Why do some airplanes leave a visible contrail and others don’t?
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Contrail formation generally depends on the altitude, air temperature, air pressure, and ambient humidity. They are mainly seen in aircraft flying above, say, 8000 m in altitude.
If the air is cold enough it will rapidly cool the hot engine exhaust, causing it to condense into fog. This is the same effect as exhaust from cars condensing in freezing weather, or fog produced from your hot exhaled breath. In most conditions this fog doesn’t persist for long, as the tiny cloud droplets evaporate again.
If the air temperature is significantly below zero, the cloud droplets will then freeze into microscopic ice crystals. Not only that but they will slowly grow in size by picking up additional water vapor from the surrounding air if conditions are right. The latter is what causes long persistent contrails. The air is so cold at that altitude that the airplane exhaust becomes a locallized snowstorm of very fine ice dust. Eventually the ice crystals sink down to a layer of warmer air where they evaporate again.
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