Equilibrium thermodynamic data for the H2-O2-He system

•

AUGUST· 1968

E~UILIBR!UM THERMODYNAMIC DATA FOR THE H2-02-He SYSTEM

by f\ Andre Benoit

•

)

•

EQUILIBRIUM THERMODYNAMIC DATA FOR THE H2-0 2 -He SYSTEM

by

Andre

Beno

~

t*

Manuscript received April 1968

*Presently with GETS (Groupe d'Etude de Technologie Spatiale), Brussels, Belgium.

•

ACKNOWLEDGEMENTS

I should like to express my thanks to Dr. Q.N. Pattersoij fo~ the opportunity to complete this work and my gratituqe to Dr. l.I. Glass for his encouragement.

The work ·was financially supported by the Aero-space Re~earch Laboratories (USAF/ARL) under contract NB. AF33(615}r 5313 and the National Research Council of Canada

(NRC) •

•

•

SUMMARY

This note presents equilibrium thermodynamic data, in graphical form, for the H2 -0 2 -He system considered as a possible high enthalpy driving gas for hypervelocity appli-cations. The weight formula of the basic system is expressed as (2H2 ~. 02) + m H2 + n He, and molar dilutions of the stoi-chiometric hydrogen-oxygen system up to

97%

are envisaged. For these mixtures, composition data, thermodynamic data and rele-vant partial derivatives are given assuming thermodynamic equi-librium, for temperatures ranging from 20000_{K to 5000}0_{K and}

pressures from 0.01 to 10,000 atm. More specifically, these data' include mole fractions, molecular weight, enthalpy, den-sity, logarithmic first partial derivatives with respect to temperature at constant pressure or with respect to pressure at constant temperature of molar fractions and molecular weight, equilibrium specific heat, isentropic exponent, and equilibrium and frozen speeds of sound .

1. 2. 3.

4 .

ACKNOWLEDGEMENTS SUMMARY NOTATlON lNTRODUCTlON TABLE OF CONTENTS

OXYGEN - HYDROGEN - HELIUM SYSTEM COMPOSlTlON AND RELATED DATA

PART lAL DERIVATIVES THERMODYNAMIC DATA CONCLUSIONS REFERENCES FIGURES iv Page i i i i i v 1 2 2 3 3 3

4

A

=

Al

=

A*

₌

Cp

=

H

=

m

=

n

=

.P

=

T

₌

Y

=

y'~

₌

)J

=

V

=

P

=

W.R.T.= NOTATION

equilibrium speed of sound, frezen speed of sound,

(y*

RT)1/2, m/sec

m/sec m/sec

specific heat at constant pressure, cal/mole/oK enthalpy, kcal/mole

hydrogen dilution index helium dilution index pressure, atm

temperature, oK isentropic exponent

equilibrium specific heat ratio molecular weight, g/mole

mole fraction density, kg/m~ with respect to

INTRODUCTION

The equilibrium properties of the hydrogen-oxygen sys-tem have, so far, essentially been considered from the point of view of rocket performance, and corresponding tables of 'relevant composition, thermodynamic data and transport properties are available (Ref. 1). This note extends these data to mixtures composed of stoichiometric hydrogen-oxygen diluted with hydro-gen and/or helium, which are suitable for use as high-enthalpy driving gases in hypervelocity techniques (Ref. 2). The com-putations' were performed according to the numerical model des-cribed in Ref. 3, with the basic thermodynamic data given in Ref.

4,

and in compliance,with the general assumptions already

used in Refs.

5

and

6.

'

1. HYDROGEN - OXYGEN - HELIUM SYSTEM

There are several equivalent ways to define the mixture. The mass ratios O/H/He apply to any thermodynamic state. Definitions in-volving mole numbers must be referred to standard conditions, such as p

=

1 atm, T

=

298.20_{K, at which the H2-02-He system is in a}

non-dissociated gaseous state. The mixture can then be characterized by the formula-weight (2H2 + 02) + m E2 + n He where mand nare the number of moles of hydrogen and helium respectively added to three moles of stoichiometrie hydrogen-oxygen.

Molar fractions, mass fractions and molecular weight associated with reference conditions, are given in Figs. 1-1, to 1-4, as functions of the dilution characteristics, mand n, for hydrogen and helium di1u-tiön&~ respectively.

2. COMPOSITION AND RELATED DATA

The composition of the mixture is expressed in terms of mole fractions. The species present in the system are H20, OH, H2' 02' H, 0, and He. The range of temperature considered extends from 20000K to 5000 o K, and results are given for pressure of 0.1, 10 and 1000 atm.

Figures 2-1a to 2-1f give the composition for helium dilution, namely for m = 0, n = 0, 2, 4, 6, which corresponds to helium molar dilution ranging from 0 to 67%. Similar results are given in Figures 2-2a to 2-2f for hydrogen dilution. In both cases, it is seen on the figures, that the dissociation of H20 is practically co~plete at

32000_{K if p}

=

_{0.1 atm, but only above 5000}0_{K when p}

=

_{10 atm. The}

intermediate species, i.e. OH, H2' and 02, exhibit a maximum concen-tration at a temperature which increases with pressure.

The molecular weights of the mixture are given in Figure 2-3 for stoichiometrie mixture (m = n = 0), in Figures 2-4a to 2-4c for helium dilution (m

=

0; n

=

2, 4, 6) and in Figures 2-5a to 2-5c for hydro-gen dilution (n

=

0; m

=

2, 4, 6). In each case, the pressure varies continuously from 0.01 atm to 10,000 atm and the temperature from 20000_{K to 5000}0_{K in steps of 200 o K.}

The enthalpies, in kcal/mole, are given in Figure 2-6 for stoi-chiometrie mixtures, in Figures 2-7a to 2-7d for helium dilutions, and

in Figures 2-8a to 2-8c for hydrogen dilutions. ~

The densities in kg/m 3 , are given in Figures 2-9 and 2-10 for helium and hydrogen dilutions, respectively. In each case, the dilu-tion varies from 0 to 67%, the pressure from 0.01 atm to 1000 atm and the temperature from 20000_{K to 5000 o K.}

3. PARTlAL DERIVATIVES

The first partial derivatives of the thermodynamic functions are easily derived (Refs. 3 and

7)

when the first partial derivatives with respect to pressure at constant temperature and with respect te

tem-perature at constant pressure have been evaluated. In most applications, i t is convenient to express these derivatives in logarithmic form.

Moreover, most of the thermodynamic functions involving first partial derivatives can be expressed in terms of the corresponding logarith-mie derivatives of the molecular weight.

The logarithmic partial derivatives of the mole fractions are given in Figures 3-1 and 3-2 for stoichiometrie mixtures. In Figures 3-la to 3-le for derivatives with respect to temperature at constant pressure, and in Figures 3-2a to 3-2e for derivatives with respect to pressure at constant temperature.

The logarithmie first partial derivatives of the molecular weight are given in Figures 3-3 and 3-4 for stoichiometrie and hydro-gen dilution. Figures 3-3a to 3-3d are relative to derivatives taken with respect to temperature at constant pressure, and Figures 3-4a to

3~4d to derivatives taken with respect to pressure at constant

tem-perature.

4. THERMODYNAMIC DATA

Additional thermodynamic data involving thermodynamic functions and first partial derivatives are given in Figures 4-1 to 4-9. These

include the equilibrium specific heat at constant pressure Cp (cal/mole/OK), the isentropic exponent and the speed of sound.

The equilibrium specific heat C is given in Figure 4-1 for the stoichiometrie mixture, in Figures

4-~a

to 4-2c for helium dilution, and in Figures 4-3a to 4-3c for hydrogen dilution. Similarly, the isentropic exponent is given in Figure 4-4 for the stoichiometrie mix-ture, in Figures 4-5a to 4-5c for helium dilution, and in Figures 4~6a to 4-6c for hydrogen dilution. In Figures 4-7 to 4-9, A repre-sents the equilibrium speed qf sound, lAl' the frozen speed of sound and A*, the quantity (y*RT)1!2 where y* is the equilibrium specific heat ratio (Cp/Cv). Figure 4-7 applies to the stoichiometrie mixture, Figure 4-8 to helium dilution, and Figure 4-9 to hydrogen dilution.

5. CONCLUSIONS

Equilibrium composition and thermodynamic data are presented graphically in order to facilitate computation and the solution of problems for hydrogen-oxygen mixtures diluted with helium or hydrogen. For the undissociated gaseous state, the mixture is chemically defined by the formula weight 2H2 + 02 + n He + m H2. Both hydrogen ( n

=

0)

and helium (m=O) are used as a diluting gas, up to

67%

molar dilu-tion. For these mixtures, the eomposition, the first partial de-rivatives, and other thermodynamie data are given for temperatures ranging from 20000_{K to 5000}0_{K and statie pressures from 0.01 to}

1000 atm.

1. 2. 3.

..

4. 5.

6.

7.

Svehla, R.A. Glas s, l.I. A-Benoi t , A. McBride, B.J. Heimel, S. Ehlers, J.G. / ' Benoit, A. À Benoit, A. Gordon, S. Zeleznik, F.J. Huff, V.N. REFERENCES

Thermodynamic and Transport Properties for the Hydrogen-Oxygen System.

NASA SP-3011, 1964.

Shock and Combustion - Wave Dynamics in an lmplosion-Driven Hypervelocity Launcher. UT lAS Review No.25, January, 1965.

Les {quilibres thermodynamiques.

Séminaire de Math{matique Appliqute et Mé'canique, Universite' Catholique de

,

'" Louvain. Rapport a paraitre.

Thermodynamic Properties to 60000K for 210 Substances involving the First 18 Elements.

NASA SP-3001, July, 1963.

Specific Heat Ratios and lsentropic Ex-ponents for Constant-Volume Combustion of Stoichiometrie Mixtures of Hydrogen-Oxygen Diluted with Helium or Hydrogen. UT lAS Technical Note No. 102,'

December, 1966.

Properties of Chapman - Jouguet Detona-tions in Stoichiometrie Hydrogen-Oxygen Mixtures Diluted with Helium and Hydrogen. UTlAS Technical Note No. 104,

December, 1966.

A General Method for Automatic Computa-tion of Equilibrium ComposiComputa-tion and Theo-retical Rocket Performance of Propellants. NASA TN D-132, October, 1959.

1.0

r---r---,---~--_..,..---

__

--_O. 5

0.8

t - - -- - - L -- -_ _ I - - - _ ! I

,

!

~ HE'lium

--J

---

--I

- - + - - - -- - + - - -----10.3

I

I

-

f

-

---+--·

- -- - - t - - - - --- 0.2

O·~~-~-~--~~-~-~~-~-~--~~O

.

O. 2. 4.

6.

8

.

10. 12. DILUTION J n FIG. 1-1

1.0

r--_ _ ~----,---~---r----r---.15.

I

i

I

1---~:___:_4---_+--- - -

+

-

-

-

--

--

-

_

___

~---+-~'----'--4 13.

I

.

1 I !

!

I

I I

I

i

-

--

-

-

r

---

---

-

-

-

-L

--

- -

-f

11.

I I 12. 0.9

Oxygt'n

.

---

r

----

--

-

-

:-0.5 i 10. , I

--

-

-

--

-

t

----

---I

0.3 _, 8. I I 0.2

-r

-

---

-

-

-

-

-

t

_-

_-

_-

_-t7

_.

0.1

f/~~~--+--+--_+====t====J

6. L-~ _ _ ~--~--~~~~---L--~~~~--~~5. 4. 6. 8. 10. 12 DlWTION. n

AG.1-2 MASS FRACTIONS ANO MOLECULAR WEIGHT FOR

HYOROGEN - OXYGEN -HELIUM SYSTEMS

l

Hydrogen

_Oxygen

-0.9

--I

0

.

11

0.8

--

-

...

< ~, I 0.7 - - j - --- - -- - -~ .. - / -1 , I 1

01

I

I 1

i

I

---

t---

-

-

I

0.3

I

I I

0.6

-/-

-+---+----

-+--~--I

~

1 1 1

I

1 I 0 ! 1

i

-'

!

I

1

I

1 ,I

0

.

5

I I I- I I ::::::;;;;aaa=.-d

J

I

I

0.7

--+---1

-

----+

----L--, -

_.-:.

__

l

L

0

_

8

I

I

I

Hydrogen - Oxygen system

--

~

-

-

j

'

"---,--

- - 7 - ---

J

-

_

..

-

--

--

-~

--

-

-f

~

-

~

~~

-

? ~~

r

~

m

H 2

09

1 : - : I . I

i

-

-

I

! -

-I

I I

--'--t--

--I

!

frdctions

I

0.5

1

-

I

-+---

-

1---

-I

f

I

~

-

.

-

1 - - 11 --- _ - L -! I - _ . . I

--r

-f

I'

~

- .

I

Qj2 _

_

_

+-I

~_

__

i

-

I

.

·

_

---

---t-0

.

1

j

-

--

+

i--

-0.4 --+~I-- --1.

o.

-

- 1.

2

.

3. 4_ 5. 6. 7.

8_

m _9.

FIG, 1-3

MOlE ANO MASS FRACTIONS OF HYOROGEN - OXYGEN SYSTEMS.

\0.

Î - - -i- ---, !

2~-+-1

+-1 -20.---- -- 1. 0.

--

1

----I t I

I

! I.

r

.I

_{I / i}

----

L-

30

_.

j

'

I

I

I

I

! I

25

J

Hyd

rog~n

-

Oxyg~n syst~m

: .

I

J. I O 2 + 2H2 +mH2

I

I

I

I

. I I - : .. _ _ _ : ____ .____ -L. ___ .. ___

+-_

!

i

!

;

. i .

I

I

....

_. , I I

I

. I

-4----

.

2.0

1

, - -- - 1S

_.

J

_i

I

_i

I

; I ~.-.--.---.-.-.- ... .. ---~-.---... --.. ---~---.-t_--- _1.0

-j

,

.

_ =:>- __ Mot~cutc3r

w

~ight

I

I

2.

,

I

I

"- - 1 _! ---. -.

+-

··

---·---~--

--

-

-

1

!

·

_0.5

J

_, . ~

I

3.

4.

5. 6.

7.

8.

m

FIG. 1-' OXYGEN-HYOROGEN MOLAR ANO MASS RATlOS ANO MOLECULAR WEIGHT .

1.0r-~~-=~.~~-.-

___

----~---~----~---~ - _ . _ _ p

=

0.1 atm.

...

.

-...

---- =

10.

"

...

-

'

-

'

=

1000.

0.81--

----'\.--

- -

-

-

-

..

-

_.

~,-_ ..

_

-"

0.7 " -.eilutionJ

,ncO.

" " FIG.2-1a

"'"

0

.

6

1- - ,---''0--- _ .. _---

-

'\

,-

-

-_ ..

-

_._-,,_._.- -._--_._--_.~-,-~ 0.1

0.20

0.18

0.16

0.14

0.12

0.10

0.08

0.06

0.04

3000.

~OH

\.

"

'-

'--.~

'\. ,,~.

4000.

_5000.

p

=

0.1

atm

=

10. FIG. 2-1 b "

=

1000. ./

....~

_{0 .. / '} -~~-+---~,---._--~--~

"

_'\,./

7-1---- --_._- - - ---- -

.

\.

FIG. 2.1 COMPOSITION DATA FOR HELIUM OILUTION H

1.0

0.9

'VH

0.8

0.7

p=

0.1

atm.

.

--- =

10.

1

-·-'

=

1000.

.

- - - -

-

-

_.-

-

-

-

-

_

.. __ ._-

---...:....

_

.

_

-

-

-, Di l ution~,,:._:n.;..;:::..;O::::.--+---'---I

FIG. 2-'

c

.

-_._---'-'---~

0.6

I - - - ----.-- ---+---F--

-0.5

2.

OV"" ",

0.4

6.

0.3

0.2

/ . . / ~ ... .,;.. . / ,./"" /

...

~ ...

--; ' / ...

-0.1

O.

~.

2000.

3000.

4(0),

_5000.

0.20r---~~---~---0.16

-- - --- ----/-_ . 0.14 p= O.latm.

=

10.

=

1000.

/

/ / ; / ' "

-

_.

_

-

/

-

---

-

-

-

-_

.

-

-/

/

/

FIG. 2-1 d

.

0/'

/

- ----I --- ---- -- /';,;;;;- -. 0.1 21--_ _ --1-_

0.10

0.06

/

",,/

/

/

/

/ /

---~~-+~-7---·-~--...,.... '--+-'::"'O";r---=--==-...;,-..,.-_~ / ,./

/

/

/

/-.~­

3000.

""

, /

/

/ " "

/

""'/

7' / '/ -- " l -___ """'-- -. / . - "

'--'

/,~. ~

...

'

4000.

FIG. 2 -1 COMPOSITION DATA FOR HELIUM DILUTION

H₂ and H molar fractions

O.5r---,---r---~

'0

0.41--

_ _ _

_

I I I p:

O.l.tm.

----

=

10.

. FIG. 2-' p

_._. =

1000

.

... -.-- . ----.-.- -.-... - - . -- - - < i f

Dilution

J

0.3~

____

---~--~--. _ .... - I - - - - : - : ' - - - t ----~ ... _---~---~~

0.2

J--- - -

--O.1.~

-~--

--J..,t.H~-

-30)),

_4COO.

0.1r---~---~---~

0.08

,

..

,._

._

.

I p= 0.1a'trTI.

=

'0,

FIG.2-1f

=

1000.

_ __w _ ... I

0.07 Di luti on,} n~O.

.

O

.

0.06

L

---/.

,

I

'

.

/,

"

, /

"

//

.

.

I

',

'

.

-/ -_.~---

---

--

"

- . .~

-_.

/

2

..

...

/

-

-~

--

g..,.. ,

. -.

.,-

J

~

-

~'

.

"

.

.,,,,,"

.

4.

.

/...

2"':0...---'

. /

--

.

.

"' .:..--,

,/

_:;.;"--

.

---6. _'

_;.;.;..

-,

.

"

X

,

~

-'

-

:'><'" --

~

~

,

,'.

_

.

.

~

...

,

.... -

.~.

.

....-

.

-'..:--

~

-s..:.,

--.c-,

.

--

--'

--:::-

.

----

...

,

0.05

0.04

0.03 0.02 0.01

.--

'

.

--:-...:-

-:-

. .

--

---~~~~~~~~~~~~~~~~~.~--~~

..

____

~

__

.J~.J

__

~-~-:J

O.

1& 2000. 3CXXl.

400J.

FIG. 2-1 COMPOSITION DATA FOR HELIUM DILUTION

02 .and 0 molar fractions

1.0

,...~_~w=::-:-:=:---r---~--r---.:v

--~-.-. - - - p

=

0.1

atm.

H 20 ... , 0.8

0

.

7

0.6

0.41--_ '

0.3

0.1

,

"

'--

'

--- =

;0.

-

"

,-,

'

=

1000.

o~o~---~---~---~

- ~ 1- - -

P

=

0.1

atm.

0.18 OH

!

---

=

10.

I

=

1000.

O.

FIG. 2-2 b 0.16~ _ _ __ _ _ 0.14 O.12~ _ _ Dilution ,

0.10

--.

-

-

/'

- ,

O~

__

1

__

'

_~

__

..

__

__

_

_

__

.

__

/--L

_

.

"

~. , / \

/

i

1/

I

X·

-

/

I

. \

--- - --f ----- ·---..

t

..

--·-~/---\

--I

I

I

_~J~

\

I

/r

,r'"

\

I / / . / ' , "

0.081--_ _ _

- 4 -_ _ __ --+

,

-7-

I

--

-'?

/ . v

, \

I' /~

.1

__

4~_;-~,

/

'

I

/

,

~

...

t

,,~

0.06

0.04

0.02

/

.//'

- - - - : - -

.-<',

"-I /

~/

.... /

1

6.

, /

"-~ &/-L

__

.. _

2.

X, "

~t--~~--~~/'/' I - . / / / / / ."... 4. / ' ./'" ' / " . , ' . I . / ' _ ... ~. / ' -

,--

----

~'

...

--'

---

'

3000.

'ü(l).

FIG.2-2 COMPOSITION DATA FOR HYDROGEN DILUTION ,

H20 and OH molar fractions

1.0r---.---~----~---~

~H

0.9 I

0.8

--_.

_

_

. __ . . __ .. , - - - p

=

0.1 atm. :

0

.

7

0.5

0.5

0.1.

0

.

3

0.2₁ _ _ _ 0.1

=

10.

=

1000. I '

·

·t

·

I

I

-

-

--

-

.-

-

r

-'-

-

-.

I

FIG. 2-2

c

/ ' / / '

1.0r---~----.---~---~

p

=

0.1

atm.

0.9

i

H2

---

=

10. _{FIG. 2-2 d}

-

'- ' =

1000. _, i

0.8

-.. -- .. -... .... -- ... . ... - -·i· - -- -- - ... - -.---.----... - -... .

-~_:.::=_

_{___}

.

_+.-._.

_{- -._} ~ fIOiluticn ' J 0.4

0.3

0.2

0.1

. - 1-. _ _{I _} - . ~_, . --m~5. _{. ___ .} -oooÀr--=-:.-::-::::' _ .

==1:' - . .::::... .

I - - . . - - _ ' " -,--,~. J - - . -~, ' ~.'" -- ·----·~----f---· .~....:.:.:----:-... 5 _._-..

--t

- _

..

-~

-

-

-5.

i ... I. " . , ' - - . 1.. : ' , '

I

' ...

"

.==-:::..:.:::c-._._.~~+. 2 -- --- -- 2 "" '-

r,

--.---.--.!..-.

.

-

--

L

--.

=::-

.: ----

-.

-

.

-.

:

,~

_-.

I " " " , ' ,

,

...

""

,'-

. ... ',"-.::::--.,

'"

.

...

"'"

~

-

_.

-

---

--"

-

-

---~---_....k=_- '> ~

o.

O

_.

-

- - -

- - -

-.

_--.

-~~

_~-~

-- ;..--'

.

--

.-

----=--

-

--

~

"

. --.~

-. -. I

O.I:::::.~J;;:.;;:.~~.±:::.:.:r:::~!...

...

..L...l..-....l-...L....J...J

2000.

3C00.

1.(0).

TOK

_J 5COl

FIG.

2:"'2

COMPOSITION

DATA

FOR

HYDROGEN

DILUTION

0.5r---~---~--~---

___

: _____ p

~

)

~~1

atm.

I

,

~O

FIG. 2-2 ~

_._. =

1000.

I

-

r -

-

----

--

-

,

0.4

-

-

- - _

.

_.

-.

-

- .

.

-.----

--_

...

__

._.

_--.

0

.

3

.

___ ..

_

..

___

_

._0-_ ... . . .

. .

.

-

-

...

...

. -

1...- --.---

-.1

0.2

! , / 0.1 , /

O /

.

/ 0.1r---~~----~----~---~---

___

0.08

0.06

0.02

----

""

1

'--i

Oilution J

m

=

O. I p

=

0.1 atm ..

=

10.

=

1000.

.

i I I

.

-

--.

-.

--

.

.

.

---·

t

-

·

! I FIG. 2-2 f

_ _____

1

---

__

.

_______

.- - - - 1

FIG.2-2 COMPOSITION DATA FOR HYDROGEN . DILUTION 02 and 0 molar fractions

20.r---~---~---~---~---~---Moltacular wtaight

gr.1

molta.

18.

~KI

16 •

...,....=--_

14 • ...",c--_ _ F - t _

0.1

1.

Dilution n

=

m

=0.

10.

100.

1CXX). 1<XX)().

Moleocular weoight

12. gr.1

moleo.

a) Oilution , ,n

=

2. } m ~.O.,

4.L-______

~

______

~

______

~

____

~--~----~~~---J 10.r,

---r---~---~--~----~---~---b)

Oilutlon n=4. m=O. 4.~

______

~

________

~

______

~

________

~

______

~

__

~

__

~ 8.r---~---~---~~---

__ ---__ ---__

0.1

1.

10.

100. 1000.

10000.

12.r---~---~---~---~---~ MolE'cular . WE'ight gr: I molE'. 8.~-- ~-6 . ..--~--~ ,

-

'

.-

----

t-

..

---

-

----

-

-I

I

---+~~~,c... ~~'-+_--~

-+

---a.Dilution: m=

2.

n=O. 8.r---~---~---~---~---~~~----_ 6.~-~-_ - + - -" -

--

t-

- - - t b.Dilution: m=4.

n=O.

2.L-______

~

________

~

______

~

________

~

__

----~~----

__

~ 8.r---~---,_---_,---~---~---~

0.1

1.

10.

100.

c. Dilution : m =6.

n=O.

.

1000.

FIG. 2-5 MOLECULAR WEIGHT FOR HYDROGEN DILUTION

'\

>

a..

...J

«

:r

t-z

W

-20

. .

-40

-

-_ . ..

~

-

q:

..

_._-•

I

. I I Dilution: m = n =0.

-

60.~

_ _ _

...,j"".., _ _ _ - ' -_ _ _ ,""""",, _ _ _ ...I. _ _ _ " "

0.01

0.1

1.

10.

100.

1COO.

PRESSURE I AlM.

70.r---~---~---~---~---~

Dilution:

~~~~~~~~~F~

m

=

o. ;

n

=

2.

60.~

~

;:---"

""""

-~i---

-I--

- - - I 50.~---""""

40.

-~

30.

o

~

-' <{ u ~

1 O.

I---'\.--._--~_. -10 ... =---~..-±- -- - - --t---- -

---20.~---

_0.01

__

_0.1

---~---~

_{1. 10. 100. 1000.} PRESSURE , ATM.

60.r---~---~---~---~---_

\ '

30.

w

...J 0 ~

'"

...J

_20.

ct u ~

10.

-10.

~---~---~---~---

..

0.01

0.1

1.

10.

100.

1000.

PRESSURE,ATM.

6Qr---~---~---~~----~---~

Oilution

m

=

0.;

n

=

6.

'O.I----~~

~

30.

o

~ ...

<J

u

~

20.

10. -10. ~ _ _ _ " ' _ _ _ ..I.. _ _ _ .""' _ _ _ ~~ _ _ ~

0.01

0.1

1.

10.

100.

'000.

PRESSURE I ATM.

60.r---~---~---~---~---~

Dilution:

m=O

.

; n =8.

50 .

. - - ----'---+-- - - --- --t- - - - + - - - - -+---:;---- - - 1

-10.~

____________

~---~---0

.

01

0.1

1.

10

.

'00.

PRE55URE, ATM.

.

80

.

, - - - r - - - r - - - , - - - r - - - .

50.

w

40.

..J 0 ~ ... ..J <{

30.

0 ~ ....

~

..J <{ :L

₂₀

_.

_-

_-

-- t-Z W

10.

-10.

2200

.

,

-

-

-

-

-

-

-

.

2000.

Dilution : n=O. m=2

.

-20 ... _ _ _

,.,."".--_ .... _ - _

... _ - _

... _ - _

...

0.01

0.1

1.

10.

100.

1(0). PRESSURE ATM • _•

SO.r---~---~---~---

__

I

Dilution :

I

n=O.

60. m=4.

50.

w ...J 0 ~

-....

...J

«

u ~ ~

..

...J <{

30.

l: t-Z w

20.

10.1---O.

--- ,- . --- - _.- ._. t - -- -- -.-- --10.~

______________

~

________

~

______

~

______

~

0.01

0.1

1.

10.

100.

1000.

PRESSURE J ATM.

W ...J .

o

~

""'-...J 80.r---~---~---r---~---~ 70 ...

-

=-60.

50.

Dilution

:

n =0.

m=6.

--

l

---

-

-<l:

40.

u ~

10.

2200.

'

200~' O.r---~~·+· -~-~_._~--~.--~--~.+- ~- ~---~-_.~- ~_.~

..

~

.

.

_~--~-.~--~. ~-~~._~---~-~~

-10

.

.... _ _ _ _ _ _ _ _

... _ _ _

... _ _ _

... _ _ _

...

0.01

0.1

1.

10.

100.

1000.

PRESSURE ATM

..

;> ~ cJ)

z

w

o

100.F-~_~

1.

F""":-::::_=

> t-.l/') Z W

o

-~. I 10 ...

....

._

.

.

-- • ~ _. t

-35r---r---~---~

p =0.01 ~tm

----30

I---

-

--

~~

-

~

--+-

.

(

3 l

n'VH 20\

.

3lnT

lp

-25.~

--20.

-15.

-10.

- 5.

oilution m=n =0.

O~~~~~==~~~-L~~~

2000.

3000.

IJ)OO.

TJoK.

sexX).

FIG. 3-1a LDGARITHMIC OERIVATIVE OF H20- MOLE FRACTION W. R.T. TEMPERATURE AT CONSTANT PRESSURE

14.r---~---~---~---~ 12. - ._

(~!~:~H)p--

-

..

j.

_.

_. __

I . . . __ . - ... - - - -- - - f i 10. -... - '.'

·

1

. _...

.\

...

-

._-

_

.. 8. .- ---- .

-.

.

... _

.. __

.~+

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_

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.

.

_

~

6" ----.. -~ .

j

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.

.. -

.

.. -

-

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o .

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....

.

_

..

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.

.

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--- 1.. ..--6 . .

-8

.

..

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.

_ ...

.

0.01 -14.~

________

~

__

~

__

~~~~

__

~

__

~

.. __

~

__

~

__

~~

__ _

2000. 300J 4000. TJoK. 5000.

FIG.3-1 b LOGARITHMIC OERIVATIVE OF OH MalE· FRACTION W. R.T. TEMPERATURE AT CONSTANT PRESSURE

12.r---r---~---~

10.

8.

6. - - ---1..

2.

O.

-

-

-

---

-

--

-

---I.. -- - -- ----6. --- -- --8. -10.

-12.

! i - --.j.- --- ---- -- -- ---- --- --- - -- -! _I -- --- - - ---1 ~~~_'-- . - -.---t - --- ---1 ! , -11..'-'--" _ _ _ _ ""'-~ __ _"'__~ ___ ... _ ... _~...I_""""""_

... ___

~

20CX). nlO. ID)(). T ,oK. 5CKX).

FIG. 3-1c LOGARITHMIC DERIVATIVE OF H2- MOLE FRACTION W.

R.

T_ TEMPERATURE AT CONSTANT PRESSURE

12.r-~--~---~---~---~~--~ 10.1---8. ! . ... -... _- .---r .. -.-.-. --- - . -.. ---.--- 4 - -- . - - - , - - - --'--'----I 1..

~

.-

.. ;

-

_

.

_

..

_._--

--

..

_~

+----

~-

'_

.

_.

~

. • .l. ____ _ __ _ -'-. ~-,-'--_ _ _ -I

6.

2.1--...,---0.1--

-..;.2.

-4.

-6

.

-8.

-10. -.-- ----.---- ....: .. -.--'--:-.-.---... ----... --.:-- ---.~<"--~--'----~ -12. -16 ... _'--... _ ... _ .... _""'-_~ ... __ · .. ' _ ... - - - - -....

,-....i.---'

2(0).

DXl.

1.(Xl).

T, oK.

5000.

FIG. 3-1 d LOGARITHMIC OERIVATIVE

CE

02- MOLE FRACTION W. R. T.· TEMPERATURE

AT CONSTANT PRESSURE

2Qr---~---~·---(a~~n~H)p

~-

~-

-

--

-

----~-

-

-+,

_ _ _ _ _ _ _ _

_

18.

---

---

!---

-

----

-

--

--

--

--

-

t--

.

- - - ' - ' - - - I 14. -.-- ... _.-_. -'- .---..

--

--.

----t

--16. .---.

I

12.

.. _.

__

_

_____

___

.

__ .

..

.

_

..

L

_

_

__

____

_ _

...

.J 10.

---.:----.-::

.. --

-

:

-

.. -t

-.-

-

.

- -- - - I

s.

6.

o.

L-.J-.-J...J._.L-..L.-J..--I:::::::::b...J....:::::::;::±;=*=-.;J:::::t:~

2000.

no.

4000.' T,

OK.

scro.

22.r---~---~~~~~---20.

~

.. -

(~~~n~)

P

- - - -

...

f

'

-

-

. -

.

--

...

-

...

-

...

-

----

--

---

-

-

-

-

--

-

-.

----

--'----'-~

18. --.. -.... -.----.--... -.-- +

I

--.--- -'--'--'-- - .. --- - - - - -.. - _ ... _ - - - - ---1 I

,

I

.

.

-

-

- ----·-

r-

-

- -

-

- -

-

-

-

- -

-16. 14.

I

12.~

---10."

-8. - ---- - -.--.---... 6.

4

.

--

·

._------ ._-~ ... _ .. - -

.

. 2.

o.

L.J...J..--1._l-.~~__l.:::::~.J...:::::~

__

~J:::=~

2000.

3000.

4000. 5000.

FIG. 3-fe LOGARITHMIC DERIVATIVE OF H andO-MOLE FRACTIONS WRJ.TEMPERATURE AT CONSTÄNT PRESSURE

2.0

r---:r---:::==r==---::::::===---,

( }ln'i'H20) I p=0.01atm .

1.6

blnp T

-

- - - -

---

--

_

... _._.

--

-

-

~

---

-

-_.

Oilution

:

I

m =n =

O

.

I

_._---_

.

_. _.

-

-

_.

-_.

_._

-'---

_.

-

+

.

I

1.'

1.2 1.0 0.8 .---.. -. -- . -- --0.6

0.4

0,2 ----.~. _ ..

I

··-

r-

--

--.-.

-

-.

-.-

L

---

---.-- -- - - - 4

I

J

1.

.... ---~: - .-.- ---- - - --4'-- - 1

I

--

-t

-

---I I . . ..

._._

--~

-

_

.-

-_.

~_

.---I

I

I

. -

-

..

-

.

_.

-

---

-+

, I

I

---_ .. ~-_._--- _.

I

I

4000.

5000.

FIG.

3-2

a

LOGARITHMIC OERIVATIVE OF ~O-MOLE FRACTION W. R. T. PRESSURE

AT CONSTANT TEMPERATURE

1.0

r---r=~-_:::=::::::-l___:=======...,

(

ëHn-V

_alnp

OH)

_T

0.8

-

---.

- - -

-

-0.6

0.2

-o.

- -

-.

---

-.

---

--0.2

~oo. ~.

sooo •

. FIG.

3-2

b LOGARITHMIC. OERIVATIVE OF OH-MalE FRACTION W.

R.

T. PRESSURE

AT CONSTANT TEMPERATURE' 5toichfomE"tric mixturE"

1,0

r----~--!_:_::~-__:::::=:::::::=-..,.-___:=====--_..,

0.8

0,6 - - --- ---+-~

-0.4

0.2

0,

-0.2

I--- -- ___/_

-0.4~~

__

~~~---~~---h--~--~~--~---~---2CXXl,

3000.

4000.

T , oK.

SCXXJ.

FIG. _{3-2c LOGARITHMIC OERIVATIVE OF H2-MOLE FRACTION}

W.

R~ T. PRESSURE

AT CONSTANT TEMPERATURE

1.0

r...,....---T----==::::::::::=.=r~~=======9

(

~l

n

"V

₀

2.)

-

-~lnp

T

0.8 1--

-

-

-

-

-

--

---

-

--

--+---+---=-:~-- -+-I

I

0.6

~---_+

0.41--

-0.2

o.

-0.2 ..

~- -I I i

AG.3-2d LOGARITHMIC OERIVATIVE OF 02- MOLE FRACTION W~ R. T. PRESSURE AT CONSTANT TEMPERATURE

-1.0r---r---~---~

.

_

(aln)7H\

alnp JT

_I

I

.

- 0.8 .---.-- - - -'--' - -'-'- ï "--'---'-'- .---.---

~--0.4

-0.2

I I

I

, O.L-...l...J_l-..J..--l_J...J.:~===-

....

_~t====~_.J....;~

2000.

3CXXl.

1.000.

SCXll.

-1

.

0r---~---~---_,

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(

ÖlnYO\

.

.

ölnp

"}r

-

._--

.

_-_

.

.

.

.

. .

..

-

..

.

--

_

.:~

_{.. -}

_{-_}

_.-

_-

_-1

_..

_-

_-

_.

_.

_{__}

_.

_-..

_.

_.

_-

-. I

I

- 0 .4

..

. ---

..

_--

.-

-

_

.- ..

.

.•...

-

-

.

-

.

....

-

.

-0.2

-O·L-~_~.J...,;....J_J_...J.._J....,;;:::.

_ _

~=====

....

IIIIÏI_.~ïiiiiI

2000.

DJO.

t.aXl.

T ~. 0 K • SOClO.

FIG.3-2E' LOGARITHMIC DERIVATIVE OF Hand O·MOlE FRACTIONS W.R.T. PRESSURE AT CONSTANT TEMPERATURE

-4.5r---~---~~----~---(

Mnp

_MnT

1

_p

- 4.0

_

___

___

_

p:=_Q.O~t~.

-3.5

-3.(31---2.5

---- - - --- -+

-- 2.0

- -

--

-

--

-

--

--1.5

-1.0

- -

--

--

-

-- 0.5 - ---- --- - - ---_._---

-

_.

_

-: . I Dilution:

m =n=O.

.-_. t ---.---.- ----

-FIG.3-3a LOGARITHMIC OERIVATIVE OF MOLECULAR WEIGHT W. R.

T.

TEMPERATURE

AT CGN5T~~NT PRESSURE

-4.0r---.---~--~---~~~--_

(

Öln~

)

-

_

MnTp

p=0.01 atm.

I

I

I

-3.5

--

...

-.

-

---

.

-

.

-t··--·-·----·--~----··-·-- .-.-. f'-' "- .. ' .. .- -.- - - t

-3.0

:

I

I

I

n =0., m=2.

-- -._-,

---

-

'.

---.---.. -

-.--

--

-

..

.

--_

. -

..

--

1---

_I

-

---

-

-

-

- - - . ! . . --Dilution:

-2.5

-

-

-

-

- -.

.

...

-

...

--

--.-

"

-2.0

-1.5 -1.0

- 0.5

3000.

IDJO.

5000.

FIG. 3- 3 b LOGARITHMIC DERIVATIVE OF MOLECULAR WEIGHT W. R. T. TEMPERATURE

AT CONSTANT

PRESSURE Hydrogen dHution

-3.5r---~---~--~--~--~~~---( _~lnT

~

l

nJ.l)

_p -3.0

-2.5

~---

-

-

--2.0

-1.5

-1.0

-

-

'

- - -

.

-

--0.5

Oilutlon:

n

=0.

'

,

m :-' •. 5CXX).

AG_ 3-3c LOGARITHMIC OERIVATIVE OF MOLECULAR WEIGHT W. R.T. TEMPERATURE AT CONSTANT PRES~E

-3.5 __

---~---~---~

-

(~)

~lnT

p

-3.0

-2.5

---

-

-

---

.-

-

-.-

..

-2.0

-1.5

-1.0 - 0.5 - ---.. --p=0.01

atm.

-

-

.

1

-· ---

.

-

-

.

- -

---

--

--

--

---·

f

-

---

-

---

-

-

-I

I

I I ! Oilution: n =0., m =6. i - _._- +---- - - -- _._ - - - - 1

FIG_ 3-3d LOGARITHMIC OERIVATIVE OF MOLECULAR WEIGHT W. R.T. TEMPERATURE

AT CONSTANT PRESSURE

0.20 __

---~~---~---~

(

Mn~)

~lnp

T

0.181--_

_

_

0.161--

-

.

--

-

- -.

-.

-0.14

0.12

_

___ -

....

-0.10

0.08

0.06

0.04

0.02

Dilution

:

n = m =0.

O.~~

. .

==~=C~

__

~~--~~--=:==~~--~~

2000.

3000

.

4000.

T ) oK.

SOOO

.

FIG. 3-4a LOGARITHMIC DERIVATIVE OF MOLECULAR WEIGHT W. R. T. PRESSURE AT CONSTANT TEMPERATURE

0.20r---~---~---~

0.18

(

_~'

è)lnp/T

Dilution:

n

=0.

J m

=2.

O.16~---···-·-··- _.-...

0.14

I

0.12

- - - -

,

-

--- - - -

. .

-.

-r-

I i !

0.10

~----'

---.

-.----

-

.

t-

-.

0.08

0.06--0.04

3000.

.-... --.--~.--.. - -_ _ t

4000.

FIG. 3 -4b LOGARITHMIC DERIVATIVE OF MOLECULAR WEIGHT W.

R.

T. PRESSURE AT CONSTANT TEMPERATURE

"

0.18

(~lnv)

_nnpT

_.

.

_0H2+0~

.

0.16

p=0.01 atm .

Oilution:

n

=0.) m=4.

0.14

0.12

0.10 1 ' 1 + + 4 '

-0.08

I---I---~-#- ·-+---0.06 ~----+----I--~-

--I---\-0.04

I - - - I -. l '

-0.02

~--+---f---f---+-+----4.d

FIG. 3-4

c

LDGARITHMIC OERIVATIVE OF MOLECULAR WEIGHT W. R. T. PRESSURE

AT CONSTANT TEMPERATURE

Hydrogen dilution

0.18

r---r---r---Oilution: n

=0.,

m

=6.

0.14

--_ . --_.--t-

.-0.12

1 '

-0.10 1--

1

-

0.081----0.06

0.04

..

4 L

-0.02 .--

--#-I I

,

D)(). -~-.---~----__f

4000.

5000.

FIG.3-4d LOGARITHMIC OERIVATIVE OF MOLECULAR WEIGHT W. R. T. PRESSURE AT CONSTANT TEMPERATURE

1~.r---~---~---~---~---~---Cp

.

C.al

I

mole

0

K

140'~---4,~---4---+---+

__ __

120'~

______

-H~ ____ ~ ______ . __ +-______ -+ ____ ~ __ ~ ______ ~

Dilution:

.

n

=

m

=

O.

.

100.

~---+---'\---+---c-80.~

______

~

____

~~

________

+-______ -+ ________ ~ ______ ~ .60.~

______

~

____

~~~

______

+-__ ~. __ -+ ____ __

Pressure

_J

atm.

O.~

__

.w~~~~~~~~~~~~~~~~~~~

. .

~

0.01

0.1

1.

10.

100.

1000.

10000.

160.r---T_---~---T_---~---~

Cal

I

mole oK

Cp

140.~---_+~---+_---._+---+_---_+---~ 12Q~---_+~---+_---_+---+_---+---~ 100.~---_+---+_-- ----_+---80 .

...---+-\.---l---_+::

ion'

"_=_2_. _' m_= __

o.-+-

_____

~

60.~---_+--~~~+_---_+.---+_---_+---~

40

.

...---+---'----~~---___+_---3~--_+__-.---~t__---_t 20.~---_+~~---+_----~~~~---_+---~~---~~~

10000.

120. __

---~---~---~---~~----~ CalE' I molE'

oK

Cp

100.~---_+---+_-

_

____

~---~---~~----~

80.1--

__

_

_

-+ _______ _

-

-

-

-

-

-

-

~

--

-

-

--

-4--1

~

~~

Oilution:

n:4.,m:o.

1

60 .I-#-_ _ . _ _ _ -+-~

-+-

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.--1

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1.

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100.

1000;

1CXXXl.

120. r---~~__r~~ ____

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Cal I mole oK

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oK.

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Dilution:

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100.

1000.

10000.

1.65 r---r---r""""":"""---"T""""'---r---,r----~

I-\---;~r-I TEMPERATURE I oK. - + - -- - - t - - - + - - -- - I m=n = O.

1.

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1.

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1.

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FIG. 4-4 ISENTROPIC EXPONENT

>Ö

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1. 10. 100. PRESSURE I ATM.

FIG.4-Sa ISENTROPIC EXPONENT

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cr:

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1.

40 1.30 1.25 I-- - - - \ ... ~ TEMPERATURE ,oK.

5000.

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FIG. 4-Sb ISENTROPIC EXPONENT HE'llum di lution

...

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1. 10. 100. PRESSURE , AlM.

FIG ,-Sc ISENTROPIC EXPONENT

Helium dilution

~

t-z

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FIG'.4-- G,a ISENTROPIC EXPONENT

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FIG. 4- 6 b ISENTROPIC EXPONENT

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FIG.4-6c ISENTROPIC EXPONENT

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FIG. ''';'8 .

a

SPEED· '

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FOR

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1.

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1000.

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..::-....:=:=.

A

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a. Dilution·~ m::2. n::O.

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-\

5 0 0 0 . , . . - - - r - - - , . . . , . - - - - , - - - r - - - r - - - - , . . . - - - -....

m/sec

• _{4000 .} 2000.

Preossureo

J atm.

0.1

1. 10. 100. 1000. . 10000.

6~.r---~---~---~---~----~~---~

m/sec

3000.

I

2000 . ..--

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1

0.1

1. A - - - - A-A1 c. Dilution· : m=6. n=-O. ----. -.-- - ---_.--- ---_.-r=--~~j;:j

--

1

--

-PrE'ssurE' J atm.

10.

100.

1~.

10000.

FIG.

,-ge

SPEED OF SOUND FOR HYDROGEN DILUTION