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Appendix

Tables for Prediction

Transport Properties

E l Intermolecular force parameters and critical properties

5E.2 Functions for prediction of transport properties of gases at low densities

Table E.l Lennard-Jones (6-12) Potential Parameters and Critical Properties

Molecular Weight Substance M

Light elements:

H2 2. He 4.

Noble gases:

Ne 20. Ar 39. Kr 83. Xe 131.

Simple polyatomic gases:

Air 2 8. 9 ~ ~

N 2 28. 0 2 31. CO 28.

co2 44.

NO 30.

No 44.

so2 64.

F 2 37.

c 12 70. Br2 159. 12 253. Hydrocarbons: CH C H g H CH2=CH C2H CH,C=CH CH3CH=CH C3H n--C4H

Lennard-Jones parameters

IT E / K Ref.

(A, (K)

Critical properties8,h

Tc PC k (K) (atm) (cm3/g-mole)

Table E.2 Collision Integrals for Use with the Lennard-Jones (6-12) Potential for the Prediction of Transport Properties of Gases at Low ~ensities",~,'

a, = ak K T / & (^) (for viscosity %AB or and thermal (for K T / & ~ , conductivity)^ diffusivity)

a, = I(Zk K T / & (^) (for viscosity %,A, or and thermal (for K T / E ~ ~ conductivity) diffusivity)

" The values in this table, applicable for the Lennard-Jones (6-12) potential, are interpolated from the results of L. Monchick and E. A. Mason, J. Chem. Phys., 35,1676-1697 (1961).The Monchick-Mason table is believed to be slightly better than the earlier table by J. 0. Hirschfelder, R. B. Bird, and E. L. Spotz, J. Chem. Phys., 16,968-981 (1948). This table has been extended to lower temperatures by C. F. Curtiss, J. Chem. Phys., 97,7679-7686 (1992).Curtiss showed that at low temperatures, the Boltzmann equation needs to be modified to take into account "orbiting pairs" of molecules. Only by making this modification is it possible to get a smooth transition from quantum to classical behavior. The deviations are appreciable below dimensionless temperatures of 0.30. 'The collision integrals have been curve-fitted by P. D. Neufeld, A. R. Jansen, and R. A. Aziz, J. Chem. Phys., 57, 1100-1102 (1972), as follows:

where F = KT/&.

Appendix F

Constants and Conversion Factors

5 F. 1 Mathematical constants 5F.2 Physical constants

5F.3 Conversion factors

1 MATHEMATICAL CONSTANTS

5F.2 PHYSICAL CONSTANTS'

Gas law constant ( R )

Standard acceleration

of gravity (go)

Joule's constant (I,)

(mechanical equivalent of heat)

Avogadro's number (N)

Boltzmann's constant (K = R / I ; I ) Faraday's constant ( F ) Planck's constant (h)

Stefan-Boltzmann constant (a)

Electron charge (e) Speed of light in a vacuum (c)

J/g-mole K

k g. m2/s2. kg-mol .K g .cm2/s2.g-mo1 K cal/ g-mol .K cm3atm/g-mol .K

lb, f$/s2 lb-mol .R

ft .lbf/lb-mol .R

molecules/g-mol

C / g-equivalent

J. s erg .s W/m2. K~ cal/s. cm2K Btu/hr ft2R

E. R. Cohen and B. N. Taylor, Physics Today (August 1996), pp. BG9-BG13; R. A. Nelson,

Physics Today (August 1996), pp. BG15-BG16. 867

Table F.3-2 Conversion Factors for Quantities Having Dimensions of F/L2 or M / L ~ ~(pressure, momentum flux)

6.8947 X lo4 4.6330 X lo3 144 1 6.8046 X lop2 5.1715 X 10' 2.

atm 1.0133 x lo6 6.8087 X lo4 2.1162 x lo3 14.696 1 760 29.

1.3332 X lo3 8.9588 X 10' (^) 2.7845 1.9337 X lo-' 1.3158 X lop3 1 3.9370 X lo-' 3.3864 X lo4 2.2756 X lo3 7.0727 X 10' 4.9116 X lo-' 3.3421 X lop2 25.400 1

" This unit is preferably abbreviated "psia" (pounds per square inch absolute) or "psig" (pounds per square inch gage). Gage pressure is absolute pressure minus the prevailing barometric pressure. Sometimes the pressure is reported in '%arsrs";to convert from bars to pascals, multiply by lo5,and to convert from bars to atmospheres, multiply by 0.98692.

Table F.3-3 Conversion Factors for Quantities Having Dimensions of FL or M L ~ / ~ ~(energy, work, torque)

Given a Multiply by quantity in table value foot

foot poundals = lb, ft2/s 3.1081 X 1.0072 X 3.9942 X 1.5698 X lo-' 1.1706 X lo-" 1.3558 X lo7 32.1740 1 3.2405 X lo-' 1.2851 X lop3 5.0505 X 3.7662 X thermochemical caloriesa 4.1840 X lo7 9.9287 X 10' 3.0860 1 3.9657 X 1.5586 X lop6 1.1622 X British thermal units 1.0550 X 10'' 2.5036 X lo4 778.16 2.5216 X lo2 1 3.9301 X 2.9307 X

Horsepower hours 2.6845 x 1013 6.3705 x lo7 1.9800 x lo6 6.4162 x lo5 2.5445 X lo3 1 7.4570 X lo-'

kilowatt hours 3.6000 X 1013 8.5429 X lo7 2.6552 X lo6 8.6042 X lo5 3.4122 X lo3 1.3410 1

" This unit, abbreviated "cal," is used in some chemical thermodynamic tables. To convert quantities expressed in International Steam Table calories (abbreviated "I. T. cal") to this unit, multiply by 1.000654.

Table F.3-4 Conversion Factors for Quantities Having dimensionsaof M/Lt or Ft/L2 (viscosity, density times diffusivity)

" When moles appear in the given and the desired units, the conversion factor is the same as for the corresponding mass units.

Table F.3-5 Conversion Factors for Quantities Having Dimensions of ML/t3T or F/tT (thermal conductivity)

Given a Multiply by

8.0068 X lo5 3.2174 X 10' 1 1.9137 X lo-' 4. cal/s .cm .K 4.1840 X lo7 1.6813 X lo3 5.2256 X 10' 1 2.4175 X 10' Btu/hr ft .F 2.1616 X lo-' 4.1365 X lop3 1