PROBLEM ${?}_2(9$ points$)$

$2$ kg Ethylene is contained in a piston$-$cylinder device. The system goes from $5$ MPa and $37C$ to $1300$ kPa at constant temperature.

$($a$)$ Assuming ethylene behaves like an ideal gas throughout the process:

Determine the initial and final volumes of the piston$-$cylinder?

$($b$)$ Assuming ethylene behaves like a real gas $($non$-$ideal$)$ throughout the process:

Determine the initial and final volumes of the piston$-$cylinder?

$($c$)$ What is the percentage of error in $V_{\text{f}\text{i}\text{n}\text{a}\text{l}}$ calculation when considering ethylene an ideal gas?