Adiabatic Compression in a Polytropic Process

$1)$ A gas undergoes adiabatic compression in a piston$-$cylinder device. The initial state of the gas is $100$ kPa and $300$ K$,$ and it is compressed to a final pressure of $1$ MPa. Calculate the final temperature of the gas, assuming it behaves as an ideal gas with gamma equals $1\mathrm{.}4.$

$2)$ Discuss the role of the adiabatic index gamma in determining the final temperature and pressure of the gas.