16.4-1
Computation of Mass Diffusivity at Low Density
The use of Maple for this problem is comparable to finding the solution by hand. The values needed for equation 16.4-13 can either be looked up in the back of the BSL or found using simple, smaller equations like equations 16.4-15 and 16.4-16. Once found, these values can simply be plugged into 16.4-13 and the mass diffusivity is calculated.
For simplicity in appearance, units are omitted and defined in text!
> restart;
> Dab:=0.0018583*(sqrt(T^3*(1/Ma+1/Mb)))/(p*sigmaAB^2*OmegaDab); Equation 16.4-13
> sigmaAB:=1/2*(sigmaA+sigmaB); Equation 16.4-15 epsilonAB:=sqrt(epsilonA*epsilonB); Equation 16.4-16
Given Parameters in Problem (Temperature in Kelvin and pressure in atm):
> T:=293.2; p:=1.0;
Parameters Found in Table B-1 on page 744 of BSL.
Ma and Mb are in g/mol; sigma values are in angstroms; epsilon values are in Kelvin;
NOTE: This solution assumes Argon is compound A and Oxygen is compound B.
> Ma:=39.944; Mb:=32.00; sigmaA:=3.418; sigmaB:=3.433; epsilonA:=124; epsilonB:=113;
> sigmaAB; epsilonAB; assume(k>0):
Here Maple is picky. On a calculator one can quickly determine the square root of 14012 and find that it is equal to 118.37 K. The necessary value in order to use Table B-2 on page 746 of BSL is KT/epsilonAB...Thus, we divide the given Temperature by this 118.37 to get...
> TableB2Value:=T/epsilonAB;
Again, Maple is too picky to reduce this to a simple number...293.2/118.5 is 2.47! This value is now used with Table B-2 on page 746 of BSL and a corresponding OmegaDab is found (make sure you look in the CORRECT column and extropolate carefully).
> OmegaDab:=1.003;
> Dab;
Thus, the mass diffusivity of a mixture of Argon and Oxygen at low density is:
0.188cm^2/sec