Task $4$

$($a$)$ A gas undergoes a polytropic expansion process shown below, given the following parameters:

$p_1=54$kPa

$p_2=2$kPa

$V_2=18m^3$

Determine the index of compression $(n)$ for this process.

$($b$)$ A gas undergoes an isobaric heating process. Show that the index of compression must be $0$ in

this circumstance.