What Is Specific Volume?

Specific Volume: Imagine a rock weighing 5 kg (about 11 pounds). You can probably picture the size of a rock like that – while you could carry it around, you couldn’t exactly start skipping it on a lake.

Now imagine a 5 kg sponge. A sponge the same size as your rock would weigh significantly less, so a 5 kg sponge would have to be pretty huge! Therefore, though they had the same weight, they would have very different volumes.

Specific volume is a measurement of a material related to its volume and mass. It relates to solids, liquids, and gasses, and it quantifies the amount of space a certain mass of material occupies.

Specific volumes are measured for different materials at standard temperature and pressure, which is defined as 0 degrees Celsius and 1 atm (or atmosphere). So you can refer to a table of specific volumes and figure out the specific volumes for air, water, or methane, for example. Because materials expand when temperatures go up and contract when pressure increases, the value will change if your material is at a higher temperature or under pressure.

Specific Volume Formula

To calculate specific volumes you need to know the volumes (V) and the mass (m). Specific volumes equal volume divided by mass. Typically, volume e is measured in cubic meters (m3), and mass is measured in kilograms. Specific volume is then calculated as volumes divided by mass.

Notice that since density is mass over volumes, specific volumes can also be defined as the inverse of density. So you can also calculate specific volume by using the formula for inverse density:

So let’s say your container is 10 gallons or 0.038 m3, and you have 5 kg worth of air in there. The specific volume is going to be: To better imagine this, let’s say you have a container with a certain amount of air inside. If you squeeze the container without letting air out, you’ve effectively reduced the volume and decreased your specific volume. However, you’ve also increased the density.

0.038 / 5 = 0.0076 m3/kg

Squeeze the container to 5 gallons, 0.019 m3, and your specific volumes are now:

0.019 / 5= 0.0038 m3/kg

Your specific volumes decreased when you decreased the volumes. If your container is made bigger, the specific volumes are going to increase, and your density is going to decrease.

What Is Specific Volume

The state of a gas is defined by various properties which we can observe with our senses, including the gas pressure (p), temperature (T), mass (number of moles – m), and volume (V) which contains the gas. It is observed that, if we have a certain amount (mass or volume) of gas present, the value of the temperature and pressure does not depend on the amount of gas that we examine. For example, suppose we have a tank of gas. If we insert a plate into the tank which cuts the volume in half, the temperature in each half remains the same, as does the pressure. The value of pressure and temperature does not depend on the amount of gas used in the measurement. The mass of the gas, on the other hand, does depend on the volume.

Cutting the volume in two cuts the mass in two.

The mass in each section of the tank is one-half the mass of the entire tank. The mass depends on the volume and, in turn, the volume depends on the mass. If we maintain the pressure and temperature of this gas and fill an object which can vary its volumes, like a balloon, or a cylinder with a sliding end, the final volume depends directly on the amount of the gas that we inject. You can try this experiment at the animated gas lab.

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When performing a thermodynamic analysis, it is much easier to deal with only intensive properties since we are able to eliminate the mass from the analysis. Since the mass and volumes are directly related to each other under static conditions, we can define a new property called the specific volume which is equal to the volume divided by the mass. Specific volumes are an intensive property of the gas, as shown in our example. The specific volumes of the original tank are the same as the specific volumes in each half. The “specific” of specific volumes simply means “divided by mass”.

A closer examination of the definition for specific volumes shows that the specific volume v is the inverse of the gas density r

Either the specific number or the density can be used in defining the state of the gas using only intensive variables. For many fluid dynamics (moving) applications, the mass varies from one location to another and aerodynamicists normally use density as the intensive property.

Specific Volume Units

Specific volumes 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 (m ³ /kg or m ³ · kg ^-1 ).

Sometimes specific volumes are 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 (cm ³ /g or cm ³ · g ^-1 ). To convert m ³ /kg to cm ³ /g, multiply by 1000; conversely, multiply by 0.001.

Specific volumes are inversely proportional to density.  If the density drops to 1/10 its former value, the specific volumes, as expressed in the same base units, increase by a factor of 10.

Imagine a volumes-volumes, airtight chamber containing a certain number of atoms of oxygen gas.

Specific Volume Symbol

Engineers and scientists typically refer to tables of specific volume values. These representative values are for standard temperature and pressure (STP), which is a temperature of 0 °C (273.15 K, 32 °F) and a pressure of 1 atm.

Since materials aren’t always under standard conditions, there are also tables for materials that list specific volume values over a range of temperatures and pressures. You can find detailed tables for air and steam.