Constants associated with the density equation for normal hydrogen i [a.sub.i] [b.sub.i] [c.sub.i] 1 0.058 884 60 1.325 1.0 2 -0.061 361 11 1.87 1.0 3 -0.002 650 473 2.5 2.0 4 0.002 731 125 2.8 2.0 5 0.001 802 374 2.938 2.42 6 -0.001 150 707 3.14 2.63 7 0.958 852 8 x [10.sup.-4] 3.37 3.0 8 -0.1109040 0 x [10.sup.-6] 3.75 4.0 9 0.126 440 3 x [10.sup.-9] 4.0 5.0 Molar Mass: M = 2.015 88 g/mol Universal

Gas Constant: R = 8.314 472 J/(mol.

The equation generates one dependent variable t, two dependent variables [alpha] and T, three unknown constants Z, Ea and n, and the universal

gas constant.

Values assigned to constants used in the numerical model Parameter Value assigned Gas viscosity ([[micro].sub.g], kg/m.s) 1.85 x [10.sup.-5] Water viscosity ([[micro].sub.w] kg/m.s) 1 x [10.sup.-3] Water density ([[rho].sub.w], kg/[m.sup.3]) 1 x [10.sup.3] Universal

gas constant (R, J/K.mol) 8.314 Molecular mass nitrogen ([M.sub.g], kg/mol) 2.8 x [10.sup.-2] Temperature (T, K) 293.15 Acceleration due to gravity (g, m/[s.sup.2]) 9.81 Table 3.

where [Rho] is the melt density, T is the processing temperature, R is the

gas constant, Mc is the critical molecular weight, M is the absolute molecular weight, and [[Eta].sub.[M.sub.c],T] is the zero-shear viscosity at the critical molecular weight and processing temperature.

Assuming that the mole fraction of C[O.sub.2] in the air, [[c.sub.a].sup.*] (in moles per mole), is constant regardless of the value of P, and noting that [c.sub.a] = (P[[c.sub.a].sup.*]/RT) (where R is the

gas constant), we can rewrite Eq.

Where [m.sub.0] is the initial nitrogen content in kilograms in the molten iron before any given half-rotation of the vessel, m is the final nitrogen content after any given half-rotation of the vessel, R is the

gas constant, T = 1.873[degrees] K, and V = 30 [m.sup.3].

Where 'Ce' is the concentration of adsorbate in solution (mgl-1 ), T is a temperature (K) and 'R' is a

gas constant (KJmol-1 k-1 ).

Interestingly this author realized that the above difference between molar heat capacities allows for a relationship between the ideal

gas constant (R) and the ability of a mole of gas molecules to do work against a gravitational field [1, 20-21], as a function of temperature.

where R is the universal

gas constant, J/(mol x K), and T is the temperature, K.

Where [R.sub.im] is intake manifold

gas constant, [T.sub.im].

R: Perfect

gas constant (J.[K.sup.-1].[mol.sup.-1])

where T is solution temperature (K), [K.sub.o] a constant, and R

gas constant (8.314 J/Kmol).