# Constants, Functions, SI Dimensions and Conversions

We provide in Appendix B.1 constants and air properties. In Appendix B.2 the dimensions of the most important quantities are given. The dimensions are in general the SI units (Systeme International d’unites), see [1, 2], where also the constants given in Appendix B.1 can be found. The basic units, the derived units, and conversions[180] to US customary units (English units) are given. Note that we write the dimensions as ‘a/bc’ instead of ‘a/(bc)’ or ‘a b-1 c-1’.

B.1 Constants and Air Properties

The molar universal gas constant R0, the Stephan-Boltzmann constant a, and standard gravitational acceleration g0 are:

Molar universal gas constant R0 = 8.314472-10[181] kgm[182]/s2 kg-molK

= 4.97201-104 lbm ft2/s2 lbm-rnol °R,

Stephan-Boltzmann constant a = 5.670400-10-8 W/m2 K4

= 1.7123-10-9 Btu/hrft2 °R4.

Standard gravitational

acceleration at sea level g0 = 9.80665 m/s2

= 32.174 ft/s2.

In Table B.1 we list some properties of air and its major constituents. The properties were addressed in Chapters 2 and 4. Listed are the molecular weights, the gas constants, and intermolecular force parameters, all for the temperature domain of our interest.

Fig. B.1 shows the dimensionless collision integrals = Qk, and QDab of air as functions of the dimensionless temperatures kT/e or кТ/єАв. The Lennard-Jones parameters e/k [K] for air and its constituents are given in Table B.1.

Table B.2 lists the characteristic rotational, vibrational, and dissociation temperatures of the molecular air constituents N2, O2, and NO.

Table B.1. Molecular weights, gas constants, and intermolecular force parameters of air constituents for the low temperature domain [3, 4]. * is the U. S. standard atmosphere value, + the value from [4].

 Gas Molecular weight M [kg/kg-mol] Specific gas constant R [m2/(s2K)] Collision dia­meter a • 1010 [m] 2nd Lennard-Jones parameter e/k [K] air 28.9644* (28.97+) 287.06 3.617 97.0 n2 28.02 296.73 3.667 99.8 o2 32.00 259.83 3.430 113.0 NO 30.01 277.06 3.470 119.0 N 14.01 593.47 2.940 66.5 О 16.00 519.65 2.330 210.0 Ar 39.948 208.13 3.432 122.4 He 4.003 2077.06 2.576 10.2

Table B.2. Characteristic rotational, vibrational, and dissociation temperatures of air molecules [5].

 Gas: N2 On NO Grot [K] 2.9 2.1 2.5 ®vibr [K] 3,390 2,270 2,740 Gdiss [K] 113,000 59,500 75,500