$[10$ Pts$]$ A Carnot air engine cycle is running between thermal reservoirs at $500C$ and $100C$ with a mass flux rate of $5k\frac{g}{s}.$ 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 T$-$s diagram. $x-$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$]$