Specific Heat

Defining 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:

c = \frac{δ Q}{d θ} = θ (\frac{d s}{d θ}),

where $δ Q$ 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:

c_{v} = {(\frac{δ Q}{d θ}) |}_{v} = {θ (\frac{\partial s}{\partial θ}) |}_{v} = {(\frac{\partial u}{\partial θ}) |}_{v},

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:

c_{p} = {(\frac{δ Q}{d θ}) |}_{p} = {θ (\frac{\partial s}{\partial θ}) |}_{p} = {(\frac{\partial h}{\partial θ}) |}_{p},

where $h = u + p v$ 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.

Defining Constant-Volume Specific Heat

The specific heat per unit mass is given as a function of temperature and field variables. By default, specific heat at constant volume is assumed.

Elements

Specific heat effects can be defined for all heat transfer, coupled thermal-electrical-structural, coupled temperature-displacement, and coupled thermal-electrical elements in Abaqus. Specific heat can also be defined for stress/displacement elements for use in adiabatic stress analysis.

Specific heat must be defined for all transient thermal analyses even if the only elements in the model are user-defined elements (User-Defined Elements), in which case a dummy specific heat must be specified.