I would expect there'd be some expansion. It will definitely expand when it gets high enough to freeze solid....like everyone on Payne Stewart's Learjet would have. It's a toss up whether everyone died of hypoxia first or hypothermia.
On average, the air temp drops below freezing above 8,000 feet. Payne's aircraft leveled off (programmable autopilot) above 46,000 where the temp would be less than -50F.
You have a complicated explanation but for the sake of kids and the JPP retards, let's KISS.
Let's start with PV = nT.