1952Mike-
I would decide how much fuel I want to assume is in the pipe. The most conservative assumption is that the air-fuel ratio in the exhaust system is the same as it is in the intake.
Then I would assume that all the fuel in the pipe burns at constant volume. Use the ideal gas law to calculate the final pressure.
Since volume is assumed to be constant, & the ideal gas law is assumed, then P/T is the same both before and after the fuel burns.