In
thermodynamics
Thermodynamics is a branch of physics that deals with heat, work, and temperature, and their relation to energy, entropy, and the physical properties of matter and radiation. The behavior of these quantities is governed by the four laws ...
, the specific volume of a
substance (symbol: ,
nu) is an
intrinsic property of the substance, defined as the
ratio
In mathematics, a ratio shows how many times one number contains another. For example, if there are eight oranges and six lemons in a bowl of fruit, then the ratio of oranges to lemons is eight to six (that is, 8:6, which is equivalent to the ...
of the substance's
volume
Volume is a measure of occupied three-dimensional space. It is often quantified numerically using SI derived units (such as the cubic metre and litre) or by various imperial or US customary units (such as the gallon, quart, cubic inch). ...
() to its
mass
Mass is an intrinsic property of a body. It was traditionally believed to be related to the quantity of matter in a physical body, until the discovery of the atom and particle physics. It was found that different atoms and different ele ...
(). It is the
reciprocal
Reciprocal may refer to:
In mathematics
* Multiplicative inverse, in mathematics, the number 1/''x'', which multiplied by ''x'' gives the product 1, also known as a ''reciprocal''
* Reciprocal polynomial, a polynomial obtained from another pol ...
of
density
Density (volumetric mass density or specific mass) is the substance's mass per unit of volume. The symbol most often used for density is ''ρ'' (the lower case Greek letter rho), although the Latin letter ''D'' can also be used. Mathematicall ...
(
rho
Rho (uppercase Ρ, lowercase ρ or ; el, ρο or el, ρω, label=none) is the 17th letter of the Greek alphabet. In the system of Greek numerals it has a value of 100. It is derived from Phoenician letter res . Its uppercase form uses the sa ...
) and it is related to the
molar volume and
molar mass
In chemistry, the molar mass of a chemical compound is defined as the mass of a sample of that compound divided by the amount of substance which is the number of moles in that sample, measured in moles. The molar mass is a bulk, not molecular, ...
:
:
The
standard unit of specific volume is cubic meters per
kilogram
The kilogram (also kilogramme) is the unit of mass in the International System of Units (SI), having the unit symbol kg. It is a widely used measure in science, engineering and commerce worldwide, and is often simply called a kilo colloquially. ...
(m
3/kg), but other units include ft
3/lb, ft
3/slug, or mL/g.
Specific volume for an
ideal gas
An ideal gas is a theoretical gas composed of many randomly moving point particles that are not subject to interparticle interactions. The ideal gas concept is useful because it obeys the ideal gas law, a simplified equation of state, and is a ...
is related to the
molar gas constant
The molar gas constant (also known as the gas constant, universal gas constant, or ideal gas constant) is denoted by the symbol or . It is the molar equivalent to the Boltzmann constant, expressed in units of energy per temperature increment pe ...
() and the gas's
temperature
Temperature is a physical quantity that expresses quantitatively the perceptions of hotness and coldness. Temperature is measured with a thermometer.
Thermometers are calibrated in various temperature scales that historically have relied o ...
(),
pressure
Pressure (symbol: ''p'' or ''P'') is the force applied perpendicular to the surface of an object per unit area over which that force is distributed. Gauge pressure (also spelled ''gage'' pressure)The preferred spelling varies by country a ...
(), and
molar mass
In chemistry, the molar mass of a chemical compound is defined as the mass of a sample of that compound divided by the amount of substance which is the number of moles in that sample, measured in moles. The molar mass is a bulk, not molecular, ...
() as shown:
Since
and
:
Applications
Specific volume is commonly applied to:
*
Molar volume
*
Volume (thermodynamics)
In thermodynamics, the volume of a system is an important extensive parameter for describing its thermodynamic state. The specific volume, an intensive property, is the system's volume per unit of mass. Volume is a function of state and is i ...
*
Partial molar volume
In thermodynamics, a partial molar property is a quantity which describes the variation of an extensive property of a solution or mixture with changes in the molar composition of the mixture at constant temperature and pressure. It is the part ...
Imagine a variable-volume, airtight chamber containing a certain number of atoms of oxygen gas. Consider the following four examples:
* If the chamber is made smaller without allowing gas in or out, the density increases and the specific volume decreases.
* If the chamber expands without letting gas in or out, the density decreases and the specific volume increases.
* If the size of the chamber remains constant and new atoms of gas are injected, the density increases and the specific volume decreases.
* If the size of the chamber remains constant and some atoms are removed, the density decreases and the specific volume increases.
Specific volume 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 volume is 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 volume is inversely proportional to density. If the density of a substance doubles, its specific volume, as expressed in the same base units, is cut in half. If the density drops to 1/10 its former value, the specific volume, as expressed in the same base units, increases by a factor of 10.
The density of gases changes with even slight variations in temperature, while densities of liquid and solids, which are generally thought of as incompressible, will change very little. Specific volume is the inverse of the density of a substance; therefore, careful consideration must be taken account when dealing with situations that involve gases. Small changes in temperature will have a noticeable effect on specific volumes.
The average density of human blood is 1060 kg/m
3. The specific volume that correlates to that density is 0.00094 m
3/kg. Notice that the average specific volume of blood is almost identical to that of water: 0.00100 m
3/kg.
Application examples
If one sets out to determine the specific volume of an ideal gas, such as super heated steam, using the equation , where pressure is 2500 lbf/in
2, ''R'' is 0.596, temperature is . In that case, the specific volume would equal 0.4672 in
3/lb. However, if the temperature is changed to , the specific volume of the super heated steam would have changed to 0.2765 in
3/lb, which is a 59% overall change.
Knowing the specific volumes of two or more substances allows one to find useful information for certain applications. For a substance X with a specific volume of 0.657 cm
3/g and a substance Y with a specific volume 0.374 cm
3/g, the density of each substance can be found by taking the inverse of the specific volume; therefore, substance X has a density of 1.522 g/cm
3 and substance Y has a density of 2.673 g/cm
3. With this information, the specific gravities of each substance relative to one another can be found. The specific gravity of substance X with respect to Y is 0.569, while the specific gravity of Y with respect to X is 1.756. Therefore, substance X will not sink if placed on Y.
Specific volume of solutions
The specific volume of a non-ideal solution is the sum of the
partial specific volumes of the components:
:
M is the molar mass of the mixture.
Table of common specific volumes
The table below displays densities and specific volumes for various common substances that may be useful. The values were recorded at standard temperature and pressure, which is defined as air at 0 °C (273.15 K, 32 °F) and 1 atm (101.325 kN/m
2, 101.325 kPa, 14.7 psia, 0 psig, 30 in Hg, 760 torr).
* values not taken at standard temperature and pressure
References
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Thermodynamic properties