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The temperature of a body varies with the KE of its particles. The maximum KE can be obtained by making the atoms move about near the speed of light. Let us take the body as a gas so that the body can move about and not just vibrate to simplify the question. Taking a maximum KE value, wouldn't there be a fixed temperature for each gas above which it cannot be heated ie, when the atoms reach the speed of light? If we cannot take atoms individually as they will break apart ( to plasma ) at high temperature then consider them just as particles.

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marked as duplicate by John Rennie, Qmechanic Dec 26 '15 at 17:08

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