A monatomic ideal gas increases in pressure adiabatically from an initial pressure of $1\mathrm{.}00105$ Pa and volume of $3\mathrm{.}00$ m$3$ to a final volume of $1\mathrm{.}00$ m$3.$ Two answers are required.

$($a$)$ Calculate the final pressure. Answer: $[$ Select $]["538$ kPa", $"4\mathrm{.}09$ kPa", $"567$ kPa", $"624$ kPa", $"599$kPa"$]$

$($b$)$ Calculate the change in the internal energy. Answer: $[$ Select $]["777$ kJ$","935$ kJ$","486$ kJ$","589$ kJ$","284$ kJ$"]$