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Internal pressure is how much change in energy a system undergoes when it expands or contracts. External pressure is the amount of energy that is applied from the outside. At equilibrium, these two are equal
If these two were not equal, then they would be attempting to reach a state of equilibrium (being equal). So if you had a closed system with a certain pressure on the inside and a different pressure on the outside, and you suddenly removed whatever was making the system closed rather than open, the pressure would immediately sort itself out as the molecules went from a more pressurized place to less (whether that may be inside or outside of the system).
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