$7\mathrm{.}7.$ Methane enters a pipe with DI of $3$ cm at $30$C and $10$ bar at an average velocity of $5\mathrm{.}00$ m$/$s and emerges at a point $200$ m lower than the inlet, at $30$C and $9$ bar.

$($a$)$ Without making calculations, predict the signs $(+$ or $-)$ of k and p$,$ where means $($outflows $-$ inflows$).$ Give a brief explanation of your reasoning.

$($b$)$ Calculate Ex and Ep $($W$),$ assuming that methane behaves as an ideal gas.