Problem $1(50$ points$)$: A rigid tank contains $2kg$ of air initially at $100$kPa and $130C($state $1).$ The air is stirred with a paddle wheel until its temperature reaches $300C($state $2).$ The paddle wheel adds $450kJ$ of energy to the air. During this process, heat is transferred from the air inside the tank to the environment. The environment is at $27C.$

Part $1)$ Sketch a schematic for this problem; show the boundary of the system and all types of energy crossing the boundary. Write all known values.

Part $2)$ Determine the specific volume, and specific internal energy at state $1.$

Part $3)$ Determine the specific volume, pressure, and specific internal energy at state $2.$

Part $4)$ Determine the change of specific entropy during this process.

Part $5)$ Determine the heat transfer during this process.