A Specific Heat Ratio Model

7/27/2019 A Specific Heat Ratio Model

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Technical university of Liberec

Faculty of Mechanical EngineeringDepartment of Transport machines

Josef Boek Research Center

PROPERTIES OF CHOSEN SUBSTANCES DEPENDING ONTEMPERATURE

(Calculation of substances properties of chosen fuel-air mixtures and their combustion products)

Authors: Blaek JosefZuhdi Salhab

Head of Department: Beroun Stanislav

Project: LN 00B073SM 393/2001Number of the page: 15

Liberec, 2001 Number of the supplement: 3


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Summary

One of the most important relationships for property determination of engine calculations is the

specific heat (heat capacity) and the specific heat ratio. The description of substance propertiesof chosen types of combustible mixtures and their combustion products (with respect to complete

combustion) is based on the reference data.

Introduction

As it is known from experience that it takes different amounts of energy to raise the temperatureof identical masses of different substances by one degree. Therefore, it is desirable to have aproperty that will enable us to compare the energy storage capabilities of various substances. This

property is the specific heat.The specific heat is defined as the energy required to raise the temperature of a unit mass of asubstance by one degree. In general, this energy will depend on how the process is executed. Inthermodynamics, there are two kinds of specific heats: specific heat at constant volume vC and

specific heat at constant pressure pC .

Physically, the specific heat at constant volume vC can be viewed as the energy required raising

the temperature of the unit mass of substances by one degree as the volume is maintainedconstant. The energy required to do the same, as the pressure is maintained constant is specificheat at constant pressure pC .

The specific heat at constant pressure pC is always greater than vC because at constant pressurethe system is allowed to expand and the energy for this expansion work must also be supplied tothe system.

Specific heats can be expressed in terms of other properties; thus they must be propertiesthemselves. From the definition of vC , the energy must be equal to vC dT, where dT is the

differential change in temperature.

Thus, dudTC v = , (1)or

v

vT

uC

= . (2)

Similarly, an expression for the specific heat at constant pressurep

C can be obtained by

considering a constant-pressure. It yields

P

pT

hC

= . (3)


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A few observations can be made from previous equations. First, these equations are propertyrelations and such as are independent on the type of processes. They are valid for any substanceundergoing any process.

The only relevancevC has to a constant volume process is that vC happens to be the energy

transferred to a system during a constant-volume process per unit mass per unit degree rise intemperature. This is how the values of

vC are determined. This is also how the name specific

heat at constant volume originated. Likewise, the energy transferred to a system per unit mass perunit temperature rise during a constant-pressure process happens to be equal to pC . This how the

values of pC can be determined and also explains the origin of the name specific heat at constant

pressure.

Another observation that can be made is that vC is related to the changes in internal energy and

pC to the changes in enthalpy. In fact, it would be more proper to define vC as the change in thespecific internal energy of substances per unit change in temperature at constant volume.Likewise, pC can be defined as the change in the specific enthalpy of a substance per unit change

in temperature at constant pressure.

In other words, vC is a measure of the variation of internal energy of a substance with

temperature, and pC is a measure of the variation of enthalpy of a substance with temperature.

A common unit for specific heat is [kJ/kgC] or [kJ/kgK]

The specific heats are sometimes given on a molar basis. They are denoted by vC~

and pC~

and

have unit [kJ/kmolC] or [kJ/kmolK].

Specific heats of real gases

The specific heat of ideal gases depends, at most, on temperature only. At low pressure all gasesapproach ideal-gas behavior and therefore their specific heats depend on temperature only. Thespecific heats of real gases at low pressure are called ideal-gas specific heats, or zero-pressurespecific heats.

Accurate analytical expressions for real-gas specific heats, based on direct measurements orcalculations from statistical behavior of molecules, are available and tabulated or given aspolynomials or empirical equations.

The use of real/gas specific heat data is limited to low pressure, but these data can be also used atmoderately high pressures with reasonable accuracy as long as the gas does not deviate fromideal/gas behavior significantly.

The specific heat values for some common gases are listed as a function of temperatures in tablesin many literatures. Tables giving the composition and thermodynamic properties of combustionproducts have been compiled. They are useful sources of property and species concentration datain burned gas mixtures for a range of temperatures.

When large numbers of computations are being made or high accuracy is required, engineprocess calculations are carried out on a computer. Relationships which model the composition


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and/or thermodynamic properties of unburned and burned gas mixtures have been developed forcomputer use. These vary considerably in range of application and accuracy.

The most complete models are based on polynomial curve fits to the thermodynamic data foreach in the mixture. For each component (i) in its standard state at temperature T (K), the specific

heat piC~

is approximated in [3] by the polynomial:

45

34

2321 ....~

~TaTaTaTaa

R

Ciiiii

pi++++= , (4)

where piC~

is in [cal/gmolK], and R~ is universal gas constant in [cal/gmolK].

Values of the coefficients aij for (CO2, H2O, CO, H2, O2, N2, OH, NO, O, and H) from the NASAprogram are given in table T 1 in [3] - supplement 1. Two temperature ranges are given. The (300to 1000)K range is appropriate for unburned mixtures property calculations. The (1000 to 5000)Krange is appropriate for burned mixtures property calculations.

Polynomial functions for various fuels (in the vapor phase) have been fitted to the functionalform (5),

2

534

2321 ...

~t

AtAtAtAAC

f

ffffpf ++++= , (5)

where t= T(K)/1000.

The values for the coefficient Af1 to Af5 for typical petroleum-based fuels are taken from [3], seetable T 2 - supplement 2. The units of the coefficients give pfC

~in [cal/gmol.K] with

t=T(K)/1000.

In other literature [2], the specific heats are given as third-degree polynomials for several gases asa function of temperature and they expressed as:

32 ...~ TdTcTbaCp +++= , (6)

where T in [K] and pC~

in [kJ/kmolK].

The values of coefficients (a, b, c, d) for chosen substances are listed in table T 3 in [2] -supplement 3.

Also a specific heat can be expressed as a function of temperature by the following empiricalequation [1] for temperature range (200-3000)K:

( )( ) ( )2/

/2

222/

/2

11

2

2

1

1

11

expTC

TC

TC

TC

pm

e

e

T

CB

eT

CBATC

+

+= , (7)

where pmC is a molar specific heat.


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Coefficients (A, B1 ,B2 ,C1 ,C2 ) depend on substances and they are listed in the table T 4.

Table T 4: Coefficients for substances CH4, C3H8, C4H8 - according to [1].

Substance A B1 B2 C1 C2CH4 33,823 54,22 37,37 2239,83 5918,8C3H8 55,852 115,27 76,70 1545,097 3970,728C4H10 75,739 94,10 148,80 3958,111 1546,537

Specific heat relations of gases

A special relationship between pC~

and vC~

for ideal gases can be obtained by differentiating the

relation

h=u+RT, (8)it yields

dh=du+RdT (9)

Replacing dh by CP.dTand du by Cv.dTand dividing the resulting expression by dT, we obtain

pC~

= vC~

+R [KJ/kg.K] (10)

This an important relationship for ideal gases since it enables us to determine vC~

from

knowledge of pC~ and the gas constantR.

When the specific heats are given on a molar basis,R in the above equation should be replaced bythe universal gas constant Ru.That is,

RuCC vp +=~~

[KJ/kmol.K] (11)

At this point, it is introduced another ideal-gas property called the specific heat ratio , defined as

=v

p

C

C[-] (12)

The specific heat ratio also varies with temperature, but this variation is very mild. Formonatomic gases, its value is essentially constant at 1,667. Many diatomic gases, including air,have a specific heat ratio of about 1,4 at room temperature, whereas the value of specific heatratio for multi-atomic gases is about 1,33.

The specific heat ratio also could be determined for diatomic gases using empirical equationSchlle [4] as:

10000572,041,1

T= (13)


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From the previous equation, a specific heat at constant volume can be expressed as:

11,287

1 =

=

RCv . (14)

Specific heats of gas-mixtures

To determine the specific heats of a gas mixture, it is necessary to know the composition of themixture as well as the specific heats of the individual components.

The determination is based on mass fraction (mf) calculating that is the ratio of the mass of acomponent to the mass of the mixture or mole fraction (Y) that is the ratio of the mole number ofa component to the mole number of the mixture.

The mass of the mixture (mm) is the sum of the masses of the individual components, and themole number of the mixture (Nm) is the sum of the mole numbers of the individual components.That is,

=

=k

i

im mm1

and=

=k

i

im NN1

, (15)

it yields

m

ifi

m

mm = and

m

ii

N

NY = . (16)

From the above equations, specific heats of gas mixture during a process depending ontemperature can be expressed as,

=

=k

i

pifipm CmC1

,=

=k

i

vifivm CmC1

[kJ/kgC] , (17)

=

=k

i

piipm CYC1

~~and

=

=k

i

viivm CYC1

~~[kJ/kmolC] (18)

Notice that properties per unit mass involve mass fractions (mfi

) and properties per unit moleinvolve mole fractions (Yi).

The relations given above are generally valid and are applicable to both ideal-and real-gasmixtures.

Similarly, the specific heats of combustion products can be expressed.

The calculations of specific heats are divided into two categories according to the excess-air ratio , which is often used to describe mixture strength:

1- stoichiometric mixture (SM) with=1,2- lean-burn mixture (LB) with various values of .


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According to various fuels using mass fractions of individual components of mixtures and theircombustion products. That are:

- hydrogen-air mixture,- natural gas (NG)-air mixture,- liquefied petroleum gas (LPG) -air mixture (60%propane/40%butane),- gasoline-air mixture,- diesel-air mixture,- empirical equation Schlle .

Values of substances ( H2O, CO2, O2, N2 and H2) are taken from tables in [4] and [2], whereas thespecific heats values of gas substances(methane CH4, propane C3H8 and butane C4H10) arecalculated by the empirical equation (7), and the values for gasoline and diesel are calculated byempirical equation (5).

The calculations are based on the mass fractions of components of mixtures and productsaccording to the following combustion equation (19):

( ) ( ) ( ) ( ) 22222222 .76,3.213

.2

1311.76,3

2

13. N

nO

nOHnCOnNO

nHC nn

++

+++++

+++ (19)

The previous equation is valid for gas fuel (type CnH2n+2), so it can be valid for CH4, C3H8, C4H10and H2 mixtures with air.

The mass of mixture is equal to the mass of combustion products and it is expressed in [kg] as

( ) Ann =+++ 64,68.92,205..142

(20)

The mass fractions of individual components of mixture are:

A

nm nfCnH

2.1422

+=+ ,

( )

A

nm

fO

1.3..162

+=

,

( )A

nm

fN

1.3..64,522

+=

(21)

The mass fractions of individual combustion products are:

A

nmfCO

.442= ,

( )A

nm OfH

1.182

+= ,

( )( )A

nmfO

1.3116

2

+=

and

( )A

nmfN

1.3.64,522

+=

(22)

The unit of mass fraction is in [%] and the sum of the individual mass fractions is equal to one.The combustion equation for (60%propane, 40%butane)-air mixture is expressed as (23) :

( ) ( ) ( ) 22222210483 .056,21..1.6,5.4,4.4,376,3..6,54.06,0 NOOHCONOHCHC ++++++ .


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Mass of mixture is equal to the mass of combustion products and it is expressed in [kg] as:

B=+ .768,7686,49 . (24)


( )B

m HCHCf6,49

10483 4,06,0=+ ,

Bm

fO

.2,1792= ,

BmfN

.568,5892= . (25)


BmfCO 6,1492 = , Bm OfH 2,792 = ,

( )B

mfO1.2,179

2

=

and

BmfN

.568.5892= . (26)

The chemical reaction of gasoline air mixture is compressed as (27):

( ) ( ) 222222515268 62764511351275726876313512 NOOHCONOHC ..,.,.,.,,..,,, +++++ ,

and mass of mixture is equal to the mass of combustion products and it is expressed in [kg] as:

C=+ .8928,166562,114 (28)


Cmfgasoline

62,114= ,

Cm

fO

.32,3882= ,

CmfN

.5728,12772= . (29)


CmfCO

44,3632=

Cm OfH

5,1392

= ,

( )C

mfO1.32,388

2

=

and

CmfN

.5728,12772= . (30)


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The chemical reaction of diesel air mixture is compressed as (31):

( ) ( ) 222222718810 1865814751535981076347515 NOOHCONOHC ..,.,.,.,,..,,, +++++ ,

and mass of mixture is equal to the mass of combustion products and it is expressed in [kg] as:

D=+ .408,21243,148 (32)


Dmfdiesel

3,148= ,

Dm

fO

.2,4952= ,

DmfN

.208,16292= (33)


DmfCO

2,4752= ,

Dm OfH

3,1682

= ,

DmfO

.2,4952= and

DmfN

.208,16292= . (34)

A few observations can be made from the above equations:

- All the above compressed chemical equations are valid for excess-air ratio 1 .

- The general combustion equation for chemical reaction (19) is valid for any gas fuel (typeCnH2n+2)-air mixture including hydrogen-air mixture.

- The mass of the mixture is equal to the mass of the combustion products in [kg].

- The mass fractions of individual components of mixture and combustion products are validfor any varying values of atom numbers of carbon and hydrogen (depends on fuel type) andvarious values of excess air ratio ..

Calculation evaluation

Specific heat of real gases is a significant gas property of substances which is affected bytemperature. A specific heat of few substances is almost similar, while it is for others different

depending on temperature and it is also expressly distinguished.Otherwise as it is seen in Fig. 1 to Fig 4 for CP, the specific heat values of substances ( N2, O2,CO2, air and empirical equation Schlle) are expressly distinguished from the specific heat valuesof hydrocarbons (CH4, C3H8, C4H10, C8,26H15,5 andC10,8H18,7), H 2O and H2 and from Cv values aswell.

Also the specific heat values of hydrocarbons above mentioned and water are clear different fromhydrogen specific heat values at both constant pressure and volume, while for othersubstances(CH4, C3H8, C4H10, C8,26H15,5 and C10,8H18,7), the specific heats are not so different,because their variation with temperature is smooth and may be approximated as linear over smalltemperature intervals (a few hundred degrees or less).


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Similarly, the specific heat ratio also depends on temperature, it decreases with temperatureincreasing as it is shown in Fig. 5 for individual substances (H2, H2O, CH4, C3H8, C4H10, N2, O2,CO2, C8,26H15,5 ,C10,8H18,7), air and empirical equation Schlle). In Fig. 6 and Fig. 7, the specificheat curves CV and CP respectively are shown, for methane-air mixture and its combustionproducts and as it is seen from curves that the CP and CV are also vary with temperature and withmixture richness -- and the specific heat is higher for fuel-rich mixtures, while its ratio =hasless values for fuel-rich mixtures as it is seen in Fig. 11 with various values of=.On the specific heat and on its ratio has a significant effect, mixture composition as it wasmentioned; Fig. 8 to Fig. 10 show the variation of Cv with temperature and with various values ofexcess air ratio for various gas-air mixture.=From the calculating values of substance properties for real fuel-air mixtures and theircombustion products (Fig. 8 to Fig. 10) compared to the calculating values for substitute diatomicgas expressed by Schlle equation, has been relatively demonstrated a large difference. Thefollowing example proves this result:

= For stoichiometric mixture of hydrocarbon fuels and air with temperature T=700 K, thespecific heat at constant volume (CV) for real mixture is higher by 20%, with temperatureT=2000 K, the specific heat (CV) of combustion products is almost higher by 13% thandiatomic gas (according to Schlle equation).

= The reciprocal relation between the values of the adiabatic exponent of real mixtures (andtheir combustion products) and the substitute diatomic gas is very important: the real mixtureshave lower value () than the substitute diatomic gas- Schlle (Fig. 11). This fact partiallyeliminates the effect of higher values of the specific heats of real mixtures.

Fig.1: Specific heat at constant pressure Cp for substances (N2, O2, CO2, air and empiricalequation Schlle) as a function of temperature.

800

900

1000

1100

1200

1300

1400

1500

0 500 1000 1500 2000 2500 300

Temperature [K]

SpecificheatCp

[J/kgK]

SchlleAir

CO2

O2

N2


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Fig. 2: Specific heat at constant pressure Cp for substances (H2, H2O, CH4, C3H8, C4H10, C8,26H15,5andC10,8H18,7) as a function of temperature.

Fig. 3: Specific heat at constant pressure Cv for substances (N2, O2, CO2, air and empiricalequation Schlle) as a function of temperature.

1300

2300

3300

4300

5300

6300

7300

0 500 1000 1500 2000 2500 3000

Temperature [K]

Spec

ificheatCp

[J/kgK]

0

2000

4000

6000

8000

10000

12000

14000

16000

18000

20000

SpecificheatCp

[J/kgK]-H2

C3H8 CH4 C4H8 C8,26H15,5

C10,8H18,7 H2O H2

C3H8

C10,8H18,7

CH4

H2O

C4H10

H2

C8,26H15,5

600

700

800

900

1000

1100

1200

0 500 1000 1500 2000 2500 3000

Temperature [K]

Specific

heatCv

[J/kgK]

SchlleAir

CO2

O2

N2


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Fig. 4: Specific heat at constant volume Cv for substances (H2, H2O, CH4, C3H8, C4H10, C8,26H15,5andC10,8H18,7) as a function of temperature

Fig. 5: Specific heat ratiofor substances (H2, H2O, CH4, C3H8, C4H10, C8,26H15,5, C10,8H18,7, andSchlle equation) as a function of temperature.

1100

2100

3100

4100

5100

6100

7100

0 500 1000 1500 2000 2500 3000

Temperature [K]

S

pecificheatCv

[J/kgK]

0

2000

4000

6000

8000

10000

12000

14000

16000

SpecificheatCv

[J/kgK]-H2

C3H8 CH4 C4H8 C8,26H15,5

C10,8H18,7 H2O H2

C3H8

C10,8H18,7

CH4

H2O

C4H10

H2

C8,26H15,5

1

1,05

1,1

1,15

1,2

1,25

1,3

1,35

1,4

1,45

0 500 1000 1500 2000 2500 3000

Temperature [K]

Specificheatratiok[-]

H2 C3H8 CH4 C4H8

C8,26H15,5 C10,8H18,7 H2O Schlle

C3H8

C10,8H18,7

CH4

H2O

C4H10H2

C8,26H15,5


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700

800

900

1000

1100

1200

1300

0 500 1000 1500 2000 2500 3000

Teplota [K]

CV

[J/kg.

C]

NG-air mixture

combustion products

=1

1,4

2

Fig. 6: Specific heat at constant

volume Cv for NG-air mixture andcombustion products as a function otemperature and excess-air ratio=.=

1000

1100

1200

1300

1400

1500

1600

0 500 1000 1500 2000 2500

Teplota [K]

Cp[J/kgC]

=1

1,4

2

NG-air m ixture

combustion products

Fig. 7: Specific heat at constant pressure

Cp for NG-air mixture and combustionproducts as a function of temperatureand excess-air ratio=.=

Fig. 8: Specific heat at constant volume Cv for various fuel-air mixture andcombustion products a a function of temperature and excess-air

ratio==1=compared to the Schlle equation=

700

800

900

1000

1100

1200

1300

0 500 1000 1500 2000 2500 3000

Temper ature [ K ]

SpecificHeatCv[

J/kg.K

]

Gasoline-air mixtureNG-air mixtureLPG-air mixtureSchlle equationgasoline-air productsNG-air productsLPG-air products

=1=1=1=1


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Fig. 9: Specific heat at constant volume Cv for various fuel-air mixture and combustion productsas a function of temperature and excess-air ratio==1,45==compared to the Schlle equation=

Fig. 10: Specific heat at constant volume Cv for various fuel-air mixture and combustionproducts as a function of temperature and excess-air ratio==1,8=compared to the Schlle

equation=

700

800

900

1000

1100

1200

1300

0 500 1000 1500 2000 2500 3000

Temper ature T[K]

SpecificHeatCv

[J/kg.K

]

NG-air mixtureDiesel-air mixtureSchlle equationH2-air mixtureNG-air productsDIESEL-air products

H2-air products

= 1,8

700

800

900

1000

1100

1200

1300

0 500 1000 1500 2000 2500 3000

Temperature T[K]

SpecificHeatCv

[J/kg.K

]

NG-air mixtureLPG-air mixtureSchlle equationH2-air mixtureNG-air productsLPG-air productsH2-air products

= 1,45


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Fig. 11: The specific heat ratio methane-air mixture and combustion products as a function oftemperature and various excess-air ratio=

The specific heat of real gases mixtures is a significant gas property of substance, which isaffected by temperature. With high temperatures of cylinder charge, the variation of specificheats is appreciable, which results in lowering maximum temperatures and pressures, cycleefficiency and mean effective pressure.

This research has been subsidized by the project of the Czech Ministry of Education, LN 00B073

References1. Bure, M., Holub, R., Lietner, J., Vonka, P.: Termodynamick veliiny organickch

slouenin, svazek 2. VCHT Praha, 1992.2. Cengel, A. Y., Boles, M.A.: Thermodynamics. An Engineering Approach. 2th Edition.

McGraw-Hill Inc. USA, 1994.3. Heywood, J., B.: Internal Combustion Engine Fundamentals. McGraw-Hill Inc. USA, 1989.

4. Jastrembskij, A.S.: Technick termodynamika, I. dl, SNTL Praha, 1954

1,2

1,25

1,3

1,35

1,4

1,45

0 500 1000 1500 2000 2500 3000Temp erature T[K]

SpecificHeatRatio

[

-]

mixturesproducts

Schlle

= 1

= 1,8

= 1,45


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Supplement1 - T 1:Coefficient for species thermodynamic properties (specific heats) - according to [3].

Species T range[K]

ai1 ai2 ai3 ai4 ai5

CO21000-5000300-1000

0,44608 (+1)0,24008 (+1)

0,30982 (-2)0,87351 (-2)

-0,12393 (-5)-0,66071 (-5)

0,22741 (-9)0,20022 (-8)

-0,15526 (-13)0,63274 (-15)

H2O1000-5000300-1000

0,27168 (+1)0,40701 (+1)

0,29451 (-2)-0,11084 (-2)

-0,80224 (-6)0,41521 (-5)

0,10227 (-9)-0,29637 (-8)

-0,48472 (-14)0,80702 (-12)

CO 1000-5000300-10000,29841 (+1)0,37101 (+1)

0,14891 (-2)-0,16191 (-2)

-0,57900 (-6)0,36724 (-5)

0,10365 (-9)-0,20320 (-8)

-0,69354 (-14)0,23953 (-12)

H21000-5000300-1000

0,31002 (+1)0,30574 (+1)

0,51119 (-3)0,26765 (-2)

0,52644 (-7)-0,58099 (-5)

-0,34310 (-10)0,55210 (-8)

0,36945 (-14)-0,18123 (-11)

O21000-5000300-1000

0,36220 (+1)0,36256 (+1)

0,73618 (-3)-0,18782 (-2)

-0,19652 (-6)0,71555 (-5)

0,36202 (-10)-0,67635 (-8)

-0,28946 (-14)0,21556 (-11)

N21000-5000300-1000

0,28963 (+1)0,36748 (+1)

0,15155 (-2)-0,12082 (-2)

-0,57235 (-6)0,23240 (-5)

0,99807 (-10)-0,63218 (-9)

- 0,65224 (-14)-0,22577 (-12)

OH 1000-5000 0,29106 (+1) 0,95932 (-3) -0,19442 (-6) 0,13757 (-10) 0,14225 (-15)

NO 1000-5000 0,31890 (+1) 0,13382 (-2) -0,52899 (-6) 0,95919 (-10) -0,64848 (-14)

O 1000-5000 0,25421 (+1) -0,27551 (-4) -0,31028 (-8) 0,45511 (-11) -0,43681 (-15)

H 1000-5000 0,25 (+1) 0,0 0,0 0,0 0,0


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Supplement 2 - T 2:Coefficients for fuels specific heats - according to [3].

Fuel Formula Molecularweight Af1 Af2 Af3 Af4 Af5 Af6 Af8

Methane CH4 16,04 -0,29149 26,327 -10,610 1,5656 0,16573 -18,331 4,300

Propane C3H8 44,10 -1,4867 74,339 -39.065 8,0543 0,01219 -27,313 8,852

Hexane C6H14 86,18 -20,777 21,48 -164,125 52,832 0,56635 -39,836 15,611

Isooctane C8H18 114,2 -0,55313 181,62 -97,787 20,402 -0,03095 -60,751 20,232

Methanol CH3OH 32,04 -20,7059 44,68 -27,501 7,2193 0,20299 -48,288 5,3375

Ethanol C2H5OH 46,07 6,990 39,741 -11,926 0,0 0,0 -60,214 7,6135

Gasoline C8.26H15.5C7.76H13.1

114,8106,4

-240,078-220,501

256,63227,99

-201,68-177,26

64,75056,048

0,58080,4845

-27.562-17,578

17,79215,235

Diesel C10,8H18.7 148,6 -90,1063 246,97 -143,74 32,329 0,0518 -50,128 23,514

Units of Afi such that fh is in kcal/gmol and f,pC is in cal/gmol.K with( )

1000

KTt = .

Af6 gives enthalpy data at 298,15 K;(Af6 + Af8) gives enthalpy data at 0 K.


18/18

18

Supplement 3 - table T 3:Specific heats of various common gases as a function of temperature

Substance Formula a b c d Temperaturerange [K]

Nitrogen N228,90

-0,1571(-2) 0,8081(-5) -2,873(-9) 273-1800

Oxygen O2 25,84 1,520(-2) -0,7155(-5) 1,312(-9) 273-1800

Air(O2+3,76N2)

28,11 0,1967(-2) 0,4802(-5) -1,966(-9) 273-1800

Hydrogen H2 29,11 -0,1916(-2) 0,4003(-5) -0,8704(-9) 273-1800

Carbonmonoxide

CO 28,16 0,1675(-2) 0,5372(-5) -2,222(-9) 273-1800

Carbon dioxide CO2 22,26 5,981(-2) -3,501(-5) 7,469(-9) 273-1800

Water vapor H2O 32,24 0,1923(-2) 1,055(-5) -3,595(-9) 273-1800

Nitric Oxide NO 29,34 -0,09395(-2) 09747(-5) -4,187(-9) 273-1500

Nitrous Oxide N2O 24,11 5,8632(-2) -3,562(-5) 10,58(-9) 273-1500

Nitrogen dioxide NO2 22,90 5,715(-2) -3,52(-5) 7,87(-9) 273-1500

Ammonia NH3 27,562 2,5630(-2) 0,99072(-5) -6,6909(-9) 273-1500

Sulfur S2 27,21 2,218(-2) -1,628(-5) 3,986(-9) 273-1800

sulfur dioxide SO2 25,78 5,795(-2) -3,812(-5) 8,612(-9) 273-1800

Sulfur trioxide SO3 16,40 14,58(-2) -11,20(-5) 32,42(-9) 273-1300

Acetylene C2H2 21,80 9,2143(-2) -6,527(-5) 18,21(-9) 273-1500

Benzene C6H6 -36,22 48,475(-2) -31,57(-5) 77,62(-9) 273-1500

Methanol CH4O 19,0 9,152(-2) -1.22(-5) -8,039(-9) 273-1000

Ethanol C2H6O 19,90 20,96(-2) -10,38(-5) 20,05(-9) 273-1500

Hydrogenchloride

HCl 30,33 -0,7620(-2) 1,327(-5) -4,338(-9) 273-1500

Methane CH4 19,89 5,024(-2) 1,269(-5) -11,01(-9) 273-1500

Ethane C2H6 6,90 17,27(-2) -6,406(-5) 7,285(-9) 273-1500

Propane C3H8 -4,04 30,48(-2) -15,72(-5) 31,74(-9) 273-1500

n-Butane C4H10 3,96 37,15(-2) -18,34(-5) 35,00(-9) 273-1500

i-Butane C4H10 -7,913 41,60(-2) -23,01(-5) 49,91(-9) 273-1500

n-Pentane C5H12 6,774 45,43(-2) -22,42(-5) 42,29(-9) 273-1500

n-Hexane C6H14 6,938 55,22(-2) -28,65(-5) 57,69(-9) 273-1500

Ethylene C2H4 3,95 15,64(-2) -8,344(-5) 17,67(-9) 273-1500

Propylene C3H6 3,15 23,83(-2) -12,18(-5) 24,62(-9) 273-1500

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