Problem $1(25$ points$)$

A piston$-$eylinder assembly contains $5$ kg of air, which is modeled as an ideal gas. The air is heated at constant pressure from a state of temperature $T_1=27C$ and pressure $p_1=500$kPa to a second state of $T_2=57C$ and $p_2=500$kPa.

a$)$ Plot state $2$ with respeet to state I on the $p-v$ and $T-v$ diagrams below.

b$)$ Find the work and heat transfer required to go from state I to state $2.($Verify signs correctly identify whether work and heat flow into or out of the assembly.$)$