Specific heat

The specific heat of a substance is defined as the amount of heat required to increase the temperature of a unit mass by one degree. Mathematically, this physical statement can be expressed as:

where $\delta Q$ is the infinitessimal heat added per unit mass and $s$ is the entropy per unit mass. Since heat transfer depends on the conditions encountered during the whole process (a path function), it is necessary to specify the conditions used in the process to unambiguously characterize the specific heat. Thus, a process where the heat is supplied keeping the volume constant defines the specific heat as:

where $u$ is the internal energy per unit mass.

Whereas, a process where the heat is supplied keeping the pressure constant defines the specific heat as:

where $h=u+pv$ is the enthalpy per unit mass. In general, the specific heats are functions of temperature. For solids and liquids, $c_v$ and $c_p$ are equivalent; thus, there is no need to distinguish between them. When possible, large changes in internal energy or enthalpy during a phase change should be modeled using Latent heat instead of specific heat.