The adiabatic flame temperature of a fuel is the temperature achieved if the fuel is burned completely in a perfectly insulated container.

You are performing an experiment to measure the adiabatic flame temperature of cyclopentane. You put $10\mathrm{.}0mL$ of liquid cyclopentane into a well$-$insulated steel vessel with a volume of $11\mathrm{.}2L$ and pressurize the vessel with air to achieve a stoichiometric ratio of oxygen to cyclopentane. You then ignite the fuel, planning to record the final temperature. The vessel is equipped with a thermocouple and a pressure gauge.

$($a$)$ If room temperature is $27C$ and barometric pressure is $\frac{1\mathrm{.}00}{b}ar,$ what should the pressure gauge read prior to ignition?

$($b$)$ Suppose you discover after the combustion has been carried out that the thermocouple is not functioning properly. Use the final pressure gauge reading of $75\mathrm{.}3$ bar to estimate the adiabatic flame temperature of cyclopentane. Do not assume ideal gas behavior.