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# Specific volume

We explain what the specific volume is, its formula, units, how it is calculated and we give several calculation examples

## What is specific volume?

The volume specific (depicted with symbol ν, Greek letter nu) is an intensive property of the material which measures the volume occupied per unit of 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, the lower 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 lowest specific volume possible, otherwise it will take up too much space which will require a very large and expensive rocket.

Specific volumes are also of great importance in the field of thermodynamics, since they allow the molar volumes of different substances to be easily calculated from their molar mass, or to determine the total volume of a sample from their mass.

Finally, the specific volume changes also allow characterizing phase changes such as melting and boiling , among others.

The following equation corresponds to the mathematical definition of the specific volume:

where V is the volume of a body or 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.

## Units of the specific volume

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 specific volume units in the major drive systems:

 Unit system Units of the specific volume YES m3 / kg MKS m3 / kg Cgs cm3 / g Anglo-Saxon system ft3 / lb Other units mL / g or cm3 / g

## Calculation of specific volume

### For regular solids

For regular solids, the easiest way to determine the specific volume is by determining the volume from the dimensions of the solid, and then dividing 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

There is a solid cylindrical bar 2.54 cm thick, 10 cm long, and 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 reads 2.50 g. Determine the specific volume of the glass.

• Solution : From the diameter we know 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. Then we use the formula for specific volume. You can also combine both equations 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. A possible solution is to determine the volume of the body by means of the volume that it displaces when immersed in water or another liquid:

#### Example 3: A meteor

A very strange shaped meteor was found. It was first weighed, after which a mass of 185.3 g was obtained. It was then placed in a graduated cylinder containing 50.0 mL of water. After submerging the meteorite, 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 from the previous example was found, another rock with a similar appearance was found. This was also weighed, obtaining a mass of 125 g and immersed 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 denatured alcohol, knowing that it has a density of 0.876 g / mL.

• Solution : We know that specific volume is the inverse of density, so:

### For gases

Since most gases comply with 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, temperature, molar mass of the gas, and pressure, respectively.

#### Example 6: Specific volume of air

Calculate the specific volume of a sample of air at 2 atm of pressure and at 350 ° C, knowing that the average molar mass of air is 28.96 g / mol.

• Solution : to use this equation, it is necessary to first 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:

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