# Specific volume

The specific volume is a property of a substance is the ratio of the substance’s volume to its mass. It is the reciprocal of density and an intrinsic property of matter as well. The symbol used to represent specific volume in equations is $$v$$ or $$\nu$$ with SI units of cubic meters per kilogram. The symbol used to represent volume in equations is $$V$$ with SI units of cubic meters.

$\nu =\dfrac{V}{m}=\dfrac{1}{\rho}=\left[\dfrac{\textrm{m}^3}{\textrm{kg}}\right]$

Specific volume is inversely proportional to density. If the density of a substance doubles, its specific volume, as expressed in the same base units, is cut in half. If the density drops to 1/10 its former value, the specific volume, as expressed in the same base units, increases by a factor of 10.

When performing a thermodynamic analysis, it is typical to speak of intensive and extensive properties. Properties which depend on the amount of gas (either by mass or volume) are called extensive properties, while properties that do not depend on the amount of gas are called intensive properties. Specific volume is an example of an intensive property because it is the ratio of the volume occupied by a unit of mass of a gas that is identical throughout a system at equilibrium.

For example, 1000 atoms a gas occupy the same space as any other 1000 atoms for any given temperature and pressure. This concept is easier to visualize for solids such as iron which are incompressible compared to gases. However, the volume itself (not specific) is an extensive property.

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