Heat capacity is a measurable physical quantity equal to the ratio of the heat added to an object to the resulting temperature change. The molar heat capacity is the heat capacity per unit amount (SI unit: mole) of a pure substance, and the specific heat capacity, often called simply specific heat, is the heat capacity per unit mass of a material. Heat capacity is a physical property of a substance, which means that it depends on the state and properties of the substance under consideration.
The specific heats of monatomic gases, such as helium, are nearly constant with temperature. Diatomic gases such as hydrogen display some temperature dependence, and triatomic gases (e.g., carbon dioxide) still more.
Before the development of the laws of thermodynamics, heat was measured by changes in the states of the participating bodies.
Some general rules, with important exceptions, can be stated as follows.
In general, most bodies expand on heating. In this circumstance, heating a body at a constant volume increases the pressure it exerts on its constraining walls, while heating at a constant pressure increases its volume.
Beyond this, most substances have three ordinarily recognized states of matter, solid, liquid, and gas. Some can also exist in a plasma. Many have further, more finely differentiated, states of matter, such as glass and liquid crystal. In many cases, at fixed temperature and pressure, a substance can exist in several distinct states of matter in what might be viewed as the same body. For example, ice may float in a glass of water. Then the ice and the water are said to constitute two phases within the body. Definite rules are known, telling how distinct phases may coexist in a body. Mostly, at a fixed pressure, there is a definite temperature at which heating causes a solid to melt or evaporate, and a definite temperature at which heating causes a liquid to evaporate. In such cases, cooling has the reverse effects.
All of these, the commonest cases, fit with a rule that heating can be measured by changes of state of a body. Such cases supply what are called thermometric bodies, that allow the definition of empirical temperatures. Before 1848, all temperatures were defined in this way. There was thus a tight link, apparently logically determined, between heat and temperature, though they were recognized as conceptually thoroughly distinct, especially by Joseph Black in the later eighteenth century.
There are important exceptions. They break the obviously apparent link between heat and temperature. They make it clear that empirical definitions of temperature are contingent on the peculiar properties of particular thermometric substances, and are thus precluded from the title absolute. For example, water contracts on being heated near 277 K. It cannot be used as a thermometric substance near that temperature. Also, over a certain temperature range, ice contracts on heating. Moreover, many substances can exist in metastable states, such as with negative pressure, that survive only transiently and in very special conditions. Such facts, sometimes called anomalous, are some of the reasons for the thermodynamic definition of absolute temperature.
In the early days of measurement of high temperatures, another factor was important, and used by Josiah Wedgwood in his pyrometer. The temperature reached in a process was estimated by the shrinkage of a sample of clay. The higher the temperature, the more the shrinkage. This was the only available more or less reliable method of measurement of temperatures above 1000 °C (1,832 °F). But such shrinkage is irreversible. The clay does not expand again on cooling. That is why it could be used for the measurement. But only once. It is not a thermometric material in the usual sense of the word.
Nevertheless, the thermodynamic definition of absolute temperature does make essential use of the concept of heat, with proper circumspection.