Cold air is heavier than hot air because of its greater density, so the QNH of an airport inside a cold front would be higher. Flying towards the cold front would be, "low to high, hello sky".
But I also know that for altimetry, cold air generates lower pressure inside the pitot-static system than warm air, and it would increase the altimeter reading, so "hot to cold, look out below".
I'm confused because of the 2 contradictory factors. If we fly towards a cold front without adjusting the altimeter setting, would there be an increase or a decrease in the indicated altitude?
There's an ATP question:
Event after an aircraft passes through a front into the colder air.
Atmospheric pressure increases.
Well, yes, that's why QNH would be higher, but our altimeter would sense the temperature and "feel" a decrease in atmospheric pressure.
So, what would be the real indication of the altimeter in this situation?