# Specific Heat

Specific heat represents the amount of energy required to raise the temperature of a substance by one degree.  This amount of energy is different for every substance.  For example, 450 Joules of energy is needed to raise 1 kg of iron by one degree Celsius.  On the other hand, 9 times that amount of energy is needed to raise 1 kg of water by one degree Celsius.  Finally, there are two kinds of specific heats, specific heat of a constant volume and specific heat of a constant pressure.

### Specific Heat Constant Volume

$c_v$ is used to represent specific heat of a constant volume. By definition this represents the amount of energy required to raise  the temperature of a substance by one degree while the volume remains constant.  In turn, the following equation is used to determine this value.

(Eq 1) $c_v=\left(\frac{∂u}{∂T}\right)_v$

$u$ = internal energy

### Specific Heat Constant Pressure

Next, $c_p$ represents the specific heat of a constant pressure.  By definition this represents the amount of energy needed to raise the temperature of a unit mass by one degree while the pressure remains constant.  In turn, the following equation represents this value.

(Eq 2) $c_p=\left(\frac{∂h}{∂T}\right)_p$

$h$ =  enthalpy

For both constant pressure and constant volume, the specific heat of a  substance is also dependent on the state of the substance.  In other words, the energy required to raise a substance by one degree is different at different temperatures and pressures.  However, this difference normally is not very large.

Finally, the following units are normally used to represent specific heat .  For the standard international system these units generally are $kJ/kg·^oC$ or $kJ/kg·K$.  In addition, it can also be represented on a molar bases.  This would be $kJ/kmol·^oC$ or $kJ/kmol·K$.