$10\mathrm{.}3$ An engine is assumed to compress intake air at $320$ K$,$ P $=0\mathrm{.}8$ atm to TDC with a compression ratio of $12$:$1.$ A flame is then assumed to propagate at constant volume until the flame is $90\%$ of the way from the spark plug in the center of the cylinder to the cylinder wall. Assume k$=1\mathrm{.}35.$ Estimate:

A$.$ The temperature of the unburned gas.

B$.$ The fraction of fuel that has burned.

C$.$ The temperature of the most recently burned gas.