$2.[10$ Pts$]$ A Carnot air engine cycle is running between thermal reservoirs at $\backslash (500^\{\backslash$circ$\}\backslash$mathrm$\{$C$\}\backslash )$ and $\backslash (100^\{\backslash$circ$\}\backslash$mathrm$\{$C$\}\backslash )$ with a mass flux rate of $\backslash (5\backslash$mathrm$\{$~kg$\}/\backslash$mathrm$\{$s$\}\backslash ).$ The air is in quasi$-$equilibrium with the thermal reservoirs. The cycle is producing $1$ MW of power. Treat air as ideal gas.

$($a$)$ Draw this in $\backslash ($ T $\backslash )-$s diagram. $\backslash ($ x $\backslash )-$axis coordinate not needed. $[2$ Pts$]$

$($b$)$ What is the thermal efficiency? $[2$ Pts$]$

$($c$)$ What are the specific entropy changes for the air $($excluding reservoirs$)$ at each heat exchanger? $[3$ Pts$]$

$($d$)$ What is the expansion ratio at the turbine? $[3$ Pts$]$