# Specific Volume

Specific volume is defined as the number of cubic meters occupied by one kilogram of matter. It is the ratio of a material's volume to its mass, which is the same as the reciprocal of its density. In other words, specific volume is inversely proportional to density. Specific volume may be calculated or measured for any state of matter, but it is most often used in calculations involving gases.

The standard unit for specific volume is cubic meters per kilogram (m3/kg), although it may be expressed in terms of milliliters per gram (mL/g) or cubic feet per pound (ft3/lb).

## Intrinsic and Intensive

The "specific" part of a specific volume means that it is expressed in terms of unit mass. It is an intrinsic property of matter, which means it does not depend on sample size. Similarly, specific volume is an intensive property of matter that is unaffected by how much of a substance exists or where it was sampled.

## Specific Volume Formulas

There are three common formulas used to calculate specific volume (ν):

1. ν = V / m where V is volume and m is mass
2. ν = 1 /ρ = ρ-1 where ρ is density
3. ν = RT / PM = RT / P where R is the ideal gas constant, T is temperature, P is pressure, and M is the molarity

The second equation usually is applied to liquids and solids because they are relatively incompressible. The equation may be used when dealing with gases, but the density of the gas (and its specific volume) may change dramatically with a slight increase or decrease in temperature.

The third equation only applies to ideal gases or to real gases at relatively low temperatures and pressures that approximate ideal gases.

## Table of Common Specific Volume Values

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 pressure of 1 atm.

Substances marked with an asterisk (*) are not at STP.

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.

## Uses of Specific Volume

Specific volume is most often used in engineering and in thermodynamics calculations for physics and chemistry. It is used to make predictions about the behavior of gases when conditions change.

Consider an airtight chamber containing a set number of molecules:

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

## Specific Volume and Specific Gravity

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

For example, if substance A has a specific volume of 0.358 cm3/g and substance B has a specific volume of 0.374 cm3/g, taking the inverse of each value will yield the density. Thus, the density of A is 2.79 g/cm3 and the density of B is 2.67 g/cm3. The specific gravity, comparing the density of A to B is 1.04 or the specific gravity of B compared to A is 0.95. A is denser than B, so A would sink into B or B would float on A.

## Example Calculation

The pressure of a sample of steam is known to be 2500 lbf/in2 at a temperature of 1960 Rankine. If the gas constant is 0.596 what is the specific volume of the steam?

ν = RT / P

ν = (0.596)(1960)/(2500) = 0.467 in3/lb

## Sources

• Moran, Michael (2014). Fundamentals of Engineering Thermodynamics, 8th Ed. Wiley. ISBN 978-1118412930.
• Silverthorn, Dee (2016). Human Physiology: An Integrated Approach. Pearson. ISBN 978-0-321-55980-7.
• Walker, Jear (2010)l. Fundamentals of Physics, 9th Ed. Halliday. ISBN 978-0470469088​.
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