Using your bicycle pump, you exert $120$ N of force to push the handle down by $100$ cm$.$ If your bicycle tire holds $1$ mole of gas initially at $300$ K$,$ what is the final temperature of the gas in the tire? Assume that the gas is monotomic, obeys the ideal gas law, and that pumping it is an adiabatic process. $($Assume also that R $8$ J$/$mol K$.)($a$)280$ K $($b$)290$ K $($c$)300$ K $($d$)310$ K $($e$)320$ K