**Early history**

Quite a number of successful explanations can be, and were, made from these hypotheses alone. We can understand why a cup of tea cools at room temperature: caloric is self-repelling, and thus slowly flows from regions dense in caloric (the hot water) to regions less dense in caloric (the cooler air in the room).

We can explain the expansion of air under heat: caloric is absorbed into the molecules of air, which increases its volume. If we say a little more about what happens to caloric during this absorption phenomenon, we can explain the radiation of heat, the state changes of matter under various temperatures, and deduce nearly all of the gas laws.

Sadi Carnot developed his principle of the Carnot cycle, which still forms the basis of heat engine theory, solely from the caloric viewpoint.

However, one of the greatest confirmations of the caloric theory was Pierre-Simon Laplace's theoretical correction of Sir Isaac Newton's

*pulse equation*. Laplace, a calorist, added a constant to Newton's equation, which we refer to today as the adiabatic index of a gas. This addition not only substantially corrected the theoretical prediction of the speed of sound, but also continued to make even more accurate predictions for almost a century afterward, even as measurements of the index became more precise.

The study of crystals in modern solid-state physics reflects a shadow of the abandoned caloric theory. Lattice vibrations of crystals, which carry thermal energy, are quantized, and consequently have wave-particle duality. The particle representation of a lattice vibration is called a phonon, by analogy with the photon.

**Later developments**

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