Amount of heat required to change the temperature of one unit of volume by one unit of temperature:

$\begin{array}{l}\displaystyle c_v = \frac{\delta Q}{\delta V \cdot \delta T}\end{array}$

Symbol	Dimension	SI units	Oil metric units	Oil field units
$\begin{array}{l}c_v\end{array}$	M L^-1T⁻²Θ⁻¹	J/(m³⋅K)	J/(m³⋅K)	BTU/(ft³⋅°F)

Volumetric Heat Capacity depends on the way the heat is transferred and as such is not a material property.

The two major heat transfer processes are isobaric and isohoric which define:

Isobaric volumetric heat capacity	Isochoric volumetric heat capacity
$\begin{array}{l}c_{vp}\end{array}$	$\begin{array}{l}c_{vV}\end{array}$

Both $\begin{array}{l}c_{vp}\end{array}$ and $\begin{array}{l}c_{vV}\end{array}$ are material properties and properly tabulated for the vast majority of materials.

Volumetric Heat Capacity $\begin{array}{l}c_v\end{array}$ relates to Specific Heat Capacity $\begin{array}{l}c_m\end{array}$ and density of the matter $\begin{array}{l}\rho\end{array}$ as:

(1)	$\begin{array}{l}\displaystyle c_v = \frac{c_m}{\rho}\end{array}$

In many technical papers the "m" or "v" index is omitted which leads to confusion between Specific Heat Capacity $\begin{array}{l}c_m\end{array}$ and Volumetric Heat Capacity $\begin{array}{l}c_v\end{array}$ .

The other confusion is made between Volumetric Heat Capacity $\begin{array}{l}c_v\end{array}$ and Isochoric Heat Capacity $\begin{array}{l}c_V\end{array}$ .

For multiphase fluid in thermodynamic equilibrium the Volumetric Heat Capacity $\begin{array}{l}c_v\end{array}$ is:

(2)	$\begin{array}{l}\displaystyle c_v = \sum_\alpha s_\alpha c_{v \alpha}\end{array}$

where

$\begin{array}{l}s_\alpha\end{array}$	$\begin{array}{l}\alpha\end{array}$ -phase volume share, subjected to $\begin{array}{l}\sum_{\alpha} s_\alpha = 1\end{array}$
$\begin{array}{l}c_{v \alpha}\end{array}$	$\begin{array}{l}\alpha\end{array}$ -phase Volumetric Heat Capacity

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See also

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Volumetric heat capacity

See also