Problem $7(30$ points$)$

Air in a piston$-$cylinder device undergoes the following cycle consisting of the following processes:

an isothermal compression; $2)$ a constant volume heat addition; $3)$ polytropic expansion; and

a constant volume heat rejection.

Air in the $0\mathrm{.}4-m^3$ piston$-$cylinder device starts at $100$ kPa and $300$ K $.$ The cycle description is as follows:

Process $12$ : The air is compressed isothermally to a volume of $0\mathrm{.}05-m^3.$

Process $23$ : The air temperature is increased to $1000$ K during a constant volume heating process.

Process $34$ : The air is expanded polytropically $(n=1\mathrm{.}336)$ to a volume of $0\mathrm{.}4-m^3.$

Process $41$ : The air temperature is reduced back to $300$ K during a constant volume cooling process.

Assume ideal gas behavior and use values of specific heat at $300$ K for your calculations.

Sketch the cycle on the included P$-AA$ diagram.

a$)$ Does the cycle produce