The specific volume is a characteristic intensive property of each element or material. It is defined mathematically as the relationship between the volume occupied by a certain amount of matter (a kilogram or a gram); in other words, it is the reciprocal of the density.
The density indicates how much 1 mL of matter weighs (liquid, solid, gaseous, or a homogeneous or heterogeneous mixture), while the specific volume refers to the volume that occupies 1 g (or 1 kg) of it. Thus, knowing the density of a substance, it is enough to calculate the reciprocal to determine its specific volume.
What does the word "specific" refer to? When any property is said to be specific, it means that it is expressed as a function of mass, which allows its transformation from an extensive property (which depends on mass) to an intensive one (continuous at all points in the system).
The units in which the specific volume is normally expressed are (m 3 / Kg) or (cm 3 / g). However, although this property does not depend on mass, it does depend on other variables, such as the temperature or pressure incident on the substance. This causes one gram of substance to occupy more volume at higher temperatures.
Of the water
In the first image you can see a drop of water about to mix with the surface of the liquid. Because it is naturally a substance, its mass occupies volume like any other. This macroscopic volume is a product of the volume and the interactions of its molecules.
The water molecule has the chemical formula H 2 O, with a molecular mass of approximately 18g / mol. The densities it presents also depend on temperature, and at a macroscale the distribution of its molecules is considered to be as homogeneous as possible.
With the density values ρ at a temperature T, to calculate the specific volume of liquid water it is sufficient to apply the following formula:
v = (1 / ρ)
It is calculated by experimentally determining the density of the water using a pycnometer and then performing the mathematical calculation. Because the molecules of each substance are different from each other, so will the resulting specific volume.
If the density of water over a wide temperature range is 0.997 kg / m 3, its specific volume is 1.003 m 3 / kg.
From air
Air is a homogeneous gaseous mixture, composed mainly of nitrogen (78%), followed by oxygen (21%) and finally by other gases in the earth's atmosphere. Its density is a macroscopic expression of all that mixture of molecules, which do not interact efficiently and propagate in all directions.
Because the substance is assumed to be continuous, its spread in a container does not change its composition. Again, by measuring the density at the described conditions of temperature and pressure, one can determine what volume 1 g of air occupies.
Since the specific volume is 1 / ρ, and its ρ is smaller than that of water, then its specific volume is larger.
The explanation for this fact is based on the molecular interactions of water versus air; the latter, even in the case of humidity, does not condense unless it is subjected to very cold temperatures and high pressures.
From steam
Under the same conditions, will a gram of vapor occupy a volume greater than that of a gram of air? Air is denser than water in the gaseous phase, because it is a mixture of gases mentioned above, unlike water molecules.
Since specific volume is the inverse of density, a gram of vapor occupies more volume (it is less dense) than a gram of air.
The physical properties of steam as a fluid are essential in many industrial processes: inside heat exchangers, to increase humidity, clean machinery, among others.
There are many variables to take into consideration when handling large quantities of steam within industries, especially concerning the mechanics of fluids.
Nitrogen
Like the rest of gases, its density depends considerably on pressure (unlike solids and liquids) and on temperature. Thus, the values for its specific volume vary according to these variables. Hence the need to determine its specific volume to express the system in terms of intensive properties.
Without experimental values, through molecular reasoning, it is difficult to compare the density of nitrogen with that of other gases. The nitrogen molecule is linear (N≡N) and that of water is angular.
Since a "line" occupies less volume than a "boomerang", then nitrogen can be expected to be denser than water by the definition of density (m / V). Using a density of 1.2506 Kg / m 3, the specific volume at the conditions in which this value was measured is 0.7996 m 3 / Kg; it is simply the reciprocal (1 / ρ).
Of the ideal gas
The ideal gas is one that obeys the equation:
P = nRT / V
It can be seen that the equation does not consider any variable such as molecular structure or volume; nor does it consider how gas molecules interact with each other in a space defined by the system.
In a limited range of temperatures and pressures, all gases “behave” the same; for this reason it is valid to some extent to assume that they obey the ideal gas equation. Thus, from this equation, several properties of gases can be determined, including the specific volume.
To solve it, it is necessary to express the equation in terms of the density variables: mass and volume. The moles are represented by n, and these are the result of dividing the mass of the gas by its molecular mass (m / M).
Taking the variable mass m in the equation, if it is divided by the volume, the density can be obtained; From here, it is enough to clear the density and then "flip" both sides of the equation. By doing this, the specific volume is finally determined.
The image below illustrates each of the steps to arrive at the final expression of the specific volume of an ideal gas.
References
- Wikipedia. (2018). Specific volume. Taken from: en.wikipedia.org
- Study.com. (August 21, 2017). What is Specific Volume? - Definition, Formula & Units Taken from: study.com
- POT. (May 5, 2015). Specific Volume. Taken from: grc.nasa.gov
- Michael J. Moran & Howard N. Shapiro. (2004). Fundamentals of technical thermodynamics. (2nd Edition). Editorial Reverté, page 13.
- Unit 1: Concepts of thermodynamics.. Taken from: 4.tecnun.es
- TLV. (2018). Main Applications for Steam. Taken from: tlv.com