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 $kJ/kmol·K$.
