Problem $10\mathrm{.}015-3-$Step Air$-$standard cycle with constant specific heats

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An air$-$standard cycle is executed within a closed piston$$cylinder system, and it consists of the following three processes:

$1-2$ V $=$ Constant heat addition from $100$ kPa and $32\mathrm{.}00$C to $850$ kPa $2-3$ Isothermal expansion until V$3=8\mathrm{.}5$V$231$V$3=8\mathrm{.}5$V$231$ P $=$ Constant heat rejection to the initial state Assume air has constant properties with cv$=0\mathrm{.}718$kJ$/$kg$$K$,$cp$=1\mathrm{.}005$kJ$/$kg$$Kcv$=0\mathrm{.}718$kJ$/$kg$$K$,$cp$=1\mathrm{.}005$kJ$/$kg$$K $,$ R $=0\mathrm{.}287$ kJ$/$kg$$K$,$ and k $=1\mathrm{.}4.$

Problem $10\mathrm{.}015.$c $-$ Cycle efficiency for air$-$standard cycle

Determine the cycle thermal efficiency.

The cycle thermal efficiency is $\%.$