The CRC Handbook of Mechanical Engineering. Chapter 2. Engineering Thermodynamics (776125), страница 13
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This checks the accuracy of both the given productanalysis and the calculations conducted to determine the unknown coefficients. Exact closurecannot be expected with measured data, however. On a molar basis, the air-fuel ratio isAF =23.1(4.76)lbmol(air )= 10.7810.2lbmol(fuel)On a mass basislb(air )28.97 = 19.47AF = (10.78) 16.04 lb(fuel)(b) The balanced chemical equation for the complete combustion of methane with the theoreticalamount of air isCH 4 + 2(O 2 + 3.76 N 2 ) → CO 2 + 2H 2 O + 7.52N 2The theoretical air-fuel ratio on a molar basis is(AF)© 1999 by CRC Press LLCtheo=2(4.76)lbmol(air )= 9.521lbmol(fuel)2-60Section 2The percent theoretical air is then% theoretical air =(AF)(AF)theo=10.78= 1.13(113%)9.52(c) Equivalence ratio = ( FA)/( FA) theo = 9.52/10.78 = 0.88.
The reactants form a lean mixture.(d) To determine the dew point temperature requires the partial pressure pv of the water vapor. Themole fraction of the water vapor isyv =20.4= 0.169100 + 20.4Since p = 1 atm, pv = 0.169 atm = 2.48 lbf/in.2. With psat = 2.48 lbf/in.2, the correspondingsaturation temperature from the steam tables is 134°F. This is the dew point temperature.Property Data for Reactive SystemsTables of thermodynamic properties such as the steam tables provide values for the specific enthalpyand entropy relative to some arbitrary datum state where the enthalpy (or alternatively the internal energy)and entropy are set to zero.
When a chemical reaction occurs, however, reactants disappear and productsare formed, and it is generally no longer possible to evaluate ∆h and ∆s so that these arbitrary datumscancel. Accordingly, special means are required to assign specific enthalpy and entropy for applicationto reacting systems.Property data suited for the analysis of reactive systems are available from several sources. Theencyclopedic JANAF Thermochemical Tables is commonly used. Data for a wide range of substancesare retrievable from Knacke et al.
(1991), which provides both tabular data and analytical expressionsreadily programmable for use with personal computers of the specific heat, enthalpy, entropy, and Gibbsfunction. Textbooks on engineering thermodynamics also provide selected data, as, for example, Moranand Shapiro (1995).Enthalpy of FormationAn enthalpy datum for reacting systems can be established by assigning arbitrarily a value of zero tothe enthalpy of the stable elements at a standard reference state where the temperature is Tref = 298.15K (25°C) and the pressure is pref , which may be 1 bar or 1 atm depending on the data source.
The termstable simply means that the particular element is chemically stable. For example, at the standard statethe stable forms of hydrogen, oxygen, and nitrogen are H2, O2, and N2 and not the monatomic H, O, and N.The molar enthalpy of a compound at the standard state equals its enthalpy of formation, symbolizedohere by h f .
The enthalpy of formation is the energy released or absorbed when the compound is formedfrom its elements, the compound and elements all being at Tref and pref . The enthalpy of formation maybe determined by application of procedures from statistical thermodynamics using observed spectroscopic data. The enthalpy of formation also can be found in principle by measuring the heat transfer ina reaction in which the compound is formed from the elements. In this chapter, the superscript ° is usedto denote pref . For the case of the enthalpy of formation, the reference temperature Tref is also intendedby this symbol. Table 2.9 gives the values of the enthalpy of formation of various substances at 298 Kand 1 atm.The molar enthalpy of a substance at a state other than the standard state is found by adding the molarenthalpy change ∆h between the standard state and the state of interest to the molar enthalpy offormation:© 1999 by CRC Press LLC2-61Engineering ThermodynamicsTABLE 2.9 Enthalpy of Formation, Gibbs Function ofFormation, and Absolute Entropy of Various Substances at 298K and 1 atmoh f and g of (kJ/kmol), s o (kJ/kmol•K)SubstanceCarbonHydrogenNitrogenOxygenCarbon monoxideCarbon dioxideWaterHydrogen peroxideAmmoniaOxygenHydrogenNitrogenHydroxylMethaneAcetyleneEthyleneEthanePropylenePropaneButanePentaneOctaneBenzeneMethyl alcoholEthyl alcoholoFormulahfg ofsoC(s)H2(g)N2(g)O2(g)CO(g)CO2(g)H2O(g)H2O(l)H2O2(g)NH3(g)O(g)H(g)N(g)OH(g)CH4(g)C2H2(g)C2H4(g)C2H6(g)C3H6(g)C3H8(g)C4H10(g)C5H12(g)C8H18(g)C8H18(l)C6H6(8)CH3OH(g)CH3OH(I)C2H5OH(g)C2H5OH(I)0000–110,530–393,520–241,820–285,830–136,310–46,190249,170218,000472,68039,460–74,850226,73052,280–84,68020,410–103,850–126,150–146,440–208,450–249,91082,930–200,890–238,810–235,310–277,6900000–137,150–394,380–228,590–237,180–105,600–16,590231,770203,290455,51034,280–50,790209,17068,120–32,89062,720–23,490–15,710–8,20017,3206,610129,660–162,140–166,290–168,570174,8905.74130.57191.50205.03197.54213.69188.7269.95232.63192.33160.95114.61153.19183.75186.16200.85219.83229.49266.94269.91310.03348.40463.67360.79269.20239.70126.80282.59160.70Source: Adapted from Wark, K.
1983. Thermodynamics, 4th ed.McGraw-Hill, New York, as based on JANAF Thermochemical Tables,NSRDS-NBS-37, 1971; Selected Values of Chemical ThermodynamicProperties, NBS Tech. Note 270-3, 1968; and API Research Project 44,Carnegie Press, 1953.[(h (T , p) = h f + h (T , p) − h Tref , prefoo)] = hof+ ∆h(2.78)That is, the enthalpy of a substance is composed of h f , associated with the formation of the substancefrom its elements, and ∆h, associated with a change of state at constant composition.
An arbitrarilychosen datum can be used to determine ∆h, since it is a difference at constant composition. Accordingly,∆h can be evaluated from sources such as the steam tables and the ideal gas tables.The enthalpy of combustion, hRP , is the difference between the enthalpy of the products and theenthalpy of the reactants, each on a per-mole-of-fuel basis, when complete combustion occurs and bothreactants and products are at the same temperature and pressure.
For hydrocarbon fuels the enthalpy ofcombustion is negative in value since chemical internal energy is liberated in the reaction. The heatingvalue of a fuel is a positive number equal to the magnitude of the enthalpy of combustion. Two heatingvalues are recognized: the higher heating value and the lower heating value. The higher heating value© 1999 by CRC Press LLC2-62Section 2is obtained when all the water formed by combustion is a liquid; the lower heating value is obtainedwhen all the water formed by combustion is a vapor. The higher heating value exceeds the lower heatingvalue by the energy that would be required to vaporize the liquid water formed at the specified temperature.
Heating values are typically reported at a temperature of 25°C (77°F) and a pressure of 1 bar (or1 atm). These values also depend on whether the fuel is a liquid or a gas. A sampling is provided on aunit-mass-of-fuel basis in Table 2.10.TABLE 2.10 Heating Values in kJ/kg of Selected Hydrocarbons at 25°CHigher ValueaLower ValuebHydrocarbonFormulaLiquid FuelGas. FuelLiquid FuelGas. FuelMethaneEthanePropanen-Butanen-Octanen-DodecaneMethanolEthanolCH4C2H6C3H8C4H10C8H18C12H26CH3OHC3H5OH——49,97349,13047,89347,47022,65729,67655,49651,87550,34349,50048,25647,82823,84030,596——45,98245,34444,42544,10919,91026,81150,01047,48446,35245,71444,78844,46721,09327,731abH2O liquid in the products.H2O vapor in the products.In the absence of work Ẇcv and appreciable kinetic and potential energy effects, the energy liberatedon combustion is transferred from a reactor at steady state in two ways: the energy accompanying theexiting combustion products and by heat transfer.
The temperature that would be achieved by the productsin the limit of adiabatic operation is the adiabatic flame or adiabatic combustion temperature.For a specified fuel and specified temperature and pressure of the reactants, the maximum adiabaticflame temperature is realized for complete combustion with the theoretical amount of air. Example 10provides an illustration. The measured value of the temperature of the combustion products may beseveral hundred degrees below the calculated maxunum adiabatic flame temperature, however, for severalreasons including the following: (1) heat loss can be reduced but not eliminated; (2) once adequateoxygen has been provided to permit complete combustion, bringing in more air dilutes the combustionproducts, lowering the temperature; (3) incomplete combustion tends to reduce the temperature of theproducts, and combustion is seldom complete; (4) as result of the high temperatures achieved, some ofthe combustion products may dissociate.
Endothermic dissociation reactions also lower the producttemperature.Absolute EntropyA common datum for assigning entropy values to substances involved in chemical reactions is realizedthrough the third law of thermodynamics, which is based on experimental observations obtained primarilyfrom studies of chemical reactions at low temperatures and specific heat measurements at temperaturesapproaching absolute zero. The third law states that the entropy of a pure crystalline substance is zeroat the absolute zero of temperature, 0 K or 0°R.
Substances not having a pure crystalline structure havea nonzero value of entropy at absolute zero.The third law provides a datum relative to which the entropy of each substance participating in areaction can be evaluated. The entropy relative to this datum is called the absolute entropy. The changein entropy of a substance between absolute zero and any given state can be determined from measurements of energy transfers and specific heat data or from procedures based on statistical thermodynamicsand observed molecular data. Table 2.9 and Tables A.2 and A.8 provide absolute entropy data for varioussubstances.
In these tables, pref =1 atm.When the absolute entropy is known at pressure pref and temperature T, the absolute entropy at thesame temperature and any pressure p can be found from© 1999 by CRC Press LLC2-63Engineering Thermodynamics) [((s (T , p) = s T , pref + s (T , p) − s T , pref)](2.79)For an ideal gas, the second term on the right side of Equation 2.79 can be evaluated by using Equation2.58, givingpprefs (T , p) = s o (T ) − R ln(ideal gas)(2.80)In this expression, s o (T) denotes the absolute entropy at temperature T and pressure pref .The entropy of the ith component of an ideal gas mixture is evaluated at the mixture temperature Tand the partial pressure pi: si (T, pi). For the ith component, Equation 2.80 takes the formsi (T , pi ) = sio (T ) − R lnpipref(2.81)yp= s (T ) − R ln ipref(ideal gas)oiwhere sio (T) is the absolute entropy of component i at temperature T and pref .Example 10Liquid octane at 25°C, 1 atm enters a well insulated reactor and reacts with dry air entering at the sametemperature and pressure.
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