Why is lightning so loud?
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Because it’s really hot, and it makes the air incredibly hot in a very short amount of time.
Sound is a moving pressure wave. When a lightning strike occurs, it heats the air it’s passing through to tens of thousands of degrees in an instant. ~~Pressure is equal to volume times temperature~~ Pressure is equal to force divided by area (corrected per /u/Astronautmatt below); Force is mass (of the displaced air) times acceleration. Lightning doesn’t displace a whole lot of air, but the rapid heating of the air does result in a very high acceleration, so the lightning has a lot of force. This forces the air molecules around the lightning strike to travel away from the strike location, propagating the sound wave away from the strike. The area bounding the lightning strike is decently large, but the acceleration component of the force is so huge that it overwhelms the rest of the equation, resulting in a large pressure spike. Because of the spike in pressure, the sound waves have a large amplitude, which our brains interpret as a large volume.
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