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What is the difference between caloric and heat? Is there a difference?

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Heat is related to energy transfer (usually dissipative). Caloric is an obsolete hypothetical fluid that explained how matter was modified when heated.

Caloric theory was popular in the at the end of 18th century and the beginning of 19th century, it was a refined version of phlogiston theory (from early 18th century) which was an hypothetical fluid that entered or left matter during combustion. For example, phlogiston flow explained why some containers gained mass when the contents inside burned. Phlogiston theory was abandoned when Antoine Lavoisier demonstrated the conservation of mass. The gain of mass was explained by oxidation (gaining oxygen atoms from the air). But Lavoisier himself refined the theory and invented caloric theory. Under the new theory, caloric was weightless, but still flowed from hot objects to cool objects increasing the temperature of the latter. Two of the problems with caloric theory are that it could not explain heat coming from friction (as it heats both the rubbing and the rubbed object) nor the heat coming from radiation (like that coming from the sun). The caloric theory was eventually superseded by mechanical theories of heat and the discovery of energy conservation.

Modern thermodynamic theory is much more subtle and it is based on the microscopic description of matter. Matter is composed of atoms which are constantly jiggling or moving around. When you heat molecular oxygen gas, for example, you increase the average speed of the molecules. If this gas A interacts with a gas B that is colder (lower average speed of the molecules), the molecules of gas A will bump with the molecules of gas B transferring them energy (heat) until the two gases are in average at the same temperature. Radiative heat is explained in the same way but it is explained by the energy that can be transferred by electromagnetic waves (photons).

I recommend this answer from physics SE:Why was caloric theory accepted despite observations that heat was produced by friction?

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