Nib asked, and Nib — askNib's tutor — drew the answer live at a whiteboard. This is the spoken transcript; enable JavaScript to watch it drawn.
why do airplanes leave white trails
That white line isn't smoke, and it isn't sprayed chemicals. It's a cloud, made by the plane itself, and it's made of ice.
Why ice? Cruising planes fly around eleven kilometers up, where the air is colder than minus forty degrees. Cold enough to freeze water in a blink.
Burning kerosene makes carbon dioxide and water. Every kilogram of fuel gives out about one and a quarter kilograms of water vapor, in a hot, wet exhaust.
That hot, wet plume meets the freezing air and mixes with it. The vapor can't stay a gas, so it freezes into countless tiny ice crystals. That's the trail.
Whether it lasts depends on the air. In dry air the ice vanishes in seconds. In very humid air it survives, grows, and spreads into a wispy cloud.
So the whole idea: hot, wet exhaust meets air colder than minus forty and freezes into ice. Dry air erases it, humid air lets it spread.
A contrail is just your plane's breath freezing in the cold sky.