My understanding of this problem is that I must find the volume of initial steam to add so that the adiabat is as large as possible without condensing the steam.  Point B to Point C on the following image is that adiabatic transition that I am talking about. 

[IMG]http://img694.imageshack.us/img694/2987/carnotcycle.png[/img]
Using a steam table from [URL=http://www.energysolutionscenter.org/BoilerBurner/Eff_Improve/Primer/SteamTables.pdf]http://www.energysolutionscenter.org/BoilerBurner/Eff_Improve/Primer/SteamTables.pdf[/URL] I got the following values.  The ɣ is from the adiabatic index on Wikipedia.

Vgas=3.5*10^-3 m^3/mol
Vliq=2.0*10^-5 m^3/mol                                                                   
Volume of full cylinder = 0.90735 m^3           
P = 992736Pa
ɣ=1.13
T=453K
P = 992736Pa
ΔHvap=36260J/mol

The following is my attempt to solve for the initial amount of steam added:
[IMG]http://img190.imageshack.us/img190/9198/mapleg.png[/img]
Equation 4 is the pressure and temperature of steam at which a phase change to liquid water will begin.  Equation 5 is a rearranged form of equation 3 giving the final pressure after expansion.  Equation 6 Is Equation 2 with pressure from equation 5 and the number of moles based on the amount of volume added.  Equation 7 is equation 4 with equation 5 and equation 6 plugged into it.  Volume is the only variable and I have attempted to solve for it, but Maple 11 will not solve for me.  Here is a picture of what happens when I attempt to solve in Maple:
[IMG]http://img19.imageshack.us/img19/4810/volume.png[/img]

Is this the right approach?