A piston$-$cylinder device contains $0\mathrm{.}13$ kg of air initially at $2$ MPa and $\backslash (350^\{\backslash$circ$\}\backslash$mathrm$\{$C$\}\backslash ).$ The air is first expanded isothermally to $500$ kPa $,$ then compressed polytropically with a polytropic exponent of $1\mathrm{.}2$ to the initial pressure, and finally compressed at the constant pressure to the initial state. Determine the boundary work for each process and the net work of the cycle. The properties of air are $\backslash ($ R$=0\mathrm{.}287\backslash )\backslash (\backslash$mathrm$\{$kJ$\}/\backslash$mathrm$\{$kg$\}\backslash$cdot $\backslash$mathrm$\{$K$\}\backslash )$ and $\backslash ($ k$=1\mathrm{.}4\backslash ).$

The boundary work for the isothermal expansion process is kJ$.$

The boundary work for the polytropic compression process is kJ$.$

The boundary work for the constant pressure compression process is

The net work for the cycle is

kJ$.$