UNCLASSIFIED 'K AD ARMED SERVICES TECHNICAL INFORMATION AGENCY ARLINGTON HALL STATION ARLINGTON 12, VIRGINIA UNCLASSIFIED

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1 UNCLASSIFIED 'K AD ARMED SERVICES TECHNICAL INFORMATION AGENCY ARLINGTON HALL STATION ARLINGTON 12, VIRGINIA UNCLASSIFIED

2 NOTICE: When government or other drawings, specifications or other data are used for any purpose other than in connection with a definitely related government procurement operation, the U. S. Government thereby incurs no responsibility, nor any obligation whatsoever; and the fact that the Government may have formulated, furnished, or in any way supplied the said drawings, specifications, or other data is not to be regarded by implication or otherwise as in any manner licensing the holder or any other person or corporation, or conveying any rights or permission to manufacture, use or sell any patented invention that may in any way be related thereto.

3 _'283_441 TABLES OF THE THERMODYNAMIC PROPERTIES OF NITROGEN FROM 100 TO K By Wanda J. Little von Ka'rma'n Gas Dynamics Facility and C. A. Neel Scientific Computing Services, Office of the D/E ARO, Inc. TECHNICAL DOCUMENTARY REPORT NO. AEDC-TDR September (Prepared under Contract No. AF 40(600)-1000 by ARO, Inc., contract operator of AEDC, Arnold Air Force Station, Tenn.) - ARNOLD ENGINEERING DEVELOPMENT CENTER AIR FORCE SYSTEMS COMMAND UNITED STATES AIR FORCE

4 Qualified requesters may obtain copies of this report from ASTIA. Orders will be expedited if placed through the librarian or other staff member designated to request and receive documents from ASTIA. When Government drawings, specifications or other data are used for any purpose other than in connection with a definitely related Government procurement operation, the United States Government thereby incurs no responsibility nor any obligation whatsoever; and the fact that the Government may have formulated, furnished, or in any way supplied the said drawings, specifications, or other data, is not to be regarded by implication or otherwise as in an), manner licensing the holder or any other person or corporation, or conveying any rights or permission to manufacture, use, or sell any patented invention that may in any way be related thereto.

5 AEDC-TDR TABLES OF THE THERMODYNAMIC PROPERTIES OF NITROGEN FROM 100 TO K By Wanda J. Little von Karman Gas Dynamics Facility and C. A. Neel Scientific Computing Services, Office of the D/E ARO, Inc., a subsidiary of Sverdrup and Parcel, Inc. September 1962 Ar - AZ- Ar Mr T..,

6 ABSTRACT Tables of the thermodynamic properties of nitrogen are presented for the range of temperatures from 100 to 1500*K. In the first table, in which temperature and pressure are the independent variables, the range of pressures extends from one to 104 atm. In the second table, with temperature and density as independent variables, the range of densities extends from 10-7 to 630 amagats. In addition to pressure and density, the tabulated properties are the compressibility factor Z and the dimensionless functions E/RT, H/RT, and S/R. The source data and the tables are discussed. iii

7 CONTENTS Page ABSTRACT iii NOMENCLATURE... vi 1.0 INTRODUCTION DATA CONVERSION CHECKING REFERENCES... 4 APPENDIX TABLES 1. Tables of the Thermodynamic Properties of Nitrogen from 100 to 1500 K with Independent Variables of Temperature and Pressure Tables of the Thermodynamic Properties of Nitrogen from 100 to 1500'K with Independent Variables of Temperature and Density v

8 A EDC-TD R NOMENCLATURE A E H log P p R S Free energy function, E - TS Internal energy in dimensionless function E/RT Enthalpy in dimensionless function H/RT Common logarithm Planck function, S/R - H/RT Pressure, atm Gas constant Entropy in dimensionless function S/R T Temperature, K Z P/Po Compressibility factor Density in amagat units based on density at 0 C and one atm of pressure (c. f. Appendix) vi

9 AEDC-TDR INTRODUCTION These tables were prepared for the purposes of data reduction in the operation of wind tunnels at the Arnold Engineering Development Center (AEDC), Air Force Systems Command (AFSC), USAF, in which nitrogen is sometimes used as the working gas. Their format is the one currently being used by the National Bureau of Standards and others, in which the dimensionless quantities Z, E/RT, H/RT, and S/R are the principal entries. The sources are the tables of Hilsenrath, Beckett, et al. (Ref. 1) and of Din (Ref. 2), both of which are formulated in terms of temperature and pressure as independent variables. The range of pressures in Ref. 1 extends from 10-2 to 102 atm, and its pressure-tabulation intervals are rather large. In Ref. 2 the tabulations begin at one atmosphere and extend upwards, sometimes as high as 104 atm. The machinecomputed interpolations were made on the IBM 7070 computer at AEDC. Two sets of tables are presented. In one, the independent variables are temperature and pressure through the range of temperature from 100 to 1500 K and of pressure from one to 104 atm. In the other, the independent variables are temperature and density. The range of temperatures is the same as above, and the density varies from about 10-7 to 630 amagats. The extension of the density range down to 10-7 amagats is based on the assumption of perfect gas conditions. 2.0 DATA CONVERSION Numerical values of the gas constant and reference density are given in the Appendix. The tables of Ref. 1 are based on the assumption that the internal energy of the perfect gas is zero at 0 K, as if to say that the gas has neither liquefied nor solidified in being cooled to absolute zero. On the other hand, the tables of Ref. 2 assume that the internal energy of the perfect crystal is zero at O K, so its tabulated values-of energy involve provisions for the latent heats and the specific heats of the liquid and solid states. Manuscript released by authors August

10 AEDC-TDR All the entries of Ref. 1 have the desired form, with the exception of the enthalpy function (H - Eo)/RTo which must be multiplied by the ratio To/T in order to yield the function H/RT. In this expression To is equal to K. In the tables of Ref. 2, the gas volume is expressed in cm 3 /mole, and these entries are converted to density in amagats by the relation p (i1 )4 Po. Tabulated value (1) The compressibility factor Z is found from the relation - (p/po) R T (2) in which the pressure p is given in atm, the relative density p/po in amagats, and the temperature in *K. The gas constant in this instance is numerically equal to (10)- 3. The entropies in Ref. 2 are given in joules/mole-*k and are converted to dimensionless form by the relation* S/R = (10)-' (Tabulated value) (3) The enthalpies in Ref. 2 are expressed in joules/mole and are converted to dimensionless form by the relation II/RT (Tabulated value) (4) T in which the two constants are averages of many numerical comparisons of corresponding pairs of entries in Refs. 1 and 2. The average deviation of entries computed from Eq. (4) is 0. 2 percent. The dimensionless internal energy function follows from the relation E/RT = I-I/RT - Z (5) The appearance of negative enthalpies and internal energies is discussed in the air tables of Humphrey and Neel (Ref. 3). The entries of Table 2 below a pressure of 10-2 were computed by assuming a perfect gas for which enthalpy is a function of temperature only and isothermal variations of entropy are proportional to the logarithm of the pressure. *Attention is directed to the misprint in the last line on p. 123 of Ref. 2. The author no doubt intended the constant to be , the reciprocal of which is

11 In the real gas domain of Table 2, the isothermal loci of Z, E/RT, H/RT, S/R, and log p, plotted as functions of log (p/po) are so nearly linear in any given region that interpolations were made with the following ratio: log (p/po) - log (P/Po)b log (P/Po)c - log (P/P.)b in which the subscript a denotes the desired value of density, the subscript b refers to the value of density nearest to and less than (p/po)a, and the subscript c denotes the value of density nearest to and greater than the desired value. The simple procedure is adequate because entries are available at fairly small intervals of density. 3.0 CHECKING Table 1 was checked and tested for internal consistency in various ways. The obvious one was to compare its entries with those of Ref. 1. Average agreement between the two was found to be within 0.2 percent. Both Tables 1 and 2 were plotted isothermally as functions of pressure and density to verify consistency. In checking for internal consistency, the verification of the general gas law p RZT (P"Po) was tested throughout both tables. The largest error disclosed by this test was one of 0. 4 percent which occurred at 750'K, where fairing had been necessary to smooth the data. However, the most interesting tests developed as the result of a question relating to the validity of Eq. (4) for the calculation of the function H/RT at high pressures. The constants in Eq. (4) were found by comparing pairs of values in Refs. 1 and 2 in the region from one to 100 atm through which their tables overlapped. The question remained whether Eq. (4) would give consistent results at the higher pressures. This question was examined by the method of characteristics functions (Ref. 4). For instance, on forming what is essentially the Planck function P = S/R - li/at and letting x = log p, it is easy to show that (ap/ax)t = - z 3

12 AEDC.TDR Also, on forming the free energy it follows that A = - TS (aa/au)t = ZR' where u = log p and (aa/at)u = - S/R These three differential relationships were tested with machine-computed derivatives. The average inconsistency turned out to be percent, and its values were slightly, over 0. 5 percent in about one-third of the test points. REFERENCES 1. Hilsenrath, J., Beckett, C. W., et al. "Tables of Thermal Properties of Gases. " National Bureau of Standards, Circular 564, November Din, F. Thermodynamic Functions of Gases, Vol. 3. Butterworths Scientific Publications, London, Humphrey, R. L. and Neel, C. A. "Tables of Thermodynamic Properties of Air from 90 to 1500 K. " AEDC-TN , August Planck, M. Treatise on Thermodynamics. Dover Publications, Inc., New York, (Third Edition) 4

13 AE DC-TDR APPENDIX Density at 00C and p = 1 atm Po = x 10-5 mole/cm x 10-3 g/cm x 10-2 lb/ft 3 Gas Constant R = cal/mole- K x 10-2 cal/gm- K Btu/lb-mole- R x 103 ft 2 /sec x 10-3 atm/amagat- K 5

14 AE DC-TDI * TABLE 1 Tables of the Thermodynamic Properties of Nitrogen from 100 to 1500 K with Independent Variables of Temperature and Pressure

15 T OK p, atm Z E/RT H/RT S/R (p/po) I.U+O O0 9.6( ( C;C Cl C0 9.0L49-C L 1.5C [

16 AEDC-TDR T K p, atm Z E/RT H/RT S/R (p/po)

17 T OK p, atm Z E/RT H/RT S/R (p/po) U O+C u79-Cl L Ii0

18 T K p, atm Z E/RT H/RT S/R (p/po) , 3.0+OC i C D C ;

19 T K p, atm Z E/RT HWRT S/R (p/po) C L : ,

20 AEDC.TDR T OK p, atm Z E/RT WRT S/R (p/po) C *

21 T K p, atm Z E/RT H/RT S/R (p/po)

22 AEDC-TDR T OK p, atm z E/RT H/RT S/R (p/po) Z

23 T OK p, atm Z E/RT H/RT S/R (p/po ) ou , Q G * " C C C S

24 AEDC-TDR T OK p, atm z E/RT H/RT S/R (p/po) d uo

25 T OK p, atm z E/RT H/RT S/R (p/po) 'i i U A C2 1.6(:

26 T OK p, atm Z E/RT f/rt S/R (p/po) C , U u ui u u U ; t C Y ý i ?

27 AEDC-TDR T K p, atm Z E/RT H/RT S/R (p/po) I.O+OC ± F b C (1[

28 T OK p, atm Z E/RT H/RT S/R (p/po) U L f U C ( C C I.1e L C

29 T OK p, atm Z E/RT H/RT S/R (pipo) O+O ( G C o

30 AEDC-TDR T OK p, atm Z E/RT H/RT S/R (p/po) d u QO b * ,2 5.0+C $ u q

31 T - 260ý K p, atm Z E/RT W/RT S/R (p/po) ý d

32 T OK p, atm Z E/RT H/RT S/R (p/po) q U L J

33 T - 28Q OK p, atm Z E/RT H/RT S/R (p/po) o l o b ?