Problem H$1$: $(50$ pts$.)$

Steam enters an adiabatic turbine at $6$MPa,$600C,$ and $80\frac{m}{s}$ and leaves at $50$ kPa $,100C,$ ad $140\frac{m}{s}.$ The power output of the turbine is $8$ MW $.$

You are asked to:

a$)$ Define the correct engincering model

b$)$ Draw an engineering diagram $($neat schematic$)$

c$)$ Determine whether the Second Law of Thermodynamics is satisfied or violated in this process. Support your conclusion with a numerical analysis.

d$)$ Determine the mass flow rate of the steam

e$)$ Determine the exit enthalpy and temperature at the isentropic condition

f$)$ Determine the power output of the turbine $(kW)$ at the isentropic condition

g$)$ Sketch the reversible and irreversible processes in a $T-$s diagram with repect to the saturation lines.

b$)$ Sketch the processes in a P$-$v diagram with respect to the saturation lines.

Instruction: Begin your response in the space provided below. If additional space is required, you may attach extra sheets to your submission. Please ensure that all attachments are properly labeled. Ensure that you provide detailed step$-$by$-$step calculations for each part of the problem.