W 0 o-'y-aw , t, '

A60 YJ Ay- ao 0

own,

AWN IS iP- tT' 9 ~''~ ~ ~~"o6 ~ 9~0o oQ'< I

-0-W

N v- -os2 Q tV~< t

low- v0

N O W Tx9~ -- P'

A 00'

00 P. to o ~400 0 T

e6 -0 46 /x ' a

X 6al rs M/Q~'

0 4g - "t"0~

191 al ' o0 -son1

00040'

_____ - >0, o~t>SOP

Li~t ____ 'b-i,< <____ vow4

Too! k t.a ____ _____ __

- 4 -t~Q4 t~t ~0 0 4- 0<

__ _____ _ 6 e

4 ~ ~ ~ ~ ~ ~ ~ ~ e n so-"' 4.- -- -- -'- 1< ' ' 0 -' ;-46< >'0

4 x

------- 0.~~~1 IX46~ -:4-

4 4 -<c'> not

. PHYSICAL AND THERMDYMI"

T311

8i

R. T. Cal defllD. M. Walley

The Garrett CorporationAiResearch Manufacturing Division

0

II

Ui I

0fi

This report was prepared by the AiResearch MnufacturingCompany of Arizona, a division of The Garrett Corporation,Phoenix, Arirona, as a part of the SAP 50/SPU liquid-potassium 1Rankine-cycle power-system pam. The activities discussed intbis report were initated mefr United States Air Force Con-tract AP5(615)-2289 LBM-: 5(63.99-657)634o9l23. This contract Iiwas administered by the Flight Vehicle Power Division, AF AeroPropulsion Laboratory, Research and Technology Division, -AirForce Systems Command, Wright-Paiterson Air Force Base, Ohio.Wr. C. H. Armbrus ter was the Proj ect Engineer for the Laboratory, Ind Mr, R. D. Gruntz directed the MW 50/SPUR engineering pro- I

Zram at AiResearch..

The authors wish to express their thanks to the many indi-viduals who aided in this work, either directly or through theirpublications. A particular debt is owed to C. T. Ewing of the InNaval Research Laboratory, A. W. Lewmwn, Jif. and H. W. Deem ofBattelle Mmorial Institute, F. M. Tepper of MSA Research Cor-voration, A. V. Grosse of Temple University, W. D. Weatherford,rr. of Southwest Research Institute, and Harold H. Coe ofNato"1 Aeronautics and Space Agency, Lewis Laboratory. I

This report presents an up-to-date compilation of thephysical and thermodynamic properties of potassium.

This report is assigned supplementary report number 1,APS-5,1 .OR by AiResearch.

This report was submitted by the authors July 1, 1966.

Publicatior of th3i report does not constitute Air Force&pproval of the findings or conclusions of the report. It isPublished only for the exchange and stimulation of ideas.

i

-1

ABST _CTfii

This report is &n up-.to-date compilation of potassiumphysi-al and thermodynamic properties. Data for the solidphase is presented, where available, over a temperature rangefror OOF to the melting point. Liquid and vapor physicalprcperties are tabulated, Ln -most cases, from the meltingpoint to 24OO0 F. The thetrmodynamic compilation extands fr-m7t4G- F to 2q1 00F and includes superheated vapor propertiesevaluated at pressures do;n to 0.1 psia. These properties arepresented btn oan a table and on a Milier diagram. Listedproperties inc!ue density, viazosity, surface tension,electrical resistiivty, ther--1l conductivity, Specizic heat,vapor pressure, latent hea-ts of fusion and vaporization,enthalpy, entropy, acoustic velocity, critical pressure andtemperature, thermal neutron absorption and activation cross Isections, ionization potential, and relative magneticsusceptibility.

[,

. ... -"--... .- *-

TABLE OF C~ONTENTS

il POIT VALUM PROFMTL1ES 3T21 PHYICAL PROPERTY DISCUSSION 4

A. Properties of Sol'i4 Potassium 41. Electrical Resistivity

2. Thermal lonductivity 4Specific Heat 5

B. Properties of Liquid Potassium 5

1. Density 5

2. Viscosity 6

3. Surface Tension 6

-. Electrical Resistivity 7

5. Thermal Conductivity 76. Specific Heat 8

C. Properties of Saturated Potassium Vapor 9

1. Vapor fpressure 92. Specific Volume 93. Heat of Vaporization 10 B4. Viscosity 10

5. Thermal Conductivity 11 H-IV THERMgDYNAMIC PROPERTY DISCUSSION 13

A. Review of Published Data 13

B. Thermodynamic Computations Employed 1in This Study

C. Description of Computer Program 15 nD. Computer Equations 16

V REFERENCES 23

TABLE OF CONTERTS Contd.

APPEIDIX I Saturation Properties of ?, assium 49

U APPENDIX II Properties of Superheaded Potas~ftumVapor 51 1Potassium Mollier Diagram Attachment

Ifr;LI

•J N

LIU

4

LIST OF TABYU

I Sunm~ay of P -i= rm int Value hropertieg 26111

11 Nuclear Data for P-0otaaium- 27

iII Sources of Informi ton on PhyFicaIProodrtiees 6of Solid Potass1.t11 2

IV Proverties of Solid ftesam 29

v Scoirces -f Iinf rntion on PhysitalProperties of Liquid Foa~ium 30

vi P tteg of Liouid -Ptsium- 31

VII Soutnces of Irn-ortat1.on on Frp~rtiesof Saturated 'Potassiumi Va-por 32

VIII Proparties of gaturatzd PotiasiUm IIVapor 33IrIi [3i

LIST OF IGURES

Figure

I Electrical Resistivity of Solid Potassium 34

2 Thermal Conductivity of Solid Potassium 35

3 Speciti- Heat of Solid Potassium 364 DernsiLy of Liquid Potassium 37

5 Visocity of Liquid Potassium 38

6 Surfa1.e Tension of Liquid Potassium 39

7 Electrical Resistivity of Liquid Potassium 40

8 1hermal Conductivity of Liquid Potassium 41

9 Specific Heat of Liquid Potassium 4210 Potassium Vapor Pressure 43

i It ..as. .UM Saturated Vapor Specific Volume 44

12 Potassium Heat of Vaporization 45

13 Viscosity of Saturated Potassium Vapor 46

14 Thermal Conductivity of Saturated Potassium 47~Vapor

15 Specific Heat of Saturated Potassium Vapor 48

IA -A9I[

4'

v~i

".~ I4-.

SYMOBLS AND UNITS

P Electrical resistivity, micirohfh-in.

- Temperature, OF

T Temperature, "R

k Thermal conductivity, Btu per hr-ft-°F

C Equilibrium specific heat, Btu per ib- "F

d Density, lb per cu ft

Absolute viscosity, lb per ft-hr

a Surface tension, lb per ft

H Enthalpy, Btu per lb

See Section IV D, page 16, for the symbols used in the FORTRANprogram to compile the saturation and superheat propertiesappearing in the tables of Appendixes I and II.

IU

Vii

SECTION IINTRODUCTION -

Over the past several years, interest in the use of liquidmetals such as potassium, sodiumrubidium, cesium, and others

has grown to such an extent that the need for more accurate andmore complete information on the physical and thermodynamicproperties of these fluids has intensified. As a result, sev-eral independent laboratories, including the U. S. Naval ResearchLaboratory, Battelle Memorial Institute, and NSA ResearchIi Corporation, have undertaken considerable experimental workunder Air Force and NASA sponsorship to evaluate these~properties.

Of all the liquid metals) potassium appears to have thegreatest potential value as a Rankine-cycle working fluid. Thespecific volume-pressure characteristics of potassium vaporpermit reasonable turbomachinery sizes and operating pressurelevels over a wide range of cycle power output. Good cycleefficiencies can be attained with potassium at temperatures lowenough to permit the use of relatively conventional materialsof construction such as stainless steel. Substantially higherefficiencies and reduced system weight can ultimately beattained at the hieher boiler temperatures permitted by the use

i U of refractory metals. In addition, potassium displays thefavorable heat-transfer characteristics of all liquid metals,and its feasibility as a'bearing lubricant has been experim-n-

Ltally verified. For these reasons, potassium cycles are underactive development or consideration for use in space, marineapplications, topping cycles in steam plants, etc.. whichdictates the need for accurate potassium properties.

An extensive review of the published literature relatingto potassium has revealed inconsistencies in the property data,L, especially in the high-temperature region where experimentaltechniques are hampered by conLainment problems and difficulties

f in temperature measurement. In some instances, the publisheddata is considered reliable over the range of measurement, butis not very useful for cycle calculations encompassing lowerand/or higher temperatures.

The purposes of this study were to conduct an exhaustivesurvey of potassium property data, identify the most reliablesources of information for each property, and compile theresulting data. In some cases, where equal weight was assignedto scattered data points, a least squares curve fit was utilizedto establish the working equations used for the compi.ation. lnall cases, selections were made to insure that this document isintcraally consistent.

The scope of this report g s limited to the physical, thermo-azc,aad s of the rlea properties of potassium. For

tee c -nvenience of the user, all charts, tables, and graphs arez=esented in appendirzes in the final section of the report.

Preceding these appetdixes a discussion of the physical proper-ties and themodymic treatment of potassium is given, alongwith a list of the references that were actually used to deter-mine or supp*rt the Pxopety dal-, selected. The list of refer-ences is" not a cavIete cempilation of everything that wasexamined during the ¢corse of the study.

The ata is presented in unjts that are in ccamon usage Binthe engineering coommity of the United Statei..

This document is intended to be used as a replacement forthat portion of Reference I which covers potassium. Reference 1has fi led a vital requirement over the past few years in stan-dardizing property data in order that everyone workizg in thefield would be using the same basic data. it is considered tohave been very well done. However, since its publication, agreat deal of additional work has been done in establishing the Lproperty data of potassium (and other liquid metals); according-ly, an updating is very much in order. Weatherford, in Reference2- also makes this observation. Since References I and 2, like Uthis documet, do not report any original measurement or propertydata, they are not listed as a primary source of information butrather the ^rig-la! seturce was quoted, when applicable. In somecases, the data does indeed agree with Reference 1, but in mostcases, additioral later measurements have been made which super-sede this work. Reference 2 contains some updating and the sug- 1gested values in that reference for many properties Agree withthe choices made herein, whereas in other instances later workagain superseded them.

This document is also more complete for potassium 'thanReference I in that mire properties over a -wider temperaturerange are included. In particular, the thermodynamic propertiesare included ip the form of superheat .ables, saturation tables,equations that can be incorporated diro-ztly into a computer pro-gram, and a Mollier diagram of substantial size and accuracy.All other properties are reported in the form of graphs, tables,and equations which can be incorporated in a computer program.

Additional property measurements in all instances would, ofcourse, increase the reliability and accuracy of all the property,data reported, but several properties in particular nee' morework efore a high confidence can be placed in the selected data.These include critical point values; the electrical resistivity,thermal conductivity, and specific heat of the solid; the spe-cific heat of the liquid at higher temperatures; and the vis-cosity and thermal conductivity of the saturated vapor.

11

U 1I

SECTION IIPOINT VALUE PROPERTIES

The sources of the point valies selected are indicated onTable I, along with the values themselves. The succeedingparagraphs supply amplifying comments and reasons 'or theselections when appropriate--a practice that will be followedthroughout.

The melting point, heat of fusion, atomic weight, densityof the solid, ionization potential, and relative magneticsusceptibility are essentially handbook values which weretaken from the sources indicated and which are more or lessaccepted and/or substantiated by later work to the accuracyindicated.

The boiling point and heat of vaporization were taken fromReference 3 for reasons discussed more fully in Section IV.These point values are repeated here fcr convenience and forinternal consistency.

The critical values are taken from the work of Grosse asreported in Reference 4 and other publications by the same'author. Novikov. Reference 5, and others have estimatedthe critical point values of potassium with widely varyingresults, but the work of Grosse appears to be betterIsubstantiated by both, the experimental data and by theory.

The nuclear data in Table II is of a different naturethan most of the data in this document, but is includedbecause of the widespread interest in the use of potassiumwith nuclear power sources. References 6 and 7 are the mostrecent soi'rces known for this information.

Li

13q'32

PHYSICAL PkMCT DlISCUSSIONi

: "A. Proa:Etlas of -Solf o.asu

I. Electrical Resistivity

Althaugh the electrical resistivity of solid potassiumshould be a relatively easy property to measuze over a range of Litempqraturea, only a limited number of measurements were foundIn the literature, and these were limited to a restricted tem-Verature range or were single-goint measurements. Sources ofdata used included References 3, 9, 10, and 11. A straightline equation is considered sufficient to represent the limiteddOta available. The equation derived is:

p = 2.06 + 0.0096 t

where p = electrical resistivity, microhm-in.

t = temperature, Oy

This equation is considered valid over the range from #OFto the melting point and was used to prepare Table IV and

2. Thermal Conuctivity

Very few directly measured values of thermal conductivity B Ifor solid potassium were found in the literature. Accordingly,it was decided to estimate this property from the electricalresistivity by means of the Wiedemann-Franz-Lorenz relationship:

kLo =p,

where Lo = Lorenz constant

p = electrical resistivity

k = thermal conductivity

T absolute temperature

The Lorenz constant ioz liquid potassium is established inReferences 9 and 12 as approximately 2.15 watt-ohcs per oK, Swhich is approximately 13 percent below the theoreticai value.It cannot be stated with certainty that the Lorenz constants forliquid and solid potassium are identical; also, the electricalresistivity of the solid is itself not well established. It wasconsidered sufficient to estimate a Lorenz constant for solid

potassi= by using the few values of the ther-al condhtivityof the solid report-ed in Reference 9 and the curve of the solid-

pphase electrical resist!vity herein. The Lorenz constant thnsderived is, in the units e plzyed in this report,0.25 B-croier-in.0.252 h, -2t-yr abou 18 percent below the theoretical

1value.The resuiting equation for the thei-l conducti-eity is:

k = .7 +. 0 .0381 t

Uwhere k = thexral conductivity, Btu per hr-ft-OF

t = temperature, OF

This equation was used to generate the data for Table IV

pand Figure . -3. Specific Heat

The primary referLice selected for Lhe specific heat of .hesolid was the work of BMI reported in Reference 13. The basicmeasurement was that of entheahy, from which an equation of theform H = At - Bt 2 was derived. For practical purrppes, thespecific heat i3 the first derivative of this equation, and theresulting equation in the units used herein is

Cp =0.1631 + 2.328 4 10-4 t

where Cp = specific heat, Btu per lb-F

t = temperature, OF

-, This equation was used to establish the values in Table IVL and Figure 3. The results reported in Reference 14 agree

closely at low temperature, but have a slightly higher slope,with the result that they are approximately 1.7 percent higheras the melting point is approached. The difference is not con-sidered significant.

B. Properties of Liquid Potassium

t- 9L. Density

Density measurements have been made by many investigators,and good agreement exists among the various sources of data.7-c fo1 1-ing densl:y equation from Reference 3 was selectedas the reco*n'zc equation, since it accuratelv correlates tnedata f.... t elt rg point 'p to 2a. O:

i

A=comz tt,"e is £sie scatter, the res-1tz of other inves-[I-itats bk&.et this c~rve falrly 7all cver tba te=zperatuzre4 ~g E-m 0P2t In particalar, rha results of

-Hfere~e 29 and the o34av ores of Referen~e I of L-rr

Thersmze cal~dzte- as a cL eck frca the fjtImrclreitvt rep Ortd In th rvm eto yc~

vafz o he lor= Lorent a rearte b-j Thrzse efrs

vales f hen'!concrsivit-ge closelyidth viues cebtained Iftcm the ebove eaquaticiA-,.

I-0 Specific Heat ~ aeclrsrcraueer

direcztly, the sat-Lrated- liqruid specific heat as farntions ozte=-vezature. Below 100OF; therei gxocd agreemtewent.arlier swark at the Ylarlonl Bmreau cf Stanards i~efereace 141,12nd more recent naaaroments at Battelle Memorial institute

(Reference 13). Both sets a' data can he correlated by pra

tween t&- two crtrves at h~igheri te=-eratyres, with the experimentalZ~ aue ~adigteextrapolated RBS crv~e in magnitrde.

4 Three isolated data poltnes obtained at the Naval aesearchLaboratozy 'i.rence 3" ten to coariz. the extrapolated Mridata up to 20OF. Horever, the RRL inves.-igato-rs noted dhatthere w-as a srobeble error of -3 percent in their results, dueij

tnonreproducibility in calorimetric mea u'eets. The lorw

The nted fur =thi-ack -walled c,,z-tainers, coupled wfth cheproblema of container oxidation, has rendered precise deterrnina-tion of liauid-heat content extre-e-_Y diffl'cult at elevated temn-peratures. For this reason i.t is considere-d inadvisable tocompuite saturated and superheated vapor prorerties via the liquid F

H ~~path. For the purpose o' 'COMgUrigiqi-ptsir seiir heat up to approxim~ately 1400'F, with cautious extmrap-Altation tohirner temperatures, the following equation based on Reference 14ddta is reccrmended:

C =0.2023- 4.33 x 10t -,2.3 x1 rp

where CP = specific heat, Btu per 1b-':T

SpecifIc heat is preser'ted as a ffuncti.on of t empra tu~efx-or the tneliin~g point to 24CY,1F in TabIa &-,a'i Figure.

C. Fro,-ris of Satr ated Fotassfrz Varor

1.VUr-rsx-After zn exte-,ive review of potassitm vapor presstme in-

formation reported in th~e literatture: the e:rmation firttn theL s~the !~LRet (eeren _1) was ch-e for tbis cozp11.aticn.The rceoe quation is -of the three - tex Virchhoff type

jlag "FSZ= a -;- WT.1 -I c 1og 7). Aftzr srtitutn the a=-r~zialcoitans 24 o~-in ezliitAfo the ecuation becows:

Consant andsoiingepratur, fo al

ar a=u abpecentltee

lthough' 1was deeil nene t o-dlt

it s blieed o b suE~centy acuat isr dexitrdas atmc-

theoO atur5aed vapo higerii at l~n was0F Sice pte 2Ro thew

ther VGNIatae vap;or vrspec-crinf~volvitena c ftpe lb

TheT r=-por presspre prsa edt s eitdasafn.

toofte =eatzc- tex~rerue, indresFhnei)nTalI iVII an iued 1i0, .cefiin 1 sa

92 Speic Viralceficetpsa

Th sat-rte var spefcii elum as opuea5 --o h

The a~one equatiom vili be recagaized as a viri~al equa~tionOf State. M:bg vixial eoeffi~uts ~,,and 6 are fuwtiors OL

gove- ing equations fr the -iral coefficients are given inSiqtic*i tI-I of this report.

Vapor specific voluzm ia listed in Table ViI from 8000F to2300 imd is Plotted versus teapererare in Figure 11. The spa-cfic vole of the superheated vapor can be obtained frem thecoputet printout sheets in Appendix Xi.

3. =f.V&Orization

The heat of vaporization was calculated from the Clapeyron Uequzation, using the ML vapor pressure-te=-erature relationship.The resulting exression is:

0.27446, 18,z111.0.5n"9lV ) 3= SAT - -

where !E = heat of vaporization, Btu per lb

T = abolute temperature, oR IPA vapor pressure, psia

VG = saturated vapor specific volume, cu ft per lb

VF saturated liquid specific volume, cu ft per lb IiThe saturated liquid specific volume is simply the inverse

of the liquid density discussed earlier. A. comparison of theheat of vaporization calculated by different investigatorsreveals rather wide discrepa.ncies at the high-temperature end. pFor example, the BIMI curve (Reference 20) is 18.5 percent lowerthan the RL curve at 2200 F, due primarily to differences inthe experimental P-V-T data.

Heat of vaporization computed from the above equation ispresented in Table VIII and Figure 12.

4. ViscositU

No experimental vapor viscosity data for ?otassium waslocated by te authors at the time this report was written.Hence, it was necessary to rely on the following theoreticalequation suggested by Grosse (Refe.rence 22) for the purpose ofthis compilation:

'9,l3

0.-001577 4FT

L where u~ = viscosity, lb per ft-hr

T = absolute temerature, OR

L The recarxmsnded equation is based on kinetic theory ands isstrictly applicable to the low-pressure atonatomic gas only.However, to a first approximaticn the presence of small concen-Ltrations of diner and tetrar-r molecules should not appreciablychange the viscosity. Weatherford (Reference 1) employed a

j simailar type of equation to calculate the viscosity of saturatedU potassium vapor. However, his values are approximately 32 per-

cent lcrwer, due apparently to the use of a largereatom -c colli-siorx diameter. --

Vapor viscosities calculated from the Reference 22 equationare listed in Table VIII and plotted in Figure 13.

5.Thermal Conductivity

It was also necessary to calculate thermal cond-*ctivitydata for the saturated vapor, since adequate experlmeutal datawas lacking. The termal cond:-SJvity --,f the =tniatomic gas canbe readily estimated, like the vli %sty, from kinetic theory.However, the saturated vapor consists of A-m4rr of hm4alreacting molecular species over the temperature range of interest,tith up to 12 mol perce-nt dimer and tetramer content. Hence,

tethermal transport mechanism involves more than simple trans- 0lational energy exchange between molecules. Since an appreciablefraction of the heat transfer may be due to dissociation, recomn-bina tion, and diffuasion of molecules through the boundary layer,Cl the ",equilibrium"' thermal conductivity is considerably higherthan the "frozen"' thermal conductivity.

For the purpose of this compilation, the equilibrium thermalconductivity was estimated from the equilibrium spt.ific heat,by use of the following equation:

_j k A (C +2.48)

IUwhere k =thermal conductivity, Btu per hr-ft-OF= viscosity, 1b per ft-hr

M=vapor molecular weight, lb per lb-ol lbF

C = eqilibrum vapr speifchaBuprl-F

-- The abov tion is based on the work of ilcken and Ma--e fox es mn of the Prandtl agmber of a yato i c gas.

The specific heat and molecular 4eight were obtained fromEi-ference 3 and the computer data desczibed late...

Calculated thermal eonductivity for the saturated vapor is- - presented in Table VIII and Figure 14.

1

ir

12 3

I B'

lSECTION IVSTHERMDYNAMIC PROPERTY DISCUSSION

B A. Review of Publist.d Data

Several attempts have been made recently to establish thethermodynamic properties of potassium liquid and vapor over anextended range of temperature and pressure. Properties ofinterest include the specific volume, enthalpy, entropy, andspecific heat og the vapor, plus a number of comparable proper-ci ties for the liquid phase. Unfortunately most of these effortshave met with only limited success because of the lack ofreliable experimental data, especially at high temperature.

UOne of the earliest published compilations of potassiumthermodynamic properties (Reference 1) treated the vapor as an

Bideal gas mixture of monomer and dimer species whose compositionvaried in a predictable manner with temperature and pressure. *iSaturated liquid enthalpy at elevated temperature was estimated

by extrapolating Bureau of Standards experimental data(Reference 14), and the saturated vapor enthalpy was calculated: ~at each temperature by adding the heat of vaporization to the i

liquid enthalpy. Internal consistency among the various proper-ties was 8ecured by adjusting the constants in the vapor pressureUequation.

The high-temperature data of Reference I was in error pri-H marily because the monomer-dimer model could not adequatelyaccount for the additional degree of polymerization taking placeat high vapor pressures. In recognition of the need for moreaaccurate potassium-vapor properties, several independent projectswere initiated to measure the specific volume of potaselim vaporat elevated temperatures along with the vapor pressure, density,

Iand heat content of the saturated liquid. Unfortunately, theL;general lack of agreement in the experimental results thus far

as rendered it necessary to scrutinize all published data veryLcarefully..L After a detailed survey of experimentally determined high-i f . temperature potassium thermodynamic properties, it was concluded

that the Naval Research Laboratory data (Reference 3) is thebest information currently available covering the temperaturerange from 1400OF to 2500 F. Due to the absence of reliablehigh-temperature liquid enthalpy Jata, the NRL investigatorswisely chose to compute enthalpies and entropies via the monomer

gas path. The P-V-T data for potassium vapor was correlated bya virial equation of state of the following type, which treats'the vapor as an imperfect monatomic gas;

PV B C DRT!RT V V 2V2 3

13

~Th -existence of several molecular species in the vapor corn-U-postion ip Seneraily accepted. The thermodynaric trentment of

coqm toh is perfectly satisfactory provided that all molecularspbbl~s can be identified and the entropy change associated with

obftS dompo9sition is taken into account. The thermodynamic1op;tatio"'imade :for this report were based on a virial equation

of -stae deriv04 fro-a actual P-V-Tx measurements, which treats!; theL'VP~ s an Imperfect gs having constant molecular weight. All

vapor -,prope; ies weie compiled From an ideal monomer gas ref-erencestate. In dffdctthiis method au~tomatically takes into account theUsituation tiat ',the potasium is in fact neither a monomeric noran Ideal gas, The virial method was favored in the present casebecau6e it expedited the mathematical computations and di -d notDrequire precise knowledge of the molecular species present in the

taken a similar approach and have demonstrated essential agree-ment-between the virial and cuasi-chemical methods at thepresaures within the realm ol interest. It is not necessary tocompute an entropy of mixing as an explicit step when calculatingproperties by means of virial coefficients. In effect, the entropy Lchange is automatically taken into account when correcting for gasimperfections. Likewise, the vapor specif-ic beat accounts forenergy changes associated with shifting composition.B. Thermodynamic Comutations EE2loyed in This tui

The MLJ equation of state requires an iteraiesltinfr Ispeciiic volum In order to eliminate the need for an iterativecomputation and simplify the ensuiuZ. equations for enthalpy andentropy corrections from the ideal Sao state, the WREL data wasBrefitted to a virial equation of the form:

Py I+ p+ yp2 + BpS

Theoretically, more virial coefficients should be requiredwith the latter type of equation to accommodate the data. H~owever, 1judicivus selection of the pressure exponents enabled the aboveequatio~n of state to correl.ate the NRL experimental data withsufficient accuracy. It is noted that a precedent exists in thata similar form of equation with one additional virial coefficientwas employed to compile the steam tables.

The coefficients y and 6 are temperature-dependent functionsof Sign.ificance only at saturated vapor temperatures above 14000F.The governing equjations for -y and 3 were therefore obtained by acurve fitting the tabulated 14RLJ data.

The second virial coefficient, , was exprecsed as a powerseries expression in recipro. ral temperature. A leQ,.,-squarescurve fic was employed to evaluaste the numeri-cal constants in theUequation. Input values of at the~ lowtr temperatures wereestimated b~y arplying Lhe NRIL vapor pressure equation in co~n- [1

junction with the mononer-diw'er equilibrium constant data fromLReference 30.

It is noted that the NRL vapor pressure equation has beenextrapolated several hundred degrees below the temperature rangeof the experimental data upon which it is based, for the purposeof computing saturated vapor compressibility and heat of vapori- vzation in the low-temperature region. The use of a single vaporpressure equation over the entire temperature range is desirablefrom the standpoint of internal consistency and continuity.

a ~Moreover, the NEL curve appears to adequately describe thej scattered experimental data within the range of probable experi-mental error between 800OF and i00F.

It is believed that the saturated and superheated vaporproperties of interest to the turbine designer can be computedmore accurately via the monomer gas path. However, internalconsistency throughout a wide temperature range is of importancefi ffor cycle calculations involving heat balances. The predictedenthalpy-temperature relationship for the saturated liquid isconsidered to be a good test of internal consistency for theequation of state and vapor pressure equation when computingproperties from the monomer gas base.

There is good agreement in the liquid specific heat datai B reported in References 13 and 14 up to about 1OOOF. This data,

in turn, is closely matched by the output data from the computerJ program developed for this study. At the present time, there ic!i no way of making a precise check on internal consistency of theI] uthermodynamic equations at higher temperature by the technique

described above, due to the lack of reliable calorimetric data.

C. Description of Computer Program

A FORTRAN program has been written to compute and ; thethermodynamic properties needed for cycle calculati nM. Thesaturated liquid and vapor properties are tabulated first'Appendix I) followed by the superheated gas properties

f(Appendix III, These tables are the actual computer print-outsand are included in this report along with a Mollier chart con-structed from the computer data.

The starting equations in the computer program includethose for the vapor pressure, saturated liquid specific volume,and ideal monomer gas properties taken from Reference 3. Theseare followed by AiResearch-derived equations for the virial co-efficients and their first and second derivatives. Finally,the real-gas and saturated liquid propertie8 are computed from

p the ideal monomer gas base,

F1 f

D.-I g~ g e guar ntiti s B j..!2ga List -ft SOo~ It/bR9

S z f nat i q u 4 -p r s e c i i v oS A T V 7 I u f t

7aird viia cofiint7IiF eorth virial coefficient si

S a t- =- a e d a p o r a p e i f i : v o - m eV IGc u f t / l b

S -2 , - -a e ao r H Gre yS I B tu /lb 0 R

E n h a p o v p ri a t o Btu/l b0 jEntropy 1 Btu/lboR

l, o oi zati on B tu/l

Saturated liquid enth~alpy I t.lSauaIL iudenrp Btu/lb 1)Superheated vapor- specific volume V jcu ft/ibSup2rheated vapor enthalpy j K IBtu/lbSuperheated vapor entropy S Btu/lb0 -R

Su?erheated vapor specific heat C PBtu/Ib 0 R

Superheated vapor acoust.L' velocity A ft/sec.

Input Qantities 1

Pressure I Rsi

16

U

L

Saturation pressure:

1.71 x. 107 -18717.22

PSAT = -T)0.-& 1 e (I)

Ideal gas enthalpy:

H0 998.95 + 0.17T + 24,836 e T (2)

IIdeal gas entropy at 1 atmosphere pressure:

n = 0.18075 + 0.2924.3 logioT + 0.7617 e T i (3)

nIdeal gas specific heat:

0L 28,070Cp -0.1270 + 2.888 e T (4)

'I Saturated liquid specific volume:

VF . T T 12 13 (5)

56.099 - 6.9828 O--) - 0.5942 (--02 + 0.0498 T

BSecond virial coefficient:

.882855816 + 1.336763701 x 104 9.581165848 x 107

+ 854_77962 x 1011 9.% 7784721 x 101" 1.548462407 x 101 8

+ T 3 T es Ts1

S1 .5 16767 x I21 8.41706354 1 1023 2.033189468 x I (6)

17

FIf.-t derivatiwe of second vi-rIzI cfaicient:

dS 1.336763701 z ' 1.91._ 70 _-

_.1-6593382 x a!02

+ 3.899113M x W-s 7.7432035 I !O + 9.12%3.0U2 z Wk-+Ts Te -"

5.90919 , x 1024 1.626515T4 x 10 F

Second derivative of second vi-ial coefficient:

d 2 2.67352UA02 x 104 574699509 x 08 . 4.6625735% 102 [-=-- Ta- - 4 Ts "

1.949556944 x 106 4 2.645387221 x 10s 6.387010421 : 1022Ts T7 Ts

+ 4727355558 x 1025 ;.4638964 ! x 1028T9 - TICE

Third virial coefficient:

Let y - T-184o

42.791 x IO-Y 5737 x 1O'-y + 4.3404 xlOT y2 - 7.6743 x lO'0:y3)(9;

First derivative of third virial coeffi .ient:

-(4.5737 x 10- 3y + 4.3404 x !0 7 y2 - 7.6743 x 10- 0 y3 )

dTe

[- 4.5737 x lO3y - 8.6808 x lO-7y" + 2.30229 x 10-9y] (10)

I 1.8

IT

0

I

5= 2-791 z - e- ._.- . , .-.

I 1j - - iL x

Fourth zi.al coefficiear:

Let z = -3

-"I -. 338 = !0Y X e -i u z e

da -(l.oO?6 x iO-a, - .6879 x l-z 2 ,

L -e

Second deri--ative e± fourth viria! coeff!L4ent:

d2 6 -(1. f6 x 10-2z - 4.6879 x 1O-czz _

}T- = -1.1138 x !0

x 2.0095 x 1O2 1.2906 x 10z - 1841 10 'z 2 + 8.79n6 !(.' "z.3-J

i]:9

S+ 2

_ -j _. IL :i +

Sap=: " a. e-tr- :

!B1-. 717.22 05

a-atro"p of vaporization:

HFGF = 71719

Satur-ned liquid enthalpy:

[10

AF~

Snp- aztec vzpc.-- sz-cifie vol-t=e:

I 0.2746- 1,32

S-mxyerze ed vapar enrzlapy:

Superhea ted vapor entropry:

IIS = s 10.0=m 3025 logio (Td3-- (

Superheated vapor speciffic beat at constant pressure:

viz C D Co-0.0579 PTF2 +T~ P" ~ L

IL, -X ~T ']5

21I

Suez-bred v-zpa. acazclsr velc-lity:

T +

L

2 2

SEWTiGN V

Uj

i i. Weatherford, WJ. D. Jr., Jon C. Tyler, and P. M. Ma, -

Properties of 1Inorganic Enere -- Canversion and Heat TransferFluild for Space Anpicat~on. WADD Reaort 'M 61-96,Nove=her 1961.

2. Weatherford, W. D. Jr., Recent E-eta on the TherionhvsicaIProperties of Alkali .e.lals, a paper presented at the 1963USAF Aerospace Fluids and Lubrication Conference, SanAnronio, April 1963.

3. Ewing. C. T.. et al, Hih-Te11 erature Proerties ofPotassium, U.S. aval. Iesearch Laboratory, Report 6233,Setember 1965.

4. . Grosse, A. V., Hiph-Temperature Research, Science 14O,781-789, 1963.

5. Novikov, I. I., A. N. Solovien, E. M. Mhobakhuasheva,V. A. Gruydev, A. I. Pridantzeo. and M. Y. Vaseniva,The Heat Transfer and High Temnerature Properties of

Liquid Alkali Metals, J. Nuclear Energy, Vol. 4, No. 3,387- 459,7957.

.4. Hughes, Donald J., and Robert B. Schwartz, Neutron CrossSections, Second Edition Brookhaven National LaboratoryReport Bn 325, July 1958.

7. Hghes, Donald J., et al, Supplement No 1. Neutron CrossL Sections, Second Edition Brc-okhaven National Laboratory

Report BNL 325, January 1960.

8. Tepper, F., J. Felenak, F. Roehlich, and V. May,Thermophysical and Transport Properties of Liquid Metals.USAF Report AFML-TR-65-99, Fay 1965.

9. Deem, H. W., and J. Matolick, Jr., Thermal Conductivity

and Electrical Resistivity of Liquid Potassium and theAlloy Niobium - I Zirconium, Battelle Mlemorial InstituteReport BATT-4673-T6, NASA CR-52315, 1963

10. Kapelner, Samuel M., and William D Bratton, The ElectricalResistivity of Sodium, Potassium. Rubidium and Cesium inthe Liquid State, Pratt and Whitney Aircraft CorporationReport PWAC-376, June 1962.

!I

11. Iezst, R. C-, editor, Han4dook of Chemistrv and rnscs,46th Edition, Cheical Rubber Publishing Co., 9b5-19b. K

12. Gresse, A. V., Eiectrical and -herpaL Conductivit y fKetallic Potassium Over its Fztire Liu d Range, i.e,ZRo6r the lfelt Point (33b.4"K) to the Critical Point U(2745O'),3. J nrg. and I cl. Chem. 26, 795-W09, E9bb. -

13,~ Dem H. W., E. A. Eldridge, and C. F. lucks, The Specific [Beat from 0 to !!0OC and Heat of Fusion of Potassium,atce1le khra1 Institute Report BAfT-.673-2 ,

August 1962.

I. Douglas, T. B., et a!, Heat Caacity of Potassi=u and TreeSod'i-Potassi- Alloys Between 0 and bO'C; the TrlpiePoint and Heat of Fusion of Potass!-i J. A-n. Chem. Soc.,U; 272-2W, 1952. _ _

15. NcvikoV, 1. ., et al, Ato=va Faerziya 1 (No. 4.):92, fJ1956.

16. Hogen, E. B., Ann Phvsik 25; 336, 1883.

17. Jackson, C. B., G. A. Wieczorck. and A. Van Andel. Densityof the System K - Na, Appendix C in Q arterly ProaressReport on the Measure-m nts of the nPhYsical and ChemicalProperties of the SOdium-Potas3i4u Alloy, I NavalResearch Laboratory Report F-3010, Sept--1er 19-

18. Walling, Joseph F., and Alexis W. Le _kn, Jr., The LiExperimental P-V-T Properties of Potassium to 15-0C,

Batell Meoril I-r-itue R! prztBAfl-'4-673-Final,WAA Report GR-52950, 1963.

19. Zwing , C. T., H. B. Atkinson., Jr., and T. K. Rice, TheMeasurements of the Physical and Chemical Properties--of theSodium-Potassium Alloy, Naval Research Laboratory ReportNRL C-3287, OPR No. 7, May 1948.

20. Lemon. A. W. Jr., et al, Engineering Properties ofPotassium, Battelle Memorial institute ReportB4-TT473-Final, NASA CR-54017, December 1963. L)

21. Chiong, Y. S., Viscosity of Liquid Sodium and PotassiumProc.Royal eSoc. (London), Ser A, Vol. 157, No. 891,pp 2-4{277., November 1936 ,1

22. Grosse, A. V , Kinematic Viscosity of Mercury, Sodium, andPotassium over T-heir Entire Licuid Range, i.e.. from thedelting Point to the Crit.cal Point J I norg. and hucl.-C .- 2-- , 31:-- " II -

23. Tepper, F., F. RoehliCk; awn. V. May, Ther wp yircai andTransport '-roperties of Liruid )-tas, ResearcbCorporation Report )EAR 65-123, Sge-embex 95

24. Cooke, 3. W., Thermo sZical Pro5pert- Rasurem~nts ofAlkali Liquid Mta , AE Report ORL-3605, 'V,, 1 ,

25. Grosse, A. V., The Relzztiozrihp Between Surface Teasion

26. Coe, Harold H., Sumzary of Thermo-aphysical Properties of

I December 1965-

27. Kiser, R. W., Department of4- Chemistry, Kansas Statefl University, TID-61412, June 1960.

28. Lyon, R. H., editor, "'liquid-getals Handbook" SecondEdition, AEC Report TID-5=277, June 1952.J ~290. Mikheev, Hi. A., editor, Problems -in Heat Transfer, AE~Cj

3.Report AE-TR-45l1, January 1962.

3.Ev4ans, W. H., et al, Thermodynamic Properties of the AlkaliMietals. J. Res, Natl. Bur. Stds., 6 3-96, 1955.

II 31. Stull, D. R., and G. C. Sinke, Thermodynamic Properties ofthe Elementsi Advancement inCeisrSrs AmericanIn Chemical Society, Vol. 18, 195b.

32. Quarterman, Lloyd A., and William~ L. Primak, The Ca21llarRise. Contact Angle, and Surface-Tension of Potassium,J. Am. Cher'. Soc. 72 3035-3037, July 1950.

33. Tepper, F., F. Roehlich, and V. May, Therinophysical andTrans ort Properties of Liquid M~etals, MSA Research

Zorpoiiatlin eport MSAR 65-192, Dlecemer 1965.

'14. Tepper, F., and F. Roehlich, Thermophysical and TransportProperties if Liquid Me-.als, 14SA Research Corporation,U, S. Air Force Materials Laboratories ReportAR-TR-60-2o6, dated May 1966.

I2n

Si.AM oi -DMSMH -OM VALUE ?RP.2M Es

________ VALUE REFERECE

I -atOf f usn~ 25T tu per 1b 13-Atmic iweigtt 39.100 31ai typ f t~he Solid

at 68OF 53.7 lbs per cu ft 11li- haperic bolli T, point 139-'F 3

eatof vaporizationat the boiling point p29.1 Btu per lb 3

Critical pressure 3380 poia 4 1Critiz al temp erature 3,C.O°C F4

Critica. density 10.6 lbs per cu ft 4Ionization potential 4.339 volts 27

'Relative magnetic 5.75 x 10-' 11susceptibility at 64.40F (MIKS dimensionless)

*Defined as -1Pv

i ere & = permeability of potassium, henry per meter

av = permeability of free space = 1.257 x 10-1 henry per meter

2I

I

I

tf i

C) a

"443.4

. u cm -r4

0 0c)

3".I

a t * 3.10 - 0 0 0u ciu u m

> c

0'0V:4

W034

a) t

zio +134 a

Bn 0 04-a

"04~ 0

0~CC)m4 0'

.00 c zP4V

00~W 4

* .0

U~ 27

-. Z,-4

-0- C; - a -AIi

0 COO Z 0 0 -(X

>0Ow 0 -4 0- 4

C, Z: 03c co

;Z 0

;u 0

00

4j1 1

V Ps 00

90>

to 0 -$4 18 14 m

I C ri -4

341

4) u

28

"4 .r -4 r-4 cm 044 4 1

r-44 I- - PC1C2

(a 1-4"

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0Hi0k. .

H _ ___ L 1 t z

0)

Q) 4-

~~;F4

4E-4cc "9

'm 3 3-.

11 1*1 ,r 3 c-1r

43 4 114 4.4 S:..4 Liz -C301 0 3-4 0440 1* 0 -4 c*

0m4 0U r400 0 c 41 -, s.4.. t4.W.b0 ^ aC m0 to10 340 dC 3 0 " OX4S: >4 0 1 Ui o ooP b o r. t 0 S..0 4 v4g 0 aok0 0 9 04to 41e. 04 i 4 . 0 4J4- M44C

49 0 00 - (a4 3.0 4 Z14M 4 -f MOad-(43 14 0, U CS Q41 D o 0o.o' 01 0 . 4414.. 0413- '34-.0 3410 1o j ari cl jw 0) 41J4 tu U0U -I4

w3 :40 4 3 Vt to0 ~ r:0 a.00 m o 4 A -0C3I04.1 d0*Q$ 00IV>l ('- o 4 4Cj

a 1~-4 VU 4 vi0CCcuMc%W 0i Cki3431 4 0344 04 toe)0003 0 ~ '4 4440 Ma4 .144.01~

Q~4. c44J. 44 WO444%Jw c

41%0 t- 3 f4 0 *0c 004z034 4 v4(0 CI-'L 120U 9 : r 4 k0r c,

'.U0 Q41 0)vi c - 4 1 4 1 o en vo '

14 (11 4 ca04 g ( a,. U 0 ( 1J )4j-. f.

,-4C F-U C 1. - i )0 HP 1 4

Hn 41. r4C ncca 4 0

449 . -4CU t

0 43

r14 T-4 ___CU____cu1

0- 0H40

o r.- $,4 rn I.' 4

4 4 J 4 2 1

U 3, t4 4 4 41-. ~ '

0 0.1 0 *~' ' -r 4

0X 1- 44 :3 X +- IJ'00 U xw. >4

41 w0 2 0) 4.t0I14( .0 -t* 0 r-4 03~ .4 U c o .43. '4 -4 C- It- "m -d3

w00 +X 44 0 4 + t '4

V~ ~ o Ui N 54\r. *C4 .kni14 4W 4) >'- t0 w- -4

MU p t,1 4 *f ( 7 (4 40O 4.1 C( o) (Y CD .4[

0- + C3 0 4 41 I -- 0.

o (1r.0 0i r$4- __ __0 ___ a\ 4C

-Z1 U* --_r4 t-- AV %0 1 M~ 0 C :r CIA .-4 !W C%%D 104. .- m 'k . n.4-m '- C-Q cu --I- Ar 0-

OJ4 r 4 4 - 3 .f 4 -4 Z ofl Cu Cii N C

9.fu D 0%1 t c-' 4 4 -4 -j -4 C4 C fn -VI t c 1 r4 .4 LrLI 1

V1 $44 ct" cu N W CV1 N- W0 4- 4 i 4 4 -

t. 41 9 .

. 4 .4 4 4 r4 -

A'Ar$4 *Il00 00 eos s 00 0 0

0 V 0 0 00 0 00 0 0 000 0 Co0oo.1 . .~ . . . . I . .

40il -9 IJ zi z('i-40 0

a0 li 0 0i3 -

0 S =-4 C0 0 -4 eA.,

0.= = = U4 "Oo at 1~0-4 o'J 0 *

0 ~ ~ i 1N 6a:00-0 oo -Cc

r-4 z 14I O.0J 4 uc 6 -44 Z~ a -Z

P~xo a~ u____c5_0- = 4c . U

Ok .. , . P f x ;u %

1; -~ 0 I-- >N9 = . wazvf

vCzd-1-46 14- ~ >4;1 0430

0 0

04..4

0 -c kr 0:t. 0 3

444 P- ~ 0.-0-z.~

00

LI I 1

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0_______ ___________________________________0_ _ ___ ___ _

14 + 32

W M k.

U> u.. I u n oA oooCh mooo U M o G o Co4

11Z cn ; _ _ _ _ _ _ r _ _ %_ _ _ _ _ _ _ _ _ _ _ __ - c

I 4

caoO

k C Tc 4 c % n)ki

IA a00000 L ot Qcu %0 00 b D00

40 a 0H 0 a 0mm w otmN -

r- ~ ~ 4 t 4 P.:> H- Cl 0\ vCU (n r4 f

__________

14 lM X, rl33

I -I

EnFtoK

Hi4

-- 4

...... ...... . . . .. .. . .

. ... .. ... E

.... .... . .. .. E..... .... .... ... .f.... ..... .. .... ....

.......... .........q ii

H IcoI

...... :1 11 ml l : . U T

0r7

:IX

AT,1' 0S (1

j0

1 0

EEn

.,fif

'331 0

00

t tttift~it -4

MOM-4

I z.

JIMJ

TI]--s0 T

4:~ ~ ~ ~ ~ ~ ~~1 12L-H~~ lt 'II~lN~~~~

LoL

11111111 ,r £11

0 04

H I

rX4

IT #f

NO

I t7V111

TI

44-1 72

XLI

UA L

.*. . .C

.. ... .---- -- --

37T

E - ' - -

1131A1

1-4$

p.4

it 0

1-1<

It. LILnr

Y1 fX4

141441 1 8o

4 ~ 4 1

2-73.9r

-- -- - -- - - - - - -

- -? U

I It~I 13

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H -2

H L

J-L

.4--44-.

11 X- M-.

il i4ill...I .

I I

Ii A ....

00IC00 I ) m "

[J FIGURE 8.THERMAL CONI)UCTIVITI OF LIQUID POTASSIUMj

5.-: 7 - .-

'AL' NJ.

se-I

L A12X 4

Ty I II aI

It I,

cEl

III FIIIA ll I'da a j. all ---

fit;

to 11006V80

111

0466

.... ..0.!4

0. 20

1 10

WCEK-ZRTURE, 0 10

In FIGURE 10. POTASSIUM VAPOR PRESSURE

- - i80

/ J4

0

.. ....

414

T W10

I.. Hll Mil. Hiit..:

How I i"1111

II 10 2000 2200 L.004

.........XE ...

FIGURE~~... 1. PO.SU .AU E .AO ..L'.I.1C .V.L.

. .... ... ..... .. .. .... ... ...

8

P-4

.... ... ... .

ao kzcC40 co oqq NA RI 'NIIVZNodA 10IHH

..- .. .. .. . . ... .. C 1

.' ..... ...

in]wU

8 8

46"

E-4* I at.

...... ... t......... .... .. ........

£t-....... ....... ....... ......

::: :::: :R :::: : :1 ........... ...141

474

1 13

1 2 A II IH0.30 ..... -- --

----- ---- -- I . I

4 tFIGURE 15~~~. SPECII Et O AUAE ~TSIMVR

APPENDIX- .1

B 'SAIURATION PROPERTIES OF POTASSIUM

0 MC O..CC. 6 0 % n V v00a$ -00111 o o. .4'0V W t4 0 a

4 - 4.41 14 4I .4 -. 4 Q.44A .4.4. .4 . 4.4 .4 4 .4A

.4. '0NC*)1.010 00V 0 A o064090 4 0 001"0. V -V V * W aw a11%f .404r Ca .4m 10z." Cmi-SA4 "M01O N O m0N00 oto *W"l.~ ~ r Nomov:N00 W 0.4w o 410 0.

-. . I

0.

14nV rl0-0V kam=4r 102r'0.0 '0'0moo,'coo,0'.4.0'0'0C 40 W V4'0'0 0 4 NAO-CA0NNNI]~~~3m W50 ONCom 00001A OOOOnoOOOC looa~~C~oo~o~ ow C m ft

0-. .0.0.40(100

WI W 4.o m14gs4140'G0.D.0 .0 KNff ,NT'0 00 00 00 00 0 0,1;,. 0 0 0, '0,0 . 4k0. f%0.0000000C

.. k.94~0 0 4 0NN04.0.00"-4N0.-.4 4.4 N00.4 1 N."14 00.4 4 4 .0. "..4" 4.'4 .Q0Nv4..40.4

(A W) cu ft W 3A I1. .f% Ar -4 .04 - 0. ft ft A0 M 4 C 0 10 0. If 4 '0 In fv a NO 10 JA 01 N f C. a a C31.7 ft N 43Ovq V V c" P% vs'0 I go 'a .N040ift C.4 0NriqN1A c %V4 9%vft . o.,4'"~AIV .q04.4 hI4 N 0

. .. .,~ N £. . .. .... .... ..0 .00 q N. . ... ... ... .0N...400 .40 441. .

00C, 0 a hC I 43,Ol 0 c o0 1 rN N a 0 .0 e4 utI VVIt"P) in jC .4 4 .4a0co00 0 1.0. 00N elf 0'0 0

10 - CQ N 0. cl co40 o40 co cc 0.440 ogo40 0 40 0.00 0''0.40 c o4 0Y4 nI o4 ot 0 to40NN04 1 0 400 e of P F t tftN N f f

0. 4 V ft VsI ft . 400o 3 0 n 0 MP o 0 c01 V 4 f%1( 40'C ) ,4 MWkV V0 0 40. o w 0 nt f 0 A 0 V0 4 0 CUW4 9

x ca & f- , t a%4 C404 9 ON 0 0 o rt V'0 0 V .4 v.03 kA a( 0, 0 N0. N O 0 400 a.0 N .4 P) V4 at no, CY lame lep 440 N 44. 'GOo x a a, 0, V~ &4 N 40044 to a .. 0 11 40.0 aY V 0 " UC I'.04 4 040004 4 0 A-0 O 0 4 N0

0 40 0. 1. MA I, M V r0 " 1.V 0 4410 N 0. 4D .0 N cN 0 NA 4 v4 4 10 0 0- v; c~ co C3 wo44 cu ) % 0."4c.cr C m C 00 kI ct) 4 v40o.V114 caInAl0 '41 4 V .. 440 .4 3Gfi01 IM"W" l0 0 NU V) 44aC

9 - ON;I P 00 C'00'0 .4 1 1 0 0N1 z ; 14 z ;1 C :V;f N :C 440.0 rNNN N t4 00; 0 .4t'4400 '0C; -4 0QN10r)VVVb %u 0 QC 1I 0co4 O 1Qa "44444444N N N N V .4 W N0 N)04040404V0V0IA40404 b 4 t, 10AD 0 1 (1 C Ma 4 4 '0'0'0M 4.441 TN N N N4IN N N N(44NC4INNNNNNNNs)0",ve~vw wv 0NN N1IN CI'.N CJ'N N N

cc 0 0o o a o o o o o o a o o o o ~ o o o o o o o o op 4 n- N01 P n1 %NC Yc 1 l Ot % )0 tW l00C C h1 4Cf , tf Ye t

C . 0 CD 9 anN44.41.0N.4.4l.0.4 N4 I'I444.4N 014V=VNooUf~ 0%VOV VI0IA 00 0h " " IA N 0.4 n 4N N '

03 e 1 4 VF)'0 d3 10 C' V 4V 0C 4 4 ' .t4.4 40.00 N "- N o'0O00.'O 0 044,..NlNr4 .4 .. .4 .4 .4.. 444. 44444444.. 4.. ... 4. 4. 44444.1NNNNNNNNNNNC 4

49411af 1 01 iC a1 o 4 3 of mI "( 4CU 30 m4n -,P tr lJ )I 1,a 4c % oC )i t4'10pIW. 0 f o 0 1 a 4 c o V 1 9 0 l = 0 3 ) P 0 f D 0 1 4 c b% 1 o a 4 W A - D 0 4 A 4

VaVI 0--Q f A4IA'S 4016 t V M130vI *ms

.

f-. a 11ll tcdI %M 01 '4 44. ni

a4 .. . .0 . .*a U P .4O6 '0...

., .. . .e a acaaaa aao0 a 0aaa"000000 0d . ~l9 D0

CB I%- * m~tt0 0 a ,vI I =o10-4 nr t"V4r %% rVVI

. .q . .. . .. . .. .NN~ N0. ..

ft1 4C 4A . 4 f Y tf vMf tNMcN YN tv ~ W N ) C cuMMCiNc .~ C ~ UNciMc ~

.44. .* V4 V4V 09 4 4V 4. . f. 4. . 4i

fsN4 = w.- mnyc %r oca Ng.NN

6- W! 1!. %.t.... ....

ofM0 Kv9 hf *Cb16 00 a 0 4a % f 0.a0)01a e 0cm

NN 9P 1 a a Wm. f

V V CNNoWWN NW ftIC"N nnvV

1% so v 10 10 le 0 ) 00) 1.1 (D ld a4 . % IV M . 0. 0 c43Q

IA w0 N C. 3 4n Inea Cb. mVt a .4 "41 oC.4O P)

01" P 4"M 1. I.4 '0 ati , N NN ACM.:.N.V.M

X1 a, N0 C.4 "P.~mtN co0Q

- 0 a 0 00 01104,C,4KWmK0 a c a .0 Vc

a coo 0 D ab C4 b 4a ca -0 a = ax " 6v C3 a C3 a CD = 0 C2

- .0 43. Vi 4 % 0 ~ ~ l Wkq 9%W%%f a 4 Ol '6ON CN.v t44 (Vf yc f N C f McmC u Nf N ( IV

.0) 00 YaO'~lf50

~ C0)~U 43~) ~ C NO .N00

UPROPERTIES OF SUPERMiATED- POTASSIUM VAPOR

a j... 00. ..... .... t . .

IL P

M V t42, uet Mra, 3 OC Q@ ca W 100 m1U' N .4 0m ,o f )v .0 o .c o 0 *e q C1 4 ~~ 4b0 m idnW) .4

.4 -

10 L

04 N CA 0N 04v C3MCO VNMD4 4N C 4k & N AN %N a CON* aI0.n4%-rOv t 2 0 me, =cm =M " N C m MN C Mmin@0C v N N o dg O , C4h m 0

- 0' 4c c: 0 C . ml 40rmQ W %cmN LM 0 04

m. CD)NN" N c C

I.. >;M-.,Mu%;, 0 N4 l' 1 lv A %,Qc L mNa KcC %& ,M0 Clv VQ 4

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