Heat capacity (Specific heat capacity)

The classical Carnot heat engine

Heat capacity, or thermal capacity, is a measurable physical quantity equal to the ratio of the heat added to (or subtracted from) an object to the resulting temperature change. The SI unit of heat capacity is joule per kelvin and the dimensional form is M¹L²T⁻²Θ⁻¹. Specific heat is the amount of heat needed to raise the temperature of a certain mass 1 degree celsius. Water has a high specific heat so a lot of heat is needed to increase the temperature. This results in water having a high specific heat.

Heat capacity is an extensive property of matter, meaning 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, so that 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 simply called specific heat, is the heat capacity per unit mass of a material. Occasionally, in engineering contexts, the volumetric heat capacity is used.

Temperature reflects the average randomized kinetic energy of constituent particles of matter (e.g. 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 a combination of the two types of energy in vibration (kinetic and potential) of atoms represent the degrees of freedom of motion which classically contribute to the heat capacity of matter, but loosely bound electrons may also participate. On a microscopic scale, each system particle absorbs thermal energy among the few degrees of freedom available to it, and at sufficient temperatures, this process contributes to the specific heat capacity that classically approaches a value per mole of particles that is set by the Dulong-Petit law. This limit, which is about 25 joules per kelvin for each mole of atoms, is achieved by many solid substances at room temperature.

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 specific heat capacity is a fraction of the maximum. As the temperature approaches absolute zero, the specific heat capacity of a system also approaches zero, due to loss of available degrees of freedom. Quantum theory can be used to quantitatively predict the specific heat capacity of simple systems

Specific heat capacity

The specific heat capacity of a material on a per mass basis is

which in the absence of phase transitions is equivalent to

where

is the heat capacity of a body made of the material in question,

is the mass of the body,

is the volume of the body, and

  is the density of the material.

For gases, and also for other materials under high pressures, there is need to distinguish between different boundary conditions for the processes under consideration (since values differ significantly between different conditions). Typical processes for which a heat capacity may be defined include isobaric (constant pressure, ) or isochoric (constant volume, ) processes. The corresponding specific heat capacities are expressed as

From the results of the previous section, dividing through by the mass gives the relation

A related parameter to is , the volumetric heat capacity. In engineering practice, for solids or liquids often signifies a volumetric heat capacity, rather than a constant-volume one. In such cases, the mass-specific heat capacity (specific heat) is often explicitly written with the subscript , as . Of course, from the above relationships, for solids one writes

For pure homogeneous chemical compounds with established molecular or molar mass or a molar quantity is established, heat capacity as an intensive property can be expressed on a per mole basis instead of a per mass basis by the following equations analogous to the per mass equations:

= molar heat capacity at constant pressure

= molar heat capacity at constant volume

where n is the number of moles in the body or thermodynamic system. One may refer to such a per mole quantity as molar heat capacity to distinguish it from specific heat capacity on a per mass basis.