Consider you are working at laboratory, and you have liquid $n-$hexane $(C_6{H}_{14})$ at ambient temperature and pressure and $($:$1(atm)\}.$ Based on your experiment procedure, you need to have vapor phase of $n-$hexane at $300C$ and $1$atm.

$($a$)$ Draw the hypothetical process path for phase change and calculate the enthalpy changes for each step. Determine the total specific enthalpy $(k\frac{J}{m}ol)$ of $n-$hexane for this process.

$($b$)$ Assuming ideal gas behavior, calculate the specific internal energy $(k\frac{J}{m}ol)$ of the $n$ hexane vapor at $300C$ and $1$atm.$||$