Problem $2.(15$ pts$)$

Consider an air$-$standard Brayton cycle with regeneration as shown. Air enters the compressor at $100F$ and $14\mathrm{.}7lb\frac{f}{i}{n}^2.$ The compressor pressure ratio is $14$ and the maximum temperature in the cycle is $2540F.$ Assuming an isentropic process in the compressor, an isentropic compression efficiency in the turbine of $90\%$ and a regenerator efficiency of $80\%,$

a$)$ Show the cycle on a T$-$s diagram then calculate:

b$)$ the net power output per unit mass of air,

c$)$ the thermal efficiency of the cycle, and

d$)$ the thermal efficiency of the cycle without the regenerator.

Notes: $1.$ To get full credit, you need to assume air ideal gas with constant specific heats $($i$.$e cold$-$air standard analysis$)$ The properties of air at room temperature are $c_v=0\mathrm{.}171$ Btu$/$bm $*R,c_p=0\mathrm{.}240Bt\frac{u}{b}m*R,k=1\mathrm{.}4,$ and Gas Constant $R=0\mathrm{.}0685Bt\frac{u}{b}m*R$