 36.288 36.917 CO 2-393.5 213.766 37.128 44.628 54.322 58.222 60.462 61.640 CH 4-74.6 186.351 35.685 46.494 73.616 90.413 100.435 106.864 C 2H 6-83.9 229.051 52.376 77.837 122.540 144.761 158.280 165.774 C 3H 8-103.8 270.141 73.530 112.409 174.614 204.334 222.359 232.305 C 4H 10-125.8 309.686 98.571 148.552 227.379 264.424 286.823 299.106 C 8H 18-208.7 466.772 187.486 286.282 431.399 494.910 534.404 557.447 C 2H 4 52.3 219.156 42.783 62.321 93.860 109.190 118.563 123.799 C 2H 2 227.4 200.892 43.989 54.715 67.908 75.906 81.045 84.262 CH 3OH -200.9 239.785 44.030 59.526 89.656 105.425 113.891 118.560 C 6H 6 82.8 269.020 82.077 138.240 210.948 240.242 257.667 267.023 H 218.0 114.706 20.786 20.786 20.786 20.786 20.786 20.786 O 249.2 161.047 21.912 21.247 20.924 20.846 20.826 20.853 OH 39.3 183.722 29.887 29.483 30.694 32.948 34.755 36.077 The thermchemical data f a large number f species has been cmpiled by the Natinal Institute f Standards and Technlgy. These data may be fund at http://webbk.nist.gv/chemistry/. Anther web-based surce f data is the Active Tables (ATcT): https://cmcs.ca.sandia.gv/cmcs/prtal/user/ann/js_pane. 1 Chase, M. W., Jr., J. Phys. Chem. Ref. Data, 4 th Editin, Mn. 9, Suppl. 1 (1998a). 1-20
Stanfrd University Versin 1.2 Fr cmbustin calculatins, a very gd surce f thermchemical data is: Alexander Burcat and Brank Ruscic Third Millennium Thermdynamic Database fr Cmbustin and Air-Pllutin Use, 2005 (http://www.technin.ac.il/~aer0201/ r http://garfield.chem.elte.hu/burcat/burcat.html). The database is the result f extensive wrk by Prfessr Alexander Burcat f Technin University, Israel ver the last 20 years. In this database, the thermchemical data are expressed in the frm f plynmial functin and are thus mre cmpact than the JANAF table. A typical recrd f thermchemical data may lk like the fllwing: Species name Reference surce Cmpsitin T Lw, T high, T mid Phase CO2 L 7/88C 1O 2 0 0G 200.000 6000.000 1000. 1 0.46365111E+01 0.27414569E-02-0.99589759E-06 0.16038666E-09-0.91619857E-14 2-0.49024904E+05-0.19348955E+01 0.23568130E+01 0.89841299E-02-0.71220632E-05 3 0.24573008E-08-0.14288548E-12-0.48371971E+05 0.99009035E+01-0.47328105E+05 4 a i (i = 1,7) fr T mid < T < T high a i (i = 1,7) fr T lw < T < T mid The plynmial fits are made fr tw separate temperature ranges (T lw T T mid and T mid T T high). There are 7 plynmial cefficients, a i (i,=1,..7), fr each temperature range. The thermchemical data are calculated frm these fits as c R = a + a T + a T 2 + a T 3 + a T 4, (1.57) p u 1 2 3 4 5 s R = a lnt + a T + a T 2 2 + a T 3 3+ a T 4 4 + a. (1.58) u 1 2 3 4 5 7 2 3 4 5 1 2 2 3 3 4 4 5 5 6 h R = at + a T + a T + a T + a T + a (1.59) T u where h T is the ttal enthalpy (Eq. 1.25b), s is the standard entrpy (1 atm). Nte that these equatins are in strict agreement with knwn relatinships amng the thermchemical prperties, i.e., T ht ( T) = cpdt + h f,298.15, 298.15 (1.60) T s ( T) = cpd lnt + s ( 298.15). 298.15 (1.61) T calculate and tabulate the thermchemical data prperties in the JANAF type frm, c p and s are directly calculated with Eqs. (1.57) and (1.58). The sensible enthalpy is determined as ( ) ( 298.15) = ( ) ( 298.15) h T h h T h, (1.62) where h T is calculated using Eq. (1.59). Fr enthalpy f frmatin, we use T ( ) = ( ) ν ( ) f T i T, i elements T h T h T h T (1.63) 1-21
Stanfrd University Versin 1.2 where ν i represents the mlecular cmpsitin f the substance. Fr example, a C xh yo z species has ν C = x, ν H = y 2 and ν O = z. 2 2 2 An EXCEL spreadsheet has been prepared fr the JANAF like tabulatin. The file may be dwnladed frm the curse web site http://melchir.usc.edu/public/ame579/week_2/nasa_ply t JANAF.xls. Burcat s database may als be dwnladed in text frm http://melchir.usc.edu/public/ame579/week_2/burcat Therm.txt, and in Excel frm http://melchir.usc.edu/public/ame579/week_2/burcat Therm.xls. 1.8 Slutin f an Equilibrium and Adiabatic Flame Temperature Prblem We shall nw return t the prblem f carbn (graphite) xidatin in sectin 1.6. We wish t calculate the adiabatic flame temperature fr cmbustin f 1 mle f carbn (graphite) in 1 mle f xygen at a pressure f 1 atm. The initial temperature is 298 K. The fur equatins are x + y = 1 2x + y+ 2z = 2 12 12 yz P 0 = exp( ΔGr RuTd) x x + y+ z ( ) + xh f CO yh f ( CO) = x h ( Tad) h ( 298) + y h ( Tad ) h ( 298) + z h ( T ) ( 298) CO ad h O2,298 2,298 CO2 Slutin f the abve prblem is prvided in an Excel sheet dwnladable frm http://melchir.usc.edu/public/ame579/week_2/carbn xidatin.xls. Nte that t run the Excel slver requires the user t dwnlad the thermchemical prperty tables frm http://melchir.usc.edu/public/ame579/week_2/nasa_ply t JANAF.xls. This file shuld be placed in the same directry as the carbn xidatin.xls file. The slutin f this set f nnlinear algebraic equatins gives x = 0.233 ml y = 0.767 ml z = 0.384 ml Tad = 3537 K. 1-22
Stanfrd University Versin 1.2 Nw suppse that the carbn is burned in air, instead f pure xygen, the set f nnlinear algebraic equatins may be revised by including the mlar number f N 2 (=1 mle O 2 79/21) and the sensible enthalpy required t heat up the nitrgen, x + y = 1 2x + y+ 2z = 2 12 12 yz P 0 = exp( ΔGr RuTd) x x + y+ z + 79 21 ( ) + xh f,298 CO2 yh f,298 ( CO) = x h ( Ta d ) h ( 298) CO2 + y h ( Tad ) h ( 298) + z h ( T ) ( 298) + 79 21 ( ) ( 298) CO ad h h T O ad h The slutin is x = 0.893 ml y = 0.107 ml z = 0.053 ml Tad = 2312 K 2 N2 Cmparing the tw sets f slutin, we find that (a) the adiabatic flame temperature is ntably lwer when air is used, and (b) the reactin is less cmplete when pure xygen is used because the higher adiabatic flame temperature frces a greater extent f CO 2 dissciatin int CO and O 2.. Tw cmmnly used equilibrium slvers are Stanjan (r the equilibrium slver EQUIL - f the ChemKin suite f package) and the NASA Equilibrium cde (cec86). We will use the equilibrium slver f the ChemKin suite f package fr the current class. Instructins abut the cmputer cde can be fund n p. 30. 1-23
Stanfrd University Versin 1.2 Appendix A1. Truncated JANAF tables Graphite (C(S)) T cp ( T ) s ( T ) h(t)-h(298) hf ( T ) g f ( T ) (K) (J/ml-K) (J/ml-K) (kj/ml) (kj/ml) (kj/ml) 298 8.523 5.730 0.000 0.000 0.000 300 8.592 5.787 0.017 0.000 0.000 400 11.832 8.713 1.042 0.000 0.000 500 14.596 11.659 2.368 0.000 0.000 600 16.836 14.526 3.944 0.000 0.000 700 18.559 17.257 5.717 0.000 0.000 800 19.835 19.823 7.640 0.000 0.000 900 20.794 22.217 9.674 0.000 0.000 1000 21.624 24.451 11.795 0.000 0.000 1100 22.169 26.538 13.985 0.000 0.000 1200 22.660 28.489 16.227 0.000 0.000 1300 23.102 30.320 18.515 0.000 0.000 1400 23.499 32.047 20.846 0.000 0.000 1500 23.857 33.681 23.214 0.000 0.000 1600 24.177 35.231 25.616 0.000 0.000 1700 24.465 36.705 28.048 0.000 0.000 1800 24.724 38.111 30.508 0.000 0.000 1900 24.957 39.454 32.992 0.000 0.000 2000 25.167 40.740 35.498 0.000 0.000 2100 25.358 41.972 38.025 0.000 0.000 2200 25.531 43.156 40.569 0.000 0.000 2300 25.691 44.295 43.131 0.000 0.000 2400 25.838 45.391 45.707 0.000 0.000 2500 25.976 46.449 48.298 0.000 0.000 1-24
Stanfrd University Versin 1.2 Hydrgen (H2) T cp ( T ) s ( T ) h(t)-h(298) hf ( T ) g f ( T ) (K) (J/ml-K) (J/ml-K) (kj/ml) (kj/ml) (kj/ml) 298 28.834 130.663 0.000 0.000 0.000 300 28.850 130.856 0.058 0.000 0.000 400 29.277 139.229 2.969 0.000 0.000 500 29.297 145.768 5.900 0.000 0.000 600 29.254 151.105 8.827 0.000 0.000 700 29.344 155.619 11.755 0.000 0.000 800 29.615 159.553 14.702 0.000 0.000 900 29.970 163.062 17.681 0.000 0.000 1000 30.163 166.232 20.690 0.000 0.000 1100 30.634 169.130 23.730 0.000 0.000 1200 31.089 171.815 26.817 0.000 0.000 1300 31.527 174.320 29.948 0.000 0.000 1400 31.950 176.672 33.122 0.000 0.000 1500 32.358 178.891 36.337 0.000 0.000 1600 32.752 180.992 39.593 0.000 0.000 1700 33.132 182.989 42.887 0.000 0.000 1800 33.499 184.893 46.219 0.000 0.000 1900 33.853 186.714 49.586 0.000 0.000 2000 34.194 188.459 52.989 0.000 0.000 2100 34.525 190.135 56.425 0.000 0.000 2200 34.843 191.749 59.893 0.000 0.000 2300 35.151 193.305 63.393 0.000 0.000 2400 35.449 194.807 66.923 0.000 0.000 2500 35.737 196.260 70.483 0.000 0.000 1-25
Stanfrd University Versin 1.2 Oxygen (O2) T cp ( T ) s ( T ) h(t)-h(298) hf ( T ) g f ( T ) (K) (J/ml-K) (J/ml-K) (kj/ml) (kj/ml) (kj/ml) 298 29.377 205.127 0.000 0.000 0.000 300 29.387 205.323 0.059 0.000 0.000 400 30.120 213.870 3.031 0.000 0.000 500 31.082 220.692 6.090 0.000 0.000 600 32.080 226.448 9.249 0.000 0.000 700 32.990 231.463 12.503 0.000 0.000 800 33.747 235.919 15.842 0.000 0.000 900 34.355 239.930 19.248 0.000 0.000 1000 34.881 243.578 22.710 0.000 0.000 1100 35.232 246.919 26.216 0.000 0.000 1200 35.569 249.999 29.756 0.000 0.000 1300 35.893 252.859 33.329 0.000 0.000 1400 36.205 255.530 36.934 0.000 0.000 1500 36.505 258.038 40.569 0.000 0.000 1600 36.795 260.404 44.234 0.000 0.000 1700 37.074 262.643 47.928 0.000 0.000 1800 37.343 264.769 51.649 0.000 0.000 1900 37.604 266.795 55.396 0.000 0.000 2000 37.855 268.731 59.169 0.000 0.000 2100 38.098 270.584 62.967 0.000 0.000 2200 38.334 272.361 66.789 0.000 0.000 2300 38.562 274.070 70.634 0.000 0.000 2400 38.784 275.716 74.501 0.000 0.000 2500 38.999 277.304 78.390 0.000 0.000 1-26
Stanfrd University Versin 1.2 Water vapr (H2O(v)) T cp ( T ) s ( T ) h(t)-h(298) hf ( T ) g f ( T ) (K) (J/ml-K) (J/ml-K) (kj/ml) (kj/ml) (kj/ml) 298 33.587 188.810 0.000-241.821-228.585 300 33.596 189.034 0.067-241.841-228.496 400 34.268 198.783 3.458-242.849-223.896 500 35.214 206.527 6.930-243.836-219.043 600 36.320 213.044 10.506-244.767-213.996 700 37.508 218.731 14.197-245.632-208.798 800 38.733 223.819 18.008-246.435-203.481 900 39.986 228.453 21.944-247.182-198.066 1000 41.294 232.733 26.007-247.859-192.571 1100 42.659 236.734 30.206-248.454-187.013 1200 43.941 240.501 34.536-248.979-181.404 1300 45.145 244.066 38.991-249.442-175.753 1400 46.275 247.454 43.563-249.847-170.070 1500 47.333 250.683 48.244-250.199-164.359 1600 48.324 253.770 53.027-250.504-158.626 1700 49.251 256.727 57.907-250.766-152.875 1800 50.117 259.567 62.876-250.989-147.110 1900 50.925 262.299 67.928-251.178-141.334 2000 51.678 264.930 73.059-251.336-135.548 2100 52.380 267.469 78.262-251.468-129.756 2200 53.034 269.921 83.533-251.576-123.957 2300 53.641 272.292 88.867-251.664-118.154 2400 54.206 274.587 94.260-251.735-112.348 2500 54.731 276.811 99.707-251.792-106.539 1-27
Stanfrd University Versin 1.2 Carbn mnxide (CO) T cp ( T ) s ( T ) h(t)-h(298) hf ( T ) g f ( T ) (K) (J/ml-K) (J/ml-K) (kj/ml) (kj/ml) (kj/ml) 298 29.140 197.640 0.000-110.529-137.155 300 29.143 197.835 0.058-110.518-137.334 400 29.375 206.246 2.982-110.105-146.344 500 29.811 212.844 5.940-110.002-155.421 600 30.415 218.330 8.950-110.147-164.495 700 31.133 223.071 12.027-110.472-173.529 800 31.894 227.278 15.178-110.912-182.509 900 32.606 231.077 18.404-111.423-191.428 1000 33.163 234.543 21.694-111.985-200.288 1100 33.637 237.726 25.035-112.588-209.089 1200 34.069 240.672 28.420-113.214-217.835 1300 34.460 243.414 31.847-113.862-226.527 1400 34.813 245.981 35.311-114.531-235.168 1500 35.132 248.394 38.808-115.220-243.761 1600 35.418 250.671 42.336-115.926-252.308 1700 35.674 252.826 45.891-116.651-260.810 1800 35.903 254.872 49.470-117.392-269.268 1900 36.107 256.818 53.071-118.149-277.685 2000 36.288 258.675 56.691-118.922-286.062 2100 36.447 260.449 60.327-119.710-294.400 2200 36.589 262.148 63.979-120.514-302.699 2300 36.713 263.778 67.645-121.332-310.962 2400 36.822 265.342 71.321-122.166-319.189 2500 36.917 266.848 75.009-123.014-327.381 1-28
Stanfrd University Versin 1.2 Carbn dixide (CO2) T cp ( T ) s ( T ) h(t)-h(298) hf ( T ) g f ( T ) (K) (J/ml-K) (J/ml-K) (kj/ml) (kj/ml) (kj/ml) 298 37.128 213.766 0.000-393.505-394.372 300 37.218 214.015 0.074-393.506-394.377 400 41.286 225.297 4.006-393.572-394.658 500 44.628 234.881 8.307-393.655-394.920 600 47.359 243.268 12.911-393.786-395.162 700 49.589 250.741 17.762-393.963-395.378 800 51.425 257.487 22.816-394.171-395.566 900 52.970 263.635 28.038-394.389-395.727 1000 54.322 269.288 33.404-394.606-395.865 1100 55.268 274.510 38.884-394.821-395.980 1200 56.124 279.356 44.454-395.033-396.076 1300 56.899 283.880 50.106-395.243-396.154 1400 57.596 288.122 55.831-395.453-396.217 1500 58.222 292.118 61.623-395.665-396.264 1600 58.782 295.894 67.473-395.882-396.297 1700 59.281 299.473 73.377-396.104-396.316 1800 59.724 302.874 79.328-396.334-396.322 1900 60.116 306.114 85.320-396.573-396.314 2000 60.462 309.206 91.349-396.823-396.294 2100 60.765 312.164 97.411-397.086-396.262 2200 61.031 314.997 103.501-397.362-396.216 2300 61.263 317.715 109.616-397.653-396.157 2400 61.464 320.326 115.753-397.960-396.086 2500 61.640 322.839 121.908-398.285-396.001 1-29
Stanfrd University Versin 1.2 Methane (CH4) T cp ( T ) s ( T ) h(t)-h(298) hf ( T ) g f ( T ) (K) (J/ml-K) (J/ml-K) (kj/ml) (kj/ml) (kj/ml) 298 35.685 186.351 0.000-74.594-50.544 300 35.760 186.590 0.071-74.655-50.383 400 40.530 197.488 3.871-77.704-41.830 500 46.494 207.161 8.217-80.544-32.527 600 52.730 216.190 13.179-83.013-22.685 700 58.650 224.769 18.752-85.070-12.462 800 63.998 232.957 24.889-86.749-1.970 900 68.850 240.778 31.535-88.096 8.711 1000 73.616 248.277 38.656-89.114 19.525 1100 77.713 255.489 46.226-89.814 30.425 1200 81.404 262.412 54.185-90.269 41.378 1300 84.728 269.061 62.495-90.510 52.360 1400 87.720 275.452 71.120-90.564 63.353 1500 90.413 281.597 80.029-90.454 74.344 1600 92.839 287.511 89.194-90.202 85.323 1700 95.028 293.206 98.589-89.828 96.282 1800 97.007 298.695 108.192-89.348 107.217 1900 98.802 303.989 117.984-88.775 118.122 2000 100.435 309.099 127.947-88.124 128.994 2100 101.929 314.036 138.066-87.403 139.833 2200 103.302 318.809 148.329-86.622 150.635 2300 104.573 323.430 158.724-85.788 161.401 2400 105.756 327.906 169.241-84.908 172.130 2500 106.864 332.246 179.872-83.986 182.821 1-30
Stanfrd University Versin 1.2 Ethane (C2H6) T cp ( T ) s ( T ) h(t)-h(298) hf ( T ) g f ( T ) (K) (J/ml-K) (J/ml-K) (kj/ml) (kj/ml) (kj/ml) 298 52.376 229.051 0.000-83.854-31.884 300 52.642 229.402 0.105-83.956-31.534 400 65.627 246.340 6.024-88.822-13.313 500 77.837 262.313 13.205-93.084 6.072 600 89.040 277.511 21.558-96.664 26.250 700 99.101 292.007 30.974-99.580 46.975 800 107.983 305.833 41.338-101.902 68.077 900 115.743 319.010 52.533-103.711 89.438 1000 122.540 331.564 64.455-105.061 110.975 1100 127.823 343.495 76.977-106.039 132.629 1200 132.662 354.827 90.005-106.753 154.359 1300 137.081 365.623 103.495-107.232 176.139 1400 141.106 375.932 117.408-107.503 197.949 1500 144.761 385.794 131.704-107.589 219.771 1600 148.069 395.244 146.348-107.516 241.593 1700 151.053 404.311 161.307-107.305 263.407 1800 153.735 413.023 176.549-106.978 285.204 1900 156.138 421.400 192.045-106.553 306.981 2000 158.280 429.465 207.768-106.050 328.733 2100 160.183 437.234 223.693-105.486 350.459 2200 161.866 444.725 239.797-104.877 372.156 2300 163.347 451.954 256.059-104.236 393.825 2400 164.644 458.934 272.460-103.579 415.466 2500 165.774 465.679 288.982-102.916 437.079 1-31
Stanfrd University Versin 1.2 Prpane (C3H8) T cp ( T ) s ( T ) h(t)-h(298) hf ( T ) g f ( T ) (K) (J/ml-K) (J/ml-K) (kj/ml) (kj/ml) (kj/ml) 298 73.530 270.141 0.000-103.842-23.472 300 73.949 270.634 0.147-103.977-22.932 400 94.097 294.707 8.564-110.281 5.058 500 112.409 317.709 18.906-115.638 34.533 600 128.644 339.671 30.976-120.004 64.993 700 142.749 360.587 44.563-123.452 96.111 800 154.863 380.460 59.459-126.111 127.667 900 165.312 399.318 75.480-128.108 159.515 1000 174.614 417.224 92.483-129.506 191.554 1100 181.688 434.203 110.303-130.416 223.707 1200 188.162 450.294 128.801-130.989 255.927 1300 194.072 465.592 147.917-131.262 288.184 1400 199.452 480.174 167.598-131.268 320.450 1500 204.334 494.104 187.791-131.042 352.709 1600 208.751 507.435 208.449-130.612 384.947 1700 212.732 520.212 229.527-130.009 417.151 1800 216.308 532.475 250.982-129.259 449.316 1900 219.508 544.257 272.776-128.389 481.436 2000 222.359 555.590 294.872-127.422 513.507 2100 224.889 566.502 317.237-126.380 545.529 2200 227.124 577.016 339.840-125.285 577.499 2300 229.090 587.157 362.653-124.155 609.418 2400 230.809 596.944 385.649-123.008 641.288 2500 232.305 606.397 408.807-121.861 673.110 1-32