The total volume of $5$ kg of air initially at $100$ kPa and $300$ K conditions is $4\mathrm{.}306$ m$^3.($Case $1).$ Enough energy is transferred to the air to double its volume and pressure $($Case $2).$ Then, State $3$ is reached by withdrawing a constant volume of heat until the pressure drops to $100$ kPa. Finally, the initial conditions $($Case $1)$ are returned by removing heat at a constant pressure of $100$ kPa. The heat capacity of air exhibiting ideal gas behavior is C $20\mathrm{.}78$ kJ mol$-1.$K$-.$ a$)$ Draw the P$-$V diagram of the cyclic process described above. b$)$ Determine the amount of heat $($kJ$)$ added between cases $1$ and $2.$ c$)$ Determine the amount of heat $($kJ$)$ removed between cases $2$ and $3.$ d$)$ Determine the amount of heat $($kJ$)$ removed between cases $3$ and $1.$ e$)$ What is the net amount of work $($kJ$)$ produced in the cyclic process?