When a chemist asserts that a substance that is subjected to heat will tend to expand, he or she verifies the assertion through experiment. It is a consequence of the definition of heat that heat will excite the atomic particles in the substance; it is plausible that this in turn will necessitate expansion of the substance. However, our knowledge of nature is not such that we may turn these theoretical ingredients into a categorical proof. Additional complications arise from the fact that the word “expand” requires detailed definition. Apply heat to water that is at temperature 40 ∘ $ 40^\circ $ https://s3-euw1-ap-pe-df-pch-content-public-u.s3.eu-west-1.amazonaws.com/9781315146898/9ce47cf6-5c02-4bc8-a80d-2160001f85a9/content/inline-math2_1.tif"/> F or above, and it expands—with enough heat it becomes a gas that surely fills more volume than the original water. But apply heat to a diamond, and there is no apparent “expansion”—at least not to the naked eye.