A monatomic ideal gas expands adiabatically from $1\mathrm{.}00$ m$3$to $1\mathrm{.}9$ m$3.$ If the initial pressure is $278$ kPa, calculate the work done by the system in kJ$.$

$($b$)$ Calculate the change in the internal energy in kJ$.$ Answer: $[$ Select $]["-47\mathrm{.}9$ kJ$","-82\mathrm{.}5$ kJ$","-58\mathrm{.}8$ kJ$","-90\mathrm{.}8$ kJ$","-75\mathrm{.}4$ kJ$"]$