Problem $2($to be graded$)$:

A new air$-$standard power cycle has been proposed in which air undergoes the following processes inside a piston$-$cylinder device. Air is compressed isothermally from $120$ kPa and $350$ K $($State $1)$ to $1500$ kPa $($State $2).$ Heat rejection of $\backslash (198\mathrm{.}3\backslash$mathrm$\{$~kJ$\}/\backslash$mathrm$\{$kg$\}\backslash )$ occurs during the isothermal compression process. Heat addition of $\backslash (1200\backslash$mathrm$\{$~kJ$\}/\backslash$mathrm$\{$kg$\}\backslash )$ occurs at constant volume $\backslash (\backslash$left$(\backslash$mathrm$\{$V$\}\_\{2\}=\backslash$mathrm$\{$V$\}\_\{3\}\backslash$right$)\backslash )($State $3).$ Air expands reversibly and adiabatically to $120$ kPa $($State $4)$ and heat is rejected at constant pressure $\backslash (\backslash$left$($P$\_\{4\}=$P$\_\{1\}\backslash$right$)\backslash )$ to complete the thermodynamic cycle. Consider constant specific heats for air at $350$ K $.$

$($a$)$ Calculate the net specific work $\backslash ((\backslash$mathrm$\{$kJ$\}/\backslash$mathrm$\{$kg$\})\backslash )$ for the cycle.

$($b$)$ Determine the thermal efficiency $(\backslash \%)$ of the cycle.

$($c$)$ Show the cycle on P$-$v and T$-$s diagrams. Label states, indicate appropriate lines of constant temperature or pressure, and show property values. Do not show specific entropy values on the T$-$s diagram.

Answers: $($a$)$ Not attached; $($b$)61\mathrm{.}6\backslash \%$; $($c$)$ Not attached