Problem $2$: Gas Turbine Power Cycle $(59$ points$)$

A Brayton cycle with intercooling, reheat, and regeneration is shown in the figure below.

o$.$

The following information is given:

$\backslash$table$[[,$Compression Ratio,Isentropic Efficiency$],[$Compressor $1,8,1],[$Compressor $2,8,0\mathrm{.}8],[$Turbine $1,\frac{1}{8},1],[$Turbine $2,$Not given,$0\mathrm{.}9]]$

The mass flow rate of air is $5k\frac{g}{s}.$

Air exits the heat exchanger at $100$ kPa and a temperature of $300$ K $.$

The heat exchanger has fluid friction that results in a pressure drop of $50$ kPa $.$ All other components that exchange heat with the surroundings are ideal and have no pressure drop across them.

Air enters Turbine $1$ and Turbine $2$ at $1700$ K$.$

The regenerator effectiveness is $80\%.$

Air exits the cooler at the same temperature as it exits the heat exchanger.

Do the following:

a$)$ Determine the pressure at the exit of Turbine $2,$ in kPa $(3$ points$).$

b$)$ Populate a scorecard showing the pressure $($ kPa $),$ temperature $($ K $),$ specific enthalpy $(k\frac{J}{k}g),$ and specific entropy $(k\frac{J}{k}g-K)$ at each state. $(22$ points$)$

c$)$ Plot a T$-$s diagram for the cycle, hand$-$drawing the paths between states, but plotting temperature and entropy to scale. $(5$ points$)$

d$)$ Determine the net power generated by the cycle, in MW$.(4$ points$)$

e$)$ Determine the thermal efficiency of the cycle. $(3$ points$)$

f$)$ Determine the ratio of heat transferred by the regenerator to the external heat input to the cycle. $(3$ points$)$

g$)$ Determine the back work ratio. $(3$ points$)$

h$)$ For each component, populate a table showing the change in system entropy $($i$.$e$.,$ net entropy transport by mass flows between the exit$($s$)$ and the inlet$($s$)),\frac{Q^{}}{T_b},$ and $S_{\text{g}\text{e}\text{n}}^{},$ all in kW$/$K$.(15$ points$)$ Assume that the ambient environment is at $285$ K and the gas combustion temperature is $1900$ K $.$ The purpose of this exercise is to help you better understand where entropy generation is coming from.

i$)$ Which component produces the most entropy? $(1$ point$)$