It has next to nothing to do with pressure, let alone temperature drop due to expansion. There are 2 things:
When each one quantity of cold and warm air mix, the temperature of the mixture is almost exactly the midpoint (average), as the heat capacity is almost a constant.
Vapor pressure of the water is a function of temperature and scales FAR more than linear.
So now when the hot, humid (burned hydrocarbon) air of the exhaust mixes with cold air the temperature drops a bit, but the vapor pressure drops massively. When conditions are right, the vapor pressure is now below the amount of vapor pressure that is actually present -> condensation.
It has next to nothing to do with pressure, let alone temperature drop due to expansion. There are 2 things:
So now when the hot, humid (burned hydrocarbon) air of the exhaust mixes with cold air the temperature drops a bit, but the vapor pressure drops massively. When conditions are right, the vapor pressure is now below the amount of vapor pressure that is actually present -> condensation.
vapor pressure over temperature data, note how it changes more than 2 orders of magnitude over only 100 K.
Just found this from NASA.