1999 Version of Problem started by Amina Qutub in 1998. The diagram is from the 1998 bonus problem.

> restart;

> jAz:=z->-(c^2/rho)*MA*MB*DAB*(D(xA)(z)+kT*diff(log(T(z)),z));

Equation 18.5-1 for diffusion in the z direction and an ideal mixture with gravity and pressure diffusion neglected. This agrees with eq. 18.5-12 when jAz(z) = 0.

> eq1:=int(jAz(z),z); For a steady state system in which there is no net flow, this should be zero for all values of z.

> xA:=solve(eq1,xA(z)); Thus we can solve for xA(z):

> xA:=unapply(xA,z); and make a function out of it.

> dxA:=xA(z1)-xA(z2); This then is the difference in mol fractions.

> T(z1):=298.*K;T(z2):=500.*K;kT:=0.0757; Setting values for a numerical example.

> dxA;

> simplify(%,assume=positive); This agrees with what Ms. Qutub found.

> Tm:=T(z1)*T(z2)/(T(z2)-T(z1))*log(T(z2)/T(z1)); This gives the recommended temperature for finding kT.

>