Specific Heat

Mathematically, specific heat 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.


Input Data	Description
Type	Select Constant Volume to define the specific heat at constant volume. Select Constant Pressure to define the specific heat at constant pressure when the energy equation is used for thermal-flow problems.
Specific Heat	Specific heat per unit mass.
Use temperature-dependent data	Specifies material parameters that depend on temperature. A Temperature field appears in the data table. For more information, see Specifying Material Data as a Function of Temperature and Independent Field Variables.
Number of field variables	Specify material parameters that depend on field variables. Field columns appear in the data table for each field variable you add. For more information, see Specifying Material Data as a Function of Temperature and Independent Field Variables.