Specific Heat Capacity

The specific heat capacity of a material is the heat capacity per unit mass of that material. If an amount of a material, with a mass $m$, has a heat capacity $C$, then its specific heat capacity, $c$, is given by

$$c = \frac{C}{m}$$

Remembering that the heat capacity of an object is the rate at which its internal energy, $E$, changes with temperature, $T$, we can write

$$c = \frac{1}{m} \frac{\mathrm{d}E}{\mathrm{d}T}$$

The specific heat capacity of a material is generally not constant with temperature. However, there are many materials where the specific heat capacity is approximately constant over certain ranges of temperature. In such cases, the above equation can be simplified to

$$c = \frac{1}{m} \frac{\Delta E}{\Delta T}$$

where $\Delta E$ and $\Delta T$ are discrete changes in energy and temperature. If the specific heat capacity of a material is known, the change in energy for a certain mass of the material is given by

$$\Delta E = m c \Delta T$$