Specific volume is a physical property of a substance that is the ratio of its volume to its mass. This is the same as the reciprocal of its density. In other words, specific volume is inversely proportional to density. Specific volume applies to all states or matter, but it finds practical application for calculations involving gases.
The SI unit for specific volume is cubic meters per kilogram (m3/kg). However, it may be expressed in other units of volume per mass, including milliliters per gram (mL/g) or cubic feet per pound (ft3/lb).
Specific Volume Formulas
There are three common specific volume formulas:
- ν = V / m where V is volume and m is mass
- ν = 1 /ρ = ρ-1 where ρ is density
- ν = RT / PM where R is the ideal gas constant, T is temperature, P is pressure, and M is molar mass
The first equation applies to all states of matter.
The second equation refers mainly to gases and liquids, since they are relatively incompressible so their density does not depend much on temperature or pressure.
The third equation applies to ideal gases or to approximate behavior of real gases at low temperature and pressures.
Specific Volume Is Intrinsic and Intensive
Because specific volume is per unit mass, its value does not depend on sample size. Thus, it is an intrinsic and intensive property of matter. Specific volume values are the same, no matter where you sample a substance.
You have 5 kg of air in a 0.037 m3 tank. What is the specific volume of the air?
ν = V / m
ν = 0.037 m3 / 5 kg = 0.0074 m3/kg
The density of silver is 10.49 g/cm3. What is its specific volume?
ν = 1 /ρ
ν = 1 /(10.49 g/cm3) = 0.095 cm3/g
Table of Specific Volume Values
Tables list specific volume values, typically in conjunction with density values. Most of the time, values are at standard temperature and pressure (STP), which is 0 °C (273.15 K, 32 °F) and 1 atm.
More extensive tables for a variety of temperature and pressure values exist for refrigerants, air, and steam.
Specific Volume Uses
Specific volume finds use in engineering, chemistry, and physics. Although the concept applies to any state of matter, it’s usually used to make predictions concerning the behavior of gases under changing conditions. It applies to volume, molar volume, and partial molar volume calculations.
For example, consider a sealed chamber containing a fixed number of gas molecules:
- If the density of the gas doubles, its specific volume is halved.
- If the specific volume doubles, density is cut in half.
- If the chamber expands (increases volume) while the number of molecules remains constant, gas density decreases and specific volume increases.
- If the chamber contracts (decreases volume) while the number of molecules remains constant, gas density increases and specific volume decreases.
- If some molecules are removed but the volume remains constant, density decreases and specific volume increases.
- If some molecules are added but the volume remains constant, density increases and specific volume decreases.
Specific Volume vs Specific Gravity
Specific gravity is the ratio between the density of one substance to the density of another substance. Since specific volume is the reciprocal of density, it can be used to determine specific gravity.
For example, specific gravity predicts whether one substance will float or sink in another substance. If substance A has a specific volume of 0.358 cm3/g and substance B has a specific volume of 0.374 cm3/g, taking the reciprocal of each value yields density. So, the density of A is 2.79 g/cm3 and the density of B is 2.67 g/cm3. The specific gravity, comparing the density of A to B is 1.04 or the specific gravity of B compared to A is 0.95. A is denser than B, so A sinks into B or B floats on A.
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- Silverthorn, Dee (2016). Human Physiology: An Integrated Approach. Pearson. ISBN 978-0-321-55980-7.
- Walker, Jear (2010). Fundamentals of Physics (9th ed.). Halliday. ISBN 978-0470469088.