I saw several questions where I had to calculate the temperature of the air coming out of a tyre due to a burst, given the external atmospheric pressure and the initial state of the gas present in the tyre.
All these questions utilised the fact that as the air comes out rapidly, it can be assumed to be adiabatic.
All this seems fine, until they apply the formula $$PV^\gamma=constant$$
According to me the air comes out rapidly so the process should be an irreversible one, and hence the formula $PV^\gamma=constant$ should not be valid, as it is only applicable for a reversible adiabatic process.
However all the questions apply this formula, so please clarify if this is faulty, or I have understood something incorrectly, or the difference on considering this to be reversible won't have a significant error over considering it irreversible.
Note:The pressure change of the gas is not small compared to the pressure state of the gas.