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 volume of a
system
A system is a group of interacting or interrelated elements that act according to a set of rules to form a unified whole. A system, surrounded and influenced by its environment, is described by its boundaries, structure and purpose and express ...
is an important
extensive parameter
Physical properties of materials and systems can often be categorized as being either intensive or extensive, according to how the property changes when the size (or extent) of the system changes. According to IUPAC, an intensive quantity is one ...
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 interdependent with other
thermodynamic properties such as
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
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 ...
. For example, volume is related to the pressure and temperature of an
ideal gas by the
ideal gas law
The ideal gas law, also called the general gas equation, is the equation of state of a hypothetical ideal gas. It is a good approximation of the behavior of many gases under many conditions, although it has several limitations. It was first s ...
.
The physical volume of a system may or may not coincide with a
control volume used to analyze the system.
Overview
The volume of a thermodynamic system typically refers to the volume of the working fluid, such as, for example, the fluid within a piston. Changes to this volume may be made through an application of
work, or may be used to produce work. An
isochoric process however operates at a constant-volume, thus no work can be produced. Many other
thermodynamic processes will result in a change in volume. A
polytropic process
A polytropic process is a thermodynamic process that obeys the relation:
p V^ = C
where ''p'' is the pressure, ''V'' is volume, ''n'' is the polytropic index, and ''C'' is a constant. The polytropic process equation describes expansion and com ...
, in particular, causes changes to the system so that the quantity
is constant (where
is pressure,
is volume, and
is the polytropic index, a constant). Note that for specific polytropic indexes, a polytropic process will be equivalent to a constant-property process. For instance, for very large values of
approaching infinity, the process becomes constant-volume.
Gases are
compressible, thus their volumes (and specific volumes) may be subject to change during thermodynamic processes. Liquids, however, are nearly incompressible, thus their volumes can be often taken as constant. In general, compressibility is defined as the relative volume change of a fluid or solid as a response to a pressure, and may be determined for substances in any phase. Similarly,
thermal expansion
Thermal expansion is the tendency of matter to change its shape, area, volume, and density in response to a change in temperature, usually not including phase transitions.
Temperature is a monotonic function of the average molecular kin ...
is the tendency of matter to change in volume in response to a change in temperature.
Many
thermodynamic cycle
A thermodynamic cycle consists of a linked sequence of thermodynamic processes that involve transfer of heat and work into and out of the system, while varying pressure, temperature, and other state variables within the system, and that eventu ...
s are made up of varying processes, some which maintain a constant volume and some which do not. A
vapor-compression refrigeration cycle, for example, follows a sequence where the refrigerant fluid transitions between the liquid and vapor
states of matter.
Typical units for volume are
(cubic
meters),
(
liters), and
(cubic
feet).
Heat and work
Mechanical work performed on a working fluid causes a change in the mechanical constraints of the system; in other words, for work to occur, the volume must be altered. Hence, volume is an important parameter in characterizing many thermodynamic processes where an exchange of energy in the form of work is involved.
Volume is one of a pair of
conjugate variables, the other being pressure. As with all conjugate pairs, the product is a form of energy. The product
is the energy lost to a system due to mechanical work. This product is one term which makes up
enthalpy
Enthalpy , a property of a thermodynamic system, is the sum of the system's internal energy and the product of its pressure and volume. It is a state function used in many measurements in chemical, biological, and physical systems at a constant ...
:
:
where
is the
internal energy of the system.
The
second law of thermodynamics
The second law of thermodynamics is a physical law based on universal experience concerning heat and energy interconversions. One simple statement of the law is that heat always moves from hotter objects to colder objects (or "downhill"), unle ...
describes constraints on the amount of useful work which can be extracted from a thermodynamic system. In thermodynamic systems where the temperature and volume are held constant, the measure of "useful" work attainable is the
Helmholtz free energy
In thermodynamics, the Helmholtz free energy (or Helmholtz energy) is a thermodynamic potential that measures the useful work obtainable from a closed thermodynamic system at a constant temperature (isothermal). The change in the Helmholtz en ...
; and in systems where the volume is not held constant, the measure of useful work attainable is the
Gibbs free energy
In thermodynamics, the Gibbs free energy (or Gibbs energy; symbol G) is a thermodynamic potential that can be used to calculate the maximum amount of work that may be performed by a thermodynamically closed system at constant temperature an ...
.
Similarly, the appropriate value of
heat capacity
Heat capacity or thermal capacity is a physical property of matter, defined as the amount of heat to be supplied to an object to produce a unit change in its temperature. The SI unit of heat capacity is joule per kelvin (J/K).
Heat cap ...
to use in a given process depends on whether the process produces a change in volume. The heat capacity is a function of the amount of heat added to a system. In the case of a constant-volume process, all the heat affects the internal energy of the system (i.e., there is no pV-work, and all the heat affects the temperature). However, in a process without a constant volume, the heat addition affects both the internal energy and the work (i.e., the enthalpy); thus the temperature changes by a different amount than in the constant-volume case and a different heat capacity value is required.
Specific volume
Specific volume (
) is the volume occupied by a unit of mass of a material. In many cases, the specific volume is a useful quantity to determine because, as an intensive property, it can be used to determine the complete state of a system in conjunction with
another independent intensive variable. The specific volume also allows systems to be studied without reference to an exact operating volume, which may not be known (nor significant) at some stages of analysis.
The specific volume of a substance is equal to the reciprocal of its
mass 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 ...
. Specific volume may be expressed in
,
,
, or
.
:
where,
is the volume,
is the mass and
is the density of the material.
For an
ideal gas,
:
where,
is the
specific gas constant,
is the temperature and
is the pressure of the gas.
Specific volume may also refer to
molar volume.
Gas volume
Dependence on pressure and temperature
The volume of gas increases proportionally to
absolute temperature
Thermodynamic temperature is a quantity defined in thermodynamics as distinct from kinetic theory or statistical mechanics.
Historically, thermodynamic temperature was defined by Kelvin in terms of a macroscopic relation between thermodynamic ...
and decreases inversely proportionally to
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 ...
, approximately according to the
ideal gas law
The ideal gas law, also called the general gas equation, is the equation of state of a hypothetical ideal gas. It is a good approximation of the behavior of many gases under many conditions, although it has several limitations. It was first s ...
:
where:
* ''p'' is the pressure
* ''V'' is the volume
* ''n'' is the
amount of substance of gas (moles)
* ''R'' is the
gas constant, 8.314
J·
K−1 mol−1
* ''T'' is the
absolute temperature
Thermodynamic temperature is a quantity defined in thermodynamics as distinct from kinetic theory or statistical mechanics.
Historically, thermodynamic temperature was defined by Kelvin in terms of a macroscopic relation between thermodynamic ...
To simplify, a volume of gas may be expressed as the volume it would have in
standard conditions for temperature and pressure, which are and 100 kPa.
Humidity exclusion
In contrast to other gas components, water content in air, or
humidity
Humidity is the concentration of water vapor present in the air. Water vapor, the gaseous state of water, is generally invisible to the human eye. Humidity indicates the likelihood for precipitation, dew, or fog to be present.
Humidity dep ...
, to a higher degree depends on vaporization and condensation from or into water, which, in turn, mainly depends on temperature. Therefore, when applying more pressure to a gas saturated with water, all components will initially decrease in volume approximately according to the ideal gas law. However, some of the water will condense until returning to almost the same humidity as before, giving the resulting total volume deviating from what the ideal gas law predicted. Conversely, decreasing temperature would also make some water condense, again making the final volume deviating from predicted by the ideal gas law.
Therefore, gas volume may alternatively be expressed excluding the humidity content: ''V''
d (volume dry). This fraction more accurately follows the ideal gas law. On the contrary, ''V''
s (volume saturated) is the volume a gas mixture would have if humidity was added to it until saturation (or 100%
relative humidity
Humidity is the concentration of water vapor present in the air. Water vapor, the gaseous state of water, is generally invisible to the human eye. Humidity indicates the likelihood for precipitation, dew, or fog to be present.
Humidity dep ...
).
General conversion
To compare gas volume between two conditions of different temperature or pressure (1 and 2), assuming nR are the same, the following equation uses humidity exclusion in addition to the ideal gas law:
Where, in addition to terms used in the ideal gas law:
* ''p
w'' is the partial pressure of gaseous water during condition 1 and 2, respectively
For example, calculating how much 1 liter of air (a) at 0 °C, 100 kPa, ''p''
''w'' = 0 kPa (known as STPD, see below) would fill when breathed into the lungs where it is mixed with water vapor (l), where it quickly becomes , 100 kPa, ''p''
''w'' = 6.2 kPa (BTPS):
Common conditions
Some common expressions of gas volume with defined or variable temperature, pressure and humidity inclusion are:
*ATPS:
Ambient temperature
Colloquially, "room temperature" is a range of air temperatures that most people prefer for indoor settings. It feels comfortable to a person when they are wearing typical indoor clothing. Human comfort can extend beyond this range depending on ...
(variable) and pressure (variable), saturated (humidity depends on temperature)
*ATPD: Ambient temperature (variable) and pressure (variable), dry (no humidity)
*BTPS: Body temperature (37 °C or 310 K) and pressure (generally same as ambient), saturated (47 mmHg or 6.2 kPa)
*STPD:
Standard temperature (0 °C or 273 K) and pressure ( or ), dry (no humidity)
Conversion factors
The following conversion factors can be used to convert between expressions for volume of a gas:
Partial volume
The partial volume of a particular gas is the volume which the gas would have if it alone occupied the volume, with unchanged pressure and temperature, and is useful in gas mixtures, e.g. air, to focus on one particular gas component, e.g. oxygen.
It can be approximated both from partial pressure and molar fraction:
[Page 200 in: Medical biophysics. Flemming Cornelius. 6th Edition, 2008.]
* ''V''
X is the partial volume of any individual gas component (X)
* ''V''
tot is the total volume in gas mixture
* ''P''
X is the
partial pressure
In a mixture of gases, each constituent gas has a partial pressure which is the notional pressure of that constituent gas as if it alone occupied the entire volume of the original mixture at the same temperature. The total pressure of an ideal g ...
of gas X
* ''P''
tot is the total pressure in gas mixture
* ''n''
X is the
amount of substance of a gas (X)
* ''n''
tot is the total amount of substance in gas mixture
See also
*
Volumetric flow rate
References
{{DEFAULTSORT:Volume (Thermodynamics)
Gases
Physical chemistry
Standards
Thermodynamic properties
Volume
State functions
ca:Volum (termodinàmica)#Volum específic