Specific volume

${\displaystyle \nu =\frac{V}{m}}$

It is a mass-specific intrinsic property of the substance. It is the reciprocal of density ρ (rho) and it is also related to the molar volume and molar mass:

${\displaystyle \nu ={\rho }^{-1}=\frac{\tilde{V}}{M}}$

The standard unit of specific volume is cubic meters per kilogram (m³/kg), but other units include ft³/lb, ft³/slug, or mL/g.

Specific volume for an ideal gas is related to the molar gas constant (R) and the gas's temperature (T), pressure (P), and molar mass (M):

${\displaystyle \nu =\frac{RT}{PM}}$

It's based on the ideal gas law, ${\displaystyle PV=nRT}$, and the amount of substance, $n=m/M$

Applications

Specific volume is commonly applied to:

• Molar volume
• Volume (thermodynamics)
• Partial molar volume

Imagine a variable-volume, airtight chamber containing a certain number of atoms of oxygen gas. Consider the following four examples:

• If the chamber is made smaller without allowing gas in or out, the density increases and the specific volume decreases.
• If the chamber expands without letting gas in or out, the density decreases and the specific volume increases.
• If the size of the chamber remains constant and new atoms of gas are injected, the density increases and the specific volume decreases.
• If the size of the chamber remains constant and some atoms are removed, the density decreases and the specific volume increases.

Specific volume is a property of materials, defined as the number of cubic meters occupied by one kilogram of a particular substance. The standard unit is the meter cubed per kilogram (m³/kg or m³·kg⁻¹).

Sometimes specific volume is expressed in terms of the number of cubic centimeters occupied by one gram of a substance. In this case, the unit is the centimeter cubed per gram (cm³/g or cm³·g⁻¹). To convert m³/kg to cm³/g, multiply by 1000; conversely, multiply by 0.001.

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.

The density of gases changes with even slight variations in temperature, while densities of liquid and solids, which are generally thought of as incompressible, will change very little. Specific volume is the inverse of the density of a substance; therefore, careful consideration must be taken account when dealing with situations that involve gases. Small changes in temperature will have a noticeable effect on specific volumes.

The average density of human blood is 1060 kg/m³. The specific volume that correlates to that density is 0.00094 m³/kg. Notice that the average specific volume of blood is almost identical to that of water: 0.00100 m³/kg.