Example 17.2-1 using the Matlab progam
>>help dcalc
Chapman-Enskog formula for mass diffusivity coefficient for binary mixtures
function D = dcalc(p,T,index)
Argument List:
p [=] pressure in kPa
T [=] temperature in the units of Tdeg
index [=] index of 2 compounds in cnms whose Dab is to be found
(If this argument is omitted, Dab will be found for the first 2)
Returns:
D [=] mass diffusivity in units of m2/s
Here are your compounds' formulae and names:
No. Formula Name
----------------------------------------
1 CO carbon monoxide
2 CO2 carbon dioxide
>>LJones
LJones =
3.5900e+00 1.1000e+02
3.9960e+00 1.9000e+02
>>dcalc(101.325,296.1)
ans =
1.4919e-05
> restart;
Using dcalc:
> DAB:=1.4919e-5*m^2/second;
> m:=100*cm;
> DAB; compared to .152cm^2/second found in the text.
![[Maple Math]](images/ex17211.gif)
Using eq. 17.2-1 with data from ceng301 data bank
Here are your compounds' formulae and names:
No. Formula Name
----------------------------------------
1 CO carbon monoxide
2 CO2 carbon dioxide
>>disp(critP')
3.4986e+03 7.3805e+03
>>disp(critT')
1.3295e+02 3.0420e+02
>>disp(mw')
2.8010e+01 4.4010e+01
> DAB:=(p,T,a,b,pCA,pCB,TCA,TCB,MWA,MWB)->(pCA*pCB)^(1/3)*(TCA*TCB)^(5/12)*(1/MWA+1/MWB)^(1/2)*a*(T/sqrt(TCA*TCB))^b/p;
> kPa:=atm/101.325;pCA:=3.499e3*kPa;pCB:=7.381e3*kPa;
> DAB(1,296.1,2.745e-4,1.823,34.53,72.84,132.9,304.2,28.01,44.01);
![[Maple Math]](images/ex17212.gif)
Note that a must have units if we assign units to the other terms in the equation.
> simplify(DAB(1*atm,296.1*K,2.745e-4,1.823,34.53*atm,72.84*atm,132.9*K,304.2*K,28.01*g/mol,44.01*g/mol),assume=positive);
![[Maple Math]](images/ex17213.gif)
Thus we need to have a with the units:
> a:=2.745e-4*cm^2/s/K^(5/6)/sqrt(mol/g)*atm^(1/3);
> simplify(DAB(1*atm,296.1*K,a,1.823,34.53*atm,72.84*atm,132.9*K,304.2*K,28.01*g/mol,44.01*g/mol),assume=positive);