VoLPs: V order Logarithmic Polynomials

A new set of mathematical functions, that is able to describe gases’ thermodynamic properties, has been developed. These functions have the form of a fifth order logarithmic polynomial (VoLP). They could be utilized for combustion processes, with “frozen composition” and “composition in equilibrium” evaluation. The VoLPs present several advantages: they are able to cover a wide range of temperatures with only a single mathematical function; they have an elevate accuracy and they present the possibility to extrapolate experimental data beyond the experimental temperature range. The VoLP coefficients have been evaluated through the least squares fit on the basis of experimental measurements (taken from scientific literature). The set of VoLPs gives the possibility to study the combustion phenomena and allows to describe specific heat at constant pressure, enthalpy, entropy and equilibrium constants for gases dissociation.

Specific heat at constant pressure:

[J/(mol K)]

Enthalpy:

[J/mol]

Entropy:

[J/(mol K)]

Gibbs function:

[J/mol]

Equilibrium constant (K_p) of a thermo-chemical dissociation reaction:

[-]

(with the convention that n_i is negative for the dissociation reaction reactant species)

Example: for the dissociation

coefficients

Species	a₅	a₄	a₃	a₂	a₁	a₀
O₂	0.06180721	-1.91808230	23.18329753	-135.04796311	377.22447890	-373.49246047
O	0.07027490	-2.31335083	30.19191662	-194.76523964	618.57117075	-748.19500164
N₂	0.21448719	-7.30576818	97.95623827	-645.21170218	2087.25937009	-2624.96917520
N	0.14239267	-4.53379847	57.24529880	-358.12331558	1109.54271743	-1340.57218387
H₂	-0.1571988	5.07583945	-64.62974617	406.63764375	-1265.40995607	1586.40614067
H	0.00000000	0.00000000	0.00000000	0.00000000	0.00000000	20.78600000
Ar	0.00000000	0.00000000	0.00000000	0.00000000	0.00000000	20.78600000
H₂O	0.14904476	-5.60452380	81.54220310	-573.43988184	1954.64102748	-2558.72544088
OH	0.03478011	-1.49678745	23.95819609	-180.33447646	643.43907081	-844.81094064
CO₂	0.09995132	-2.84698619	29.97175824	-139.36548820	262.46393332	-77.60476812
CO	0.22518502	-7.60385762	101.08195929	-660.23411744	2118.61214474	-2644.11606414
NO	0.22148616	-7.36223109	96.15006747	-615.33775005	1927.66396650	-2333.02836259
NO₂	0.19152294	-5.86302804	69.10109523	-388.90870179	1041.04770615	-1021.47920094

Table 1: a_i coefficients for (T) logarithmic polynomial (=[J/(mol K)]). T range 100-5000 K

Species	b₆	[J/mol]	c₀	[J/(mol K)]
CO	7800.122163	-110530	2599.24460	197.54
CO₂	-9799.444922	-393520	-272.97823	213.69
H₂O	6509.129599	-241830	2604.14357	188.72
H₂	-17906.36645	0	-1741.84295	130.57
OH	-3897.017179	38990	774.89000	183.6
O₂	-6650.197901	0	174.43449	205.04
O	-2214.908597	249170	653.63407	160.95
H	-6197.3459	218000	-118.43025	114.61
N₂	7785.831947	0	2599.39565	191.5
NO	4728.18155	90290	2188.40197	210.65
N	2102.605182	472690	1259.03834	153.19
Ar	-6197.3459	0	-118.43025	154.74
NO₂	-5094.0761401	33100	643.35865	239.92

Table 2 : Constants of integration, enthalpy of formation and entropy at standard temperature and pressure (T₀=298.15 K; p₀=101325 Pa).

b_i coefficients

For with if .

c_i coefficients

For

g_i coefficients

For ; ; ; .

FUELS

where Tr=T/Tc, and Tc is the critical temperature.

Gases	a₅	a₄	a₃	a₂	a₁	a₀	Tc [K]
CH₄	1.113859542417	-8.126750445589	15.025961612383	8.352335756601	-2.404135926621	33.795315991848	190.6
H₂	-0.550917399284	8.017500998798	-44.303786812909	116.180997229773	-142.745181228842	92.723369415269	33.18
C₂H₂	-0.685785450427	2.518552060825	-2.583752519696	-0.393383689077	21.146593031886	44.657822823590	308.3
C₂H₆	1.457419131544	-6.417868237502	-2.216122356576	26.864672365436	37.425406759034	53.402669829242	305.3
C₂H₄	0.869739220990	-3.711682191020	-2.638789345297	19.484575858130	26.129392212759	41.822396850196	282.5
C₃H₆ Propylene	1.428847247677	-4.532044443762	-7.920453792757	22.974005052290	56.985504816355	75.100379950903	365.2
C₄H₈ Isobutene	1.865344616292	-5.062391642773	-12.213362041771	24.386936189875	84.426210096985	113.383421571580	417.9
C₆H₆ Benzene	1.635491384823	1.874523186055	-19.525673274541	-4.962242141294	112.384804738456	151.973495753845	562
C₂H₅OH Ethanol	1.406449620188	-1.706745625638	-12.273943910039	10.791673475246	66.913660398690	97.301090949513	514
C₂H₆O Dimethyl Ether	1.741753260725	-5.279712512663	-7.892002067064	22.526711137421	52.198156726227	78.806477323085	401
CH₃OH Methanol	1.252049265734	-2.354757843251	-8.560257334851	12.844477210231	39.101511197012	60.606728470937	513

C₃H₈ Propane	2.574463389529	-6.108276774152	-11.646243309120	29.352775907335	72.860102727303	88.057699295447	369.8
C₄H₁₀ n-Butane	4.081926973040	-6.014749912413	-20.404917243700	30.695600769273	103.165833594102	130.809320121216	425
C₄H₁₀ Isobutane	4.172373106751	-6.102997248632	-20.254921490994	29.874057392009	105.058301457939	126.391862206308	407.7
C₆H₁₂ Cyclohexane	8.663061219494	0.424827359963	-50.753681958148	10.233541509341	190.647385669939	208.068597432136	554
C₈H₁₀ Ethylbenzene	7.423756470282	9.296388299484	-35.063301754915	-14.498955815686	165.102631065286	241.097002083027	617
(CH₃)₂CO Acetone	2.558004187811	-2.112206476350	-16.494167681729	14.714491484398	75.903738746707	109.164509352917	508

C₇H₈ Toluene	0.232332728211	5.800974440390	-22.456596375320	-9.356103392090	138.096042867477	194.430789869627	593
C₅H₁₂ n-Pentane	5.971767165123	-2.893108938525	-32.331240603903	29.518376457842	137.781247187080	173.788694897066	469.7
C₇H₁₆ n-Heptane	8.272402992493	6.627828947469	-45.597895797777	10.611329615533	194.117084022317	266.863703069824	540
C₈H₁₈ n-Octane	6.514781099349	9.573211425471	-47.927505630343	0.866570314137	219.241682396858	314.987178863040	568.9
C₈H₁₈ (2,2,4-Trimethyl pentane)	4.975658204206	-1.101165006849	-32.943169193235	22.340443163095	231.245787291135	312.674401159893	543.9
C6H14 n-Hexane	13.127616255887	5.119027362386	-45.935938792348	11.854919521635	170.525103989822	231.325598244493	507.6

Table 3: a_i coefficients for (T) logarithmic polynomial (=[J/(mol K)];
T range 200-3000 K).

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