Specific volume: what it means and how to calculate it

Volume ( V ) is the space that a material occupies. It is a general or extensive property , because it depends on the amount of matter and does not allow one material to be identified or differentiated from another. That is, all materials have a volume regardless of their physical state and other characteristics; Two materials can have the same volume despite being different.

The unit of measurement for volume is the cubic meter m ³ . ^{Units such as the cubic centimeter cm 3} are also used to measure regular solids. For liquids and gases, the cubic decimeter dm ³ and the milliliter ml are used.

Unlike volume, specific volume ( v ) refers to the volume of a material per unit mass (m). It is an intensive or specific property , because it is characteristic of each material and, therefore, it allows differentiating some materials from others.

The unit of measurement for specific volume is the cubic meter per kilogram (m ³ /kg), although it can be expressed in terms of milliliters per gram (ml/g) or cubic feet per pound (ft ³ /lb). The specific volume (v) is expressed through the equality

Example. Calculate the specific volume of a 15.29 kg object on a 15.2 m ³ surface .

Taking into account that

so:

The specific volume and density

From the formula of the specific volume ( v ) the volume ( V ) can be solved. again, yes

then equation [1] is obtained:

On the other hand, density ( ρ ) is the amount of mass of a substance in a unit of volume. This property is inverse to the specific volume ( v ). This, taking into account that if the density is

by replacing V with equation [1]:

And by removing the mass ( m ) from both the numerator and the denominator:

so that:

In turn, the specific volume (v) is reciprocal to the density ( ρ ), knowing that if

when clearing the unit:

Now, solving for the specific volume ( v ):

In short, ρ =1/v and v=1/ρ which shows that these are two reciprocals.

Example. Consider a liquid with a density of 750 kg/m ³ . What is its specific volume?

Yeah

so

The correspondence between the density and the specific volume allows predicting the behavior of fluids when the conditions of the system in which they are found change. For example, when considering an airtight chamber containing a given number of gas molecules:

• If the chamber expands while the number of molecules remains constant, the density of the gas decreases and the specific volume increases.
• If the chamber contracts while the number of molecules remains constant, the density of the gas increases and the specific volume decreases.
• If the volume of the chamber is held constant while some molecules are removed, the density decreases and the specific volume increases.
• If the volume of the chamber is held constant while new molecules are added, the density increases and the specific volume decreases.
• If the density is doubled, its specific volume is halved.
• If the specific volume is doubled, the density is halved.

The infinitesimal specific volume

The specific volume of a material in a gravitational field can vary from one point to another. For example, the specific volume of a fluid such as the atmosphere increases with increasing height. This variation is represented by the letter δ (delta), so that δV is the change in volume (or infinitesimal volume) and δm is the change in mass.

The infinitesimal specific volume is then expressed as:

Specific volume and gravity

If the specific volumes of two substances are known, this information can be used to calculate and compare their densities. By comparing the density, specific gravity values ​​are obtained. One application of specific gravity is to predict whether a substance will float or sink when placed on top of another substance.

Example. If substance A has a specific volume of 0.358 cm ³ /g and substance B has a specific volume of 0.374 cm ³ /g, which substance would sink or float on top of the other?

As

taking the inverse of each value will obtain the density.

substance A

which is equivalent to 2.79 g/cm ³ .

substance B

which is equivalent to 2.67 g/cm ³ .

The specific gravity, comparing the density of substance A with that of substance B is

While the specific gravity of substance B compared to that of substance A is

Therefore, substance A is denser than substance B, so substance A would sink in substance B or B would float in A.

Sources

Dobson, K et al . Physical sciences . New York: Holt Mcdougal, 2013
Hewitt, P. Conceptual Physics . Mexico: Pearson Education, tenth edition, 2007.
Kirkpatricj, L., Francis, G. Physics: A look at the world . Mexico: Cengage Learning Publishers, 2010.