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Introduction to Engineering14 chapters | 123 lessons

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Lesson Transcript

Instructor:
*Dina El Chammas Gass*

Dina has taught college Environmental Studies classes and has a master's degree in Environmental and Water Resource Engineering.

In this lesson, you'll learn what specific volume is, how to calculate it for ideal gases, and what units are associated. The lesson also includes numerical examples to better understand how the calculations are done.

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.

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

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

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.

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:

0.038 / 5 = 0.0076 m3/kg

Squeeze the container to 5 gallons, 0.019 m3, and your specific volume is now:

0.019 / 5= 0.0038 m3/kg

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

Now, let's discuss specific volume for ideal gasesâ€¦

The ideal gas law is based on assumptions that greatly simplify the motion of gaseous particles. This law makes analyzing the properties of gases much more manageable. Most gases at standard temperature and pressure behave like 'ideal' gases anyway.

The **ideal gas law** relates pressure and volume to a gas constant, temperature and moles; moles being a way to quantify the number of atoms or molecules in your material. The gas constant *R* is a universal constant equal to 0.08206 L (atm) / mol (K). The ideal gas law states that:

Specific volume for ideal gases is related to the gas constant *R*, the temperature *T*, the pressure *P*, and molar mass *M*. The formula is:

Now, make sure you get the units correct:

- R is 0.08206 L (atm) / mol (K)
- Temperature is in Kelvin (K)
- Pressure is in atmospheres (atm)
- Molar mass is in weight per moles (typically grams per mole (g/mol))
- Specific volume is in liters per gram (L/g)

So for an ideal gas, if the pressure increases, the whole gas is going to contract, which means the volume is going to get smaller. If the volume gets smaller, your specific volume will get smaller, too.

Again consider the 10 gallon container (0.038 m3) at a temperature of 278 K and a pressure of 1.5 atm. If you're working with methane, which has a molar mass of 16 g/mol, your specific volume will be:

(0.08206 x 278) / (1.5 x 16)

22.81 / 24

specific volume = 0.95 L/g

Let's say you add pressure and you're now at 2.5 atm. Your specific volume will be:

(0.08206 x 278) / (2.5 x 16)

22.81 / 40

specific volume = 0.57 L/g

Increasing the pressure reduced your specific volume. Conversely, if you increase the temperature; you're going to expand the gas, and your specific volume is going to increase.

The most common unit for specific volume in metric units is cubic meter per kilogram (m3/kg), but cubic centimeter per gram (cm3/g) is also used. Sometimes cubic feet per pound (ft3/lb), milliliter per gram (ml/g) or liter per gram (L/g) are used.

In this lesson, you learned that **specific volume** is a measure of volume divided by mass, or:

*v* = *V / m*

It's also the inverse of density.

For ideal gases, specific volume is the gas constant (0.08206 L (atm) / mol (K)) represented by *R*, multiplied by temperature (*T*), and divided by pressure (*P*) times the molar mass (*M*).

*v* =* RT / PM*

Common units for specific volume are (m3/kg), but cubic centimeter per gram (cm3/g) is also used. Sometimes cubic feet per pound (ft3/lb), milliliter per gram (ml/g), or liter per gram (L/g) are used.

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Introduction to Engineering14 chapters | 123 lessons

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