molar heat capacity

The molar heat capacity of a chemical substance is the amount of energy that must be added, in the form of heat, to one mole of the substance in order to cause an increase of one unit in its temperature. Alternatively, it is the heat capacity of a sample of the substance divided by the amount of substance of the sample; or also the specific heat capacity of the substance times its molar mass. The SI unit of molar heat capacity is joule per kelvin per mole, J⋅K−1⋅mol−1.
Like the specific heat, the measured molar heat capacity of a substance, especially a gas, may be significantly higher when the sample is allowed to expand as it is heated (at constant pressure, or isobaric) than when it is heated in a closed vessel that prevents expansion (at constant volume, or isochoric). The ratio between the two, however, is the same heat capacity ratio obtained from the corresponding specific heat capacities.
This property is most relevant in chemistry, when amounts of substances are often specified in moles rather than by mass or volume. The molar heat capacity generally increases with the molar mass, often varies with temperature and pressure, and is different for each state of matter. For example, at atmospheric pressure, the (isobaric) molar heat capacity of water just above the melting point is about 76 J⋅K−1⋅mol−1, but that of ice just below that point is about 37.84 J⋅K−1⋅mol−1. While the substance is undergoing a phase transition, such as melting or boiling, its molar heat capacity is technically infinite, because the heat goes into changing its state rather than raising its temperature. The concept is not appropriate for substances whose precise composition is not known, or whose molar mass is not well defined, such as polymers and oligomers of indeterminate molecular size.
A closely related property of a substance is the heat capacity per mole of atoms, or atom-molar heat capacity, in which the heat capacity of the sample is divided by the number of moles of atoms instead of moles of molecules. So, for example, the atom-molar heat capacity of water is 1/3 of its molar heat capacity, namely 25.3 J⋅K−1⋅mol−1.
In informal chemistry contexts, the molar heat capacity may be called just "heat capacity" or "specific heat". However, international standards now recommend that "specific heat capacity" always refer to capacity per unit of mass, to avoid possible confusion. Therefore, the word "molar", not "specific", should always be used for this quantity.

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