Explain how the Kinetic Theory of Matter supports the changes of state observed in matter.

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The KTM can be assumed to be an acronym for the Kinetic Theory of Matter since this question refers to 'changes observed in matter'.

The Kinetic Theory of Matter is

"A theory which states that the particles of matter in all states of aggregation are in vigorous motion." (see first link below)

'States of aggregation' here refers to possible physical states matter can be in, most notably gas, liquid, or solid (though Bose-Einstein condensates and plasma are also recognized states).

The essential idea is that the particles (molecules or atoms) in a grouped physical entity, for example a gas, are in constant motion (hence kinetic) due to their harbouring energy. The vigorous movement of the particles causes them to give off energy which can be characterized by wavelengths of the electromagnetic spectrum (radio waves, infrared, visible light, ultraviolet light, x-rays, gamma rays) or photons, depending on how the energy is measured (this is known as the wave-particle duality of light). This determines the temperature of the matter, which can be affected by the emission or absorption (from other matter) of energy and by pressure, both of which determine the volume that the matter takes up in physical space. Boyle's Law (for ideal gases) states that 

The absolute pressure exerted by a given mass of an ideal gas is inversely proportional to the volume it occupies if the temperature and amount of gas remain unchanged within a closed system.

That is, `P propto 1/V `   where `P ` is the pressure in Pascals and `V ` the volume in ` `cubic cm.

If the temperature and/or pressure are affected enough by external conditions, the matter changes state. A gas losing energy becomes a liquid for example, and a liquid losing energy becomes a solid.

The particles in gases move the most vigorously and freely, at random. If in perfect equilibrium, they are said to be in thermodynamic equilibrium and give off a special wavelength composition called black body radiation. The particles in liquids however move less vigorously and are fluid as they rub together, affecting their random trajectories. The particles in solids move less vigorously still and are held in a regular configuration where they vibrate only and do not travel randomly.

The way matter changes state can be well explained by the KTM because movement can be seen to affect temperature (and hence energy levels) on a larger physical scale, for example when objects spin or are rubbed together (friction). It wasn't until the 19th century that the kinetic theory was preferred over Newton's caloric theory which was based on the idea that a caloric fluid contained particles that repelled ordinary particles of matter. 

"But there was [an] anomalous observation, whose significance was not appreciated until much later: Gay-Lussac found that in the free expansion of a gas (into a vacuum rather than pushing back a piston) there is practically no change in temperature". (see second link below)

Thus the KTM came to be preferred over Newton's caloric theory.

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