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Actually, the usual phases of matter, solid, liquid, and gas, take up space and exert pressure for the same reason, which is that they are composed of atoms which all have electrons on the outside, so that they all present a negative charge which repels other negative charges. Atoms do also have a positively charged protons in the middle (or nucleus) of the atom, however, it is the electrons which are closer to each other, since they are all on the outside of the atoms. When two atoms get very close to each other, at some point they won't get any closer, because of the electrostatic repulsion of the electrons for other electrons. This creates the phenomenon that we know as solidity. Matter can exert pressure on other matter for exactly the same reason. That pressure is simply the electrostatic repulsion of electrons for other electrons. This repulsion is only felt at very close range. If the atoms are not very close, then the electrons will be at approximately the same distance as the protons, and therefore there is no repulsion. But at very close range, the electrons are significantly closer than the protons.

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