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There are more than two classes (called "states") of matter.

We are accustomed to three of them: Liquids, Solids, and Gases.

On top of those three, there are another two, rarer states: Plasmas and Bose-Einstein Condensates.

Here are their definitions:

Gas: has neither fixed volume nor fixed shape, and will conform to the size of its container.

Liquid: has a fixed volume, but not a fixed shape, and will conform to the size of its container.

Solid: has both a fixed volume and a fixed shape.

Plasma: is a super-heated gas with partially-ionized molecules.

BEC: an incredibly rare state of matter that tends to only occur at incredibly low temperatures nearing absolute zero. You won't encounter this in Chemistry or Physics, unless dealing with Quantum Mechanics. (Because the temperature is so low, the particles in a BEC move so slowly that they are subject to Quantum Uncertainty, and thus don't occupy single, fixed positions in space.)

Typically speaking, any material can occupy any state of matter. Heating will turn a BEC into a solid, into a liquid, into a gas, into a plasma.

Cooling will turn a plasma into a gas, into a liquid, into a solid, and into a BEC.

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Mathematics student at University of Washington

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Q: What 2 areas can matter be classified?
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