$(50$ points$)$ A steam turbine operates by taking in superheated steam at $800$ psia and $1000F$ and adiabatically exhausting it as saturated steam at $100F.$ The mass flow rate is $1000lb$ per hour through a $3$ inch diameter pipe.

What is the form of the general energy equation that applies to this flow system? What is the numerical value of each term in the applicable energy equation expressed in BTU? If the turbine is poorly insulated such that $100$ BTU per pound of steam fed is lost to the surroundings as heat energy, what is the maximum amount of shaft work that can be extracted?