Specific Heat Capacity and Molar Heat Capacity

Specific Heat Capacity and Molar Heat Capacity

Experience shows that different substances need very different quantities of heat energy to produce the

same rise in temperature, even when equal masses are compared -- heating a kilogram of water by

$10\,^\circ\text{C}$ takes noticeably more heat than heating a kilogram of iron by the same

$10\,^\circ\text{C}$.

Specific heat capacity

The specific heat capacity $c$ of a substance is defined as the quantity of heat required to raise

the temperature of unit mass of that substance through one degree (equivalently, one kelvin or one

degree Celsius, since the two are the same size). If a mass $m$ of a substance absorbs a quantity of heat

$Q$ and its temperature rises by $\Delta T$ as a result (with no change of state occurring), then

with SI unit $\text{J kg}^{-1}\text{K}^{-1}$. Specific heat capacity is an intrinsic property of the

material, independent of how much of it is present.

Heat capacity (thermal capacity)

The heat capacity (or thermal capacity) of a particular body, as distinct from the specific heat

capacity of the material it happens to be made of, is the quantity of heat needed to raise the

temperature of that whole body -- of whatever mass $m$ it actually has -- by one degree:

with SI unit $\text{J K}^{-1}$. Two objects made of the same material but of different mass have the same

specific heat capacity (a material property) but different heat capacities (a whole-body property).

Molar heat capacity

When the quantity of a substance present is expressed in moles rather than in kilograms, the analogous

quantity is the molar heat capacity $C$, the heat required to raise the temperature of one mole of

the substance through one degree. It is related to the specific heat capacity by

where $M$ is the molar mass of the substance (in $\text{kg mol}^{-1}$), so that $C$ has SI unit

$\text{J mol}^{-1}\text{K}^{-1}$.

Water's unusually high specific heat capacity

Water's specific heat capacity, about $4200\ \text{J kg}^{-1}\text{K}^{-1}$, is unusually large compared

with almost every other common substance (the reference table below compares it against ice, steam, and

three common metals). This single fact has enormous practical consequences. A large body of water -- a

sea, a lake, even a large reservoir -- can absorb (or release) an enormous quantity of heat energy while …