A monatomic ideal gas that is initially at a pressure of $1\mathrm{.}50105$ PaPa and with a volume of $8\mathrm{.}50102$ m$3$m$3$ is compressed adiabatically to a volume of $4\mathrm{.}00102$ m$3$m$3.$ a$)$ What is the final pressure? b$)$ How much work is done by the gas during the compression? c$)$ What is the ratio of the final temperature of the gas to its initial temperature?