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

Sixteen $(24\frac{m^3}{m}in)$ of superheated steam enter a well$-$insulated turbine operating at steady state at $8\mathrm{.}0$ MPa and a Temperature of $550C($Celsius$).$ The steam expands to the turbine exit where the pressure is $200$ KPa $.$ If the Turbine has an adiabatic efficiency of $88\%,$ Determine:

a$)$ The ideal power developed by the turbine and the corresponding exit temperature.

b$)$ The real power developed by the turbine and the corresponding exit temperature.

c$)$ The entropy change, for the process when it is irreversible.

d$)$ Sketch the ideal and real processes in a P$-$v diagram.

e$)$ Sketch the ideal and real processes in a $T-$s diagram

Problem #$2$: $(50$ pts$.)$

Five $(5)$ kilograms of air $R=0\mathrm{.}286K\frac{J}{K}gK,$ are contained in a piston$-$cylinder device with an initial volume of $0\mathrm{.}82m^3$ and a pressure of $15$ bar $.$ The piston is then allowed to move until the pressure is reduced to $3$ bar in a reversible process. Determine:

a$)$ The temperature of the final state in Kelvin and the work in $KJ$ if the process is considered adiabatic.

b$)$ The entropy changes in $K\frac{J}{K}$ if heat losses during the process cause the final temperature to reach $650$ K $.$

c$)$ Sketch the adiabatic and heat loss processes in a P$-$v diagram.

d$)$ Sketch the adiabatic and heat loss processes in a $T-$s diagram.