oblem $1.(35$ pts$)$ A gas turbine engine operates as an air$-$standard Brayton cycle with reheat and regeneration shown. Air enters the compressor at $14\mathrm{.}7lb\frac{f}{i}{n}^2$ and $60F.$ The compressor pressure ratio is $12$ with an isentropic efficiency of $90\%.$ The temperature at the inlet of the first turbine stage is $2240F.$ The expansion takes place isentropically in two stages with reheat to $2040F$ between the stages at a constant pressure of $50lb\frac{f}{i}{n}^2.$ A regenerator having an effectiveness of $85\%$ is also used in the cycle.

a$)$ Show the cycle on a temperatureentropy diagram, and calculate:

b$)$ the thermal efficiency of the cycle,

c$)$ The total exergy destroyed for the cycle per lb of air, and

d$)$ Compare the result in $($b$)$ to the thermal efficiency of the cycle without the regenerator.

Note: To get full credit, you need to assume air as ideal gas with constant specific heats $($i$.$e$.$ cold$-$air standard analysis$)$ Properties of air: $C_V=0\mathrm{.}171Bt\frac{u}{l}bm*R,C_p=0\mathrm{.}24Bt\frac{u}{l}bm*R,k=1\mathrm{.}4,$ and Gas Constant: $R=0\mathrm{.}0685Bt\frac{u}{l}bm*R$