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.
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.
Volume of full cylinder = 0.90735 m^3
P = 992736Pa
P = 992736Pa
The following is my attempt to solve for the initial amount of steam added:
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:
Is this the right approach?