$2.[50$ points$]$ Consider a power plant operating steadily on the air$-$standard cycle shown below. Air enters the compressor at $1$ bar and $280$ K $($State $1)$ with mass flow rate of $\backslash (1\mathrm{.}5\backslash$mathrm$\{$~kg$\}/\backslash$mathrm$\{$s$\}\backslash ).$ Air is compressed to $20$ bar $($State $2)$ in a compressor having an isentropic efficiency of $\backslash (90\backslash \%\backslash ).$ Compressed air then enters a constant$-$pressure heat exchanger in which heat is added to air and the heated air exits at $2200$ K $($State $3).$ Air expands to $1$ bar $($State $4)$ through a turbine having an isentropic efficiency of $\backslash (90\backslash \%\backslash ).$ Consider variable specific heats for air.

Molecular weight of air: $\backslash (28\mathrm{.}97\backslash$mathrm$\{$~kg$\}/\backslash$mathrm$\{$kmol$\}\backslash )$

Use the closest value in ideal gas table; do not interpolate.

$($a$)$ Find the missing information in the table $($You need to draw table on your solution$).$

$($b$)$ Determine the rate of entropy generation $\backslash ((\backslash$mathrm$\{$kW$\}/\backslash$mathrm$\{$K$\})\backslash )$ for the heat exchanger if heat transferred to the air of $1600$ kW which occurs at a boundary temperature of $1750$ K $.$