# Heat capacity

Heat capacity or thermal capacity is a measurable physical quantity equal to the ratio of the heat added to (or removed from) an object to the resulting temperature change.[1] The unit of heat capacity is joule per kelvin ${\displaystyle \mathrm {\tfrac {J}{K}} }$, or kilogram metre squared per kelvin second squared ${\displaystyle \mathrm {\tfrac {kg\cdot m^{2}}{K\cdot s^{2}}} }$ in the International System of Units (SI). The dimensional form is L2MT−2Θ−1. Specific heat is the amount of heat needed to raise the temperature of one kilogram of mass by 1 kelvin.

Heat capacity is an extensive property of matter, meaning that it is proportional to the size of the system. When expressing the same phenomenon as an intensive property, the heat capacity is divided by the amount of substance, mass, or volume, thus the quantity is independent of the size or extent of the sample. 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. Nonetheless some authors use the term specific heat to refer to the ratio of the specific heat capacity of a substance at any given temperature to the specific heat capacity of another substance at a reference temperature, much in the fashion of specific gravity. In some engineering contexts, the volumetric heat capacity is used.

Temperature reflects the average randomized kinetic energy of constituent particles of matter (i.e., atoms or molecules) relative to the centre of mass of the system, while heat is the transfer of energy across a system boundary into the body other than by work or matter transfer. Translation, rotation, and vibration of atoms represent the degrees of freedom of motion which classically contribute to the heat capacity of gases, while only vibrations are needed to describe the heat capacities of most solids,[2] as shown by the Dulong–Petit law. Other contributions can come from magnetic[3] and electronic[4] degrees of freedom in solids, but these rarely make substantial contributions.

For quantum mechanical reasons, at any given temperature, some of these degrees of freedom may be unavailable, or only partially available, to store thermal energy. In such cases, the heat capacity is a fraction of the maximum. As the temperature approaches absolute zero, the heat capacity of a system approaches zero because of loss of available degrees of freedom. Quantum theory can be used to quantitatively predict the heat capacity of simple systems.

In a previous theory of heat common in the early modern period, heat was thought to be a measurement of an invisible fluid, known as the caloric. Bodies were capable of holding a certain amount of this fluid, hence the term heat capacity, named and first investigated by Scottish chemist Joseph Black in the 1750s.[5]

Since the development of thermodynamics in the 18th and 19th centuries, scientists have abandoned the idea of a physical caloric, and instead understand heat as a manifestation of a system's internal energy. Heat is no longer considered a fluid, but rather a transfer of disordered energy. Nevertheless, at least in English, the term "heat capacity" survives. In some other languages, the term thermal capacity is preferred, and it is also sometimes used in English.

In the International System of Units, heat capacity has the unit joules per Kelvin (J/K). The heat capacity (symbol C) of a system is defined as the ratio of heat transferred to or from the system and the resulting change in temperature in the system,

where the symbol δ designates heat as a path function. If the temperature change is sufficiently small the heat capacity may be assumed to be constant:

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