During the compression stroke of a certain gasoline engine, the pressure increases from $1\mathrm{.}00$ atm to $20\mathrm{.}0$ atm. If

the process is adiabatic and the air$-$fuel mixture behaves as a diatomic ideal gas, $($a$)$ by what factor does the

volume change and $($b$)$ by what factor does the temperature change? Assuming the compression starts with

$0\mathrm{.}0160$ mol of gas at $27.$oC$,$ find the values of $($c$)$ Q$,($d$)$Eint$,$ and $($e$)$ W that characterize the process.

$($e$)$ Since Q$=0,$ W is just $$Eint or $135$ J$.$