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Studying high speed aerodynamics I have found a question asking for what happens to static temperature for an airflow passing through an expansion wave.
The correct answer states that it decreases- the opposite of that on a shock wave.
What is the difference between these two waves that makes them contraries?

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An adiabatic expansion lowers temperature, an adiabatic compression raises temperature, analogous to the way a refrigerator and an air conditioner work. Or a bicycle pump, it gets quite hot while you're pumping air.

A shock wave compresses air - at supersonic speeds the object travels faster than the pressure information, and when the object arrives at a bit of air it compresses suddenly in a shock wave, with corresponding higher temperature.

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