During the compression stroke of a certain petrol engine, the pressure increases from $1\mathrm{.}0$ atm to $20\mathrm{.}0$ atm. If the process is adiabatic and the air$-$fuel mixture behaves as a diatomic ideal gas, by what factor does the volume change? Assuming the compression starts with $0\mathrm{.}016$ mole of gas at $27$ C find the following values that characterize the compression process: a$.$ The heat transferred, b$.$ the final temperature, c$.$ the change in internal energy, and d$.$ the work done