Heat Capacity

Heat Capacity

When heat is transferred to a system, the temperature of the system rises. The increase in temperature is proportional to the amount of heat transferred:

The constant of proportionality depends on the size, composition, and nature of the system. We write:

where $C$ is called the heat capacity of the system. Heat capacity tells us how much heat is needed to raise the temperature of the system by one degree (either $1^\circ\text{C}$ or $1\ \text{K}$). When $C$ is large, a given amount of heat produces only a small temperature rise. Water, for example, has a large heat capacity — a lot of energy is needed to raise its temperature.

Heat capacity is an extensive property — it depends on how much substance is present. Two related intensive quantities are defined:

Molar heat capacity, $C_m$, is the heat capacity for one mole of the substance:

It is the quantity of heat needed to raise the temperature of one mole of the substance by one degree celsius (or one kelvin).

Specific heat capacity (often called simply specific heat), $c$, is the quantity of heat required to raise the temperature of one unit mass of a substance by one degree celsius (or one kelvin). …