Problem $3(30$ Points$)$ A $1$ liter $(0\mathrm{.}001m^3)$ piston cylinder contains air at $500$ kPa and $25C.$ The air is heated to $125C$ at a constant pressure. Find:

a$)$ The volume at the final state. $(10$ points$)$

b$)$ The work performed by the air on the piston. $(10$ points$)$

c$)$ The amount of heat required for the process. $(10$ points$)$