por We explain what the specific volume is, its formula, units, how it is calculated and we give several calculation examples.
What is the specific volume?
He specific volume (represented with the symbol ν, Greek letter nu) is an intensive property of matter that measures the volume occupied by unit mass of a body. It corresponds to the relationship between volume and mass, so it represents the inverse of density. This means that the denser a body is, the smaller its specific volume and vice versa.
Knowing the specific volume of a substance is important in applications where the available volume is limited. For example, when selecting fuel for a space rocket, ideally the fuel should have the smallest specific volume possible, otherwise it will take up too much space, requiring a very large and expensive rocket.
Specific volumes are also of great importance in the field of thermodynamics, since they allow to easily calculate the molar volumes of different substances from their molar mass, or to determine the total volume of a sample from its mass.
Finally, specific volume changes also allow characterizing phase changes such as melting and boiling, among others.
Specific Volume Formula
The following equation corresponds to the mathematical definition of the specific volume:
where V is the volume of a body or a substance, m is its mass and ν is the specific volume. However, it can also be calculated from density, since, as mentioned above, specific volume is the inverse of density:
where ρ represents the density.
Specific volume units
Units of specific volume are units of volume over units of mass. As usual, these quantities can be expressed in different systems of units, so the specific volume can also be expressed in different units.
The following table shows the units of the specific volume in the most important unit systems:
Specific volume units
Calculation of the specific volume
for regular solids
For regular solids, the easiest way to determine the specific volume is to determine the volume from the dimensions of the solid, and then divide by the mass.
To determine the volume of the solid, the volume formula corresponding to the particular shape of the solid (sphere, cone, cylinder, etc.) is used.
Example 1: Cylindrical bar
You have a solid cylindrical rod that is 2.54 cm thick, 10 cm long, and has a mass of 1.50 kg. Determine the specific volume of the material in SI units.
Solution: Since we know that it is a cylinder, then we must use the formula for the volume of a cylinder and then apply the formula for specific volume. Both equations can be combined into one as shown below:
Example 2: Glass sphere
A glass marble 1 cm in diameter is weighed on a balance. This one reads 2.50 g. Determine the specific volume of the glass.
Solution: from the diameter it is known that the radius of the sphere is 0.50 cm. With this radius and using the formula for the volume of a sphere we can determine the volume of the marble. Next, we use the specific volume formula. Both equations can also be combined into one:
For amorphous solids
In the case of amorphous solids, it is not possible to determine their volume by means of formulas, since they are not regular solids. One possible solution is to determine the volume of the body by means of the volume it displaces when submerged in water or another liquid:
Example 3: A meteorite
A very strange shaped meteorite was found. First it was weighed, after which a mass of 185.3 g was obtained. Then it was introduced into a graduated cylinder containing 50.0 mL of water. After the meteorite was submerged, the water level rose to 73.5 mL. Determine the specific volume of the meteorite.
Solution: As mentioned above, the volume of the meteorite is determined by the displacement of liquid. The difference between the volumes of water in the graduated cylinder before and after submerging the meteorite gives the volume of the meteorite. Then, the specific volume formula is applied:
Example 4: A rock
Near the site where the meteorite in the previous example was found, another rock with a similar appearance was found. This was also weighed, obtaining a mass of 125 g, and it was submerged in water, where it displaced 15.90 mL of the liquid. Determine whether or not it is a meteorite fragment.
Solution: Specific volume is an intensive property, so if the rock is made of the same material as the meteorite, it should have the same specific volume.
As can be seen, the specific volume of the rock is identical to that of the meteorite, so it is possible that the rock is a fragment of it.
Liquid
Calculating the specific volume of a liquid is done in the same way as shown in the previous examples. Volume can be easily measured using volumetric material. You can also calculate the specific volume from the density of the liquid, as shown in the following example.
Example 5: Specific volume of denatured alcohol
Determine the specific volume of the denatured alcohol, knowing that it has a density of 0.876 g/mL.
Solution: we know that the specific volume is the inverse of the density, so:
for gases
Since most gases obey the ideal gas law relatively well, then this equation can be used to determine the value of the specific volume of a gas. After rearranging this equation, the following relationship is obtained:
where R, T, M, and P are the ideal gas constant, the temperature, the molar mass of the gas, and the pressure, respectively.
Example 6: Specific volume of air
Calculate the specific volume of a sample of air that is at 2 atm pressure and 350 °C, knowing that the average molar mass of air is 28.96 g/mol.
Solution: to use this equation it is necessary first to transform the temperature to Kelvin by adding 273 to the temperature in degrees Celsius: T=350+273 = 623 K. Now we can apply the previous equation, using the value of the constant R = 0.08206 atl .L/mol.K: