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{{for|the general geometric concept|volume}} | |||
{{Infobox Physical quantity | |||
| bgcolour = {default} | |||
| name = Volume (thermodynamics) | |||
| image = | |||
| caption = | |||
| unit = [[metre|m]]<sup>3</sup> | |||
| symbols = ''V'' | |||
| derivations = | |||
}} | |||
{{Thermodynamics|cTopic=[[List of thermodynamic properties|System properties]]}} | |||
In [[thermodynamics]], the '''volume''' of a [[thermodynamic system|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 interdependent with other thermodynamic properties such as [[pressure]] and [[thermodynamic temperature|temperature]]. For example, volume is related to the [[pressure]] and [[thermodynamic temperature|temperature]] of an [[ideal gas]] by the [[ideal gas law]]. | |||
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 (thermodynamics)|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 process]]es will result in a change in volume. A [[polytropic process]], in particular, causes changes to the system so that the quantity <math>pV^n</math> is constant (where <math>p</math> is pressure, <math>V</math> is volume, and <math>n</math> 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 <math>n</math> 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]] is the tendency of matter to change in volume in response to a change in temperature. | |||
Many [[thermodynamic cycle]]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 <math>\mathrm{m^3}</math> (cubic [[meter]]s), <math>\mathrm{l}</math> ([[liter]]s), and <math>\mathrm{ft}^3</math> (cubic [[foot (unit)|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 (thermodynamics)|conjugate variable]]s, the other being pressure. As with all conjugate pairs, the product is a form of energy. The product <math>pV</math> is the energy lost to a system due to mechanical work. This product is one term which makes up [[enthalpy]] <math>H</math>: | |||
:<math>H = U + pV,\,</math> | |||
where <math>U</math> is the [[internal energy]] of the system. | |||
The [[second law of thermodynamics]] 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]]; and in systems where the volume is not held constant, the measure of useful work attainable is the [[Gibbs free energy]]. | |||
Similarly, the appropriate value of [[heat capacity]] 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== | |||
{{see also|Specific volume#Specific volume|l1=Specific volume}} | |||
[[Specific volume]] (<math>\nu</math>) is the volume occupied by a unit of mass of a material.<ref>{{Cite book | last1 = Cengel | first1 = Yunus A. | last2 = Boles | first2 = Michael A. | title = Thermodynamics: an engineering approach | year = 2002 | publisher = McGraw-Hill | location = Boston | isbn = 0-07-238332-1 | pages = 11}} | |||
</ref> 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 [[state postulate|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]]. Specific volume may be expressed in <math> \frac{\mathrm{m^3}}{\mathrm{kg}} </math>, <math> \frac{\mathrm{ft^3}}{\mathrm{lbm}} </math>, <math> \frac{\mathrm{ft^3}}{\mathrm{slug}} </math>, or <math> \frac{\mathrm{mL}}{\mathrm{g}} </math> . | |||
:<math> \nu = \frac{V}{m} = \frac{1}{\rho} </math> | |||
where, <math>V</math> is the volume, <math>m</math> is the mass and <math>\rho</math> is the density of the material. | |||
For an [[ideal gas]], | |||
:<math>\nu = \frac{{\bar{R}} T}{P}</math> | |||
where, <math>{\bar{R}} </math> is the [[specific gas constant]], <math>T</math> is the temperature and <math>P</math> 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]] and decreases inversely proportionally to [[pressure]], approximately according to the [[ideal gas law]]: | |||
<math>V = \frac{nRT}{p}</math> | |||
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 [[joule|J]]·[[kelvin|K]]<sup>−1</sup>[[mole (unit)|mol]]<sup>−1</sup> | |||
:* ''T'' is the [[absolute temperature]] | |||
To simplify, a volume of gas may be expressed as the volume it would have in [[standard conditions for temperature and pressure]], which are 0 °C and 100 kPa.<ref name="IUPAC">{{cite book |author= A. D. McNaught, A. Wilkinson |title=Compendium of Chemical Terminology, The Gold Book |url=http://www.iupac.org/goldbook/S05910.pdf |edition=2nd |year=1997 |publisher=Blackwell Science |isbn=0-86542-684-8}}</ref> | |||
=== Humidity exclusion === | |||
In contrast to other gas components, water content in air, or [[humidity]], 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''<sub>d</sub> (volume dry). This fraction more accurately follows the ideal gas law. On the contrary ''V''<sub>s</sub> (volume saturated) is the volume a gas mixture would have if humidity was added to it until saturation (or 100% [[relative humidity]]). | |||
=== 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: | |||
<math> V_2 = V_1 \times \frac{T_2}{T_1} \times \frac{p_1-p_{w,1}}{p_2-p_{w,2}}</math> | |||
Where, in addition to terms used in the ideal gas law: | |||
:* ''p<sub>w</sub>'' 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''<sub>''w''</sub> = 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 37 °C, 100 kPa, ''p''<sub>''w''</sub> = 6.2 kPa (BTPS): | |||
<math> V_{l} = 1\ \mathrm{l} \times \frac{310\ \mathrm{K}}{273\ \mathrm{K}} \times \frac{100\ \mathrm{kPa}-0\ \mathrm{kPa}}{100\ \mathrm{kPa}-6.2\ \mathrm{kPa}} = 1.21\ \mathrm{l} </math> | |||
=== Common conditions === | |||
Some common expressions of gas volume with defined or variable temperature, pressure and humidity inclusion are: | |||
*'''ATPS''': Ambient temperature (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 conditions for temperature and pressure|Standard temperature (0 °C or 273 K) and pressure ({{convert|760|mmHg|kPa|2|abbr=on}} or {{convert|100|kPa|mmHg|2|abbr=on}}<!--was written as if they were the same, but they are not-->)]], dry (no humidity) | |||
===Conversion factors=== | |||
{|class="wikitable" | |||
|+ Conversion factors between expressions of volume of gas | |||
! To convert from !! To !! Multiply by | |||
|- | |||
|rowspan=3| ATPS || STPD || [(''P''<sub>A</sub> – ''P''<sub>water S</sub>) / ''P''<sub>S</sub>] * [''T''<sub>S</sub> / ''T''<sub>A</sub>] | |||
|- | |||
| BTPS || [(''P''<sub>A</sub> – ''P''<sub>water S</sub>)/(''P''<sub>A</sub> – ''P''<sub>water B</sub>)] * [''T''<sub>B</sub>/''T''<sub>A</sub>] [http://www.dynamicmt.com/btpsform.html online calculator] | |||
|- | |||
| ATPD || (''P''<sub>A</sub> – ''P''<sub>water S</sub>)/''P''<sub>A</sub> | |||
|- | |||
|rowspan=3| ATPD || STPD || (''P''<sub>A</sub>/''P''<sub>S</sub>) * (''T''<sub>S</sub> / ''T''<sub>A</sub>) | |||
|- | |||
| BTPS || [''P''<sub>A</sub>/(''P''<sub>A</sub> – ''P''<sub>water B</sub>) * (''T''<sub>B</sub> / ''T''<sub>A</sub>) | |||
|- | |||
| ATPS || P<sub>A</sub>/(''P''<sub>A</sub> – ''P''<sub>water S</sub>) | |||
|- | |||
| BTPS || || [http://books.google.com/books?id=1b0iwv8-jGcC&printsec=frontcover#PPA113,M1] | |||
|- | |||
| STPD || || [http://books.google.com/books?id=1b0iwv8-jGcC&printsec=frontcover#PPA113,M1] | |||
|- | |||
|colspan=3| <span style="font-size:87%;">Legend: | |||
*''P''<sub>A</sub> = Ambient pressure | |||
*''P''<sub>S</sub> = Standard pressure (100 kPa or 750 mmHg) | |||
*''P''<sub>water S</sub> = Partial pressure of water in saturated air (100% relative humidity, dependent on ambient temperature (See [[Humidity#Dew point and frost point|dew point and frost point]]) | |||
*''P''<sub>water B</sub> = Partial pressure of water in saturated air in 37 °C = 47 mmHg | |||
*''T''<sub>S</sub> = Standard temperature in [[Kelvin (unit)|kelvins]] (K) = 273 K | |||
*''T''<sub>A</sub> = Ambient temperature in kelvins = 273 + ''t'' (where ''t'' is ambient temperature in °C) | |||
*''T''<sub>B</sub> = [[Body temperature]] in kelvins = 310 K | |||
|- | |||
|colspan=3| <span style="font-size:87%;"> Unless else specified in table, then reference is:<ref>[http://books.google.com/books?id=1b0iwv8-jGcC&printsec=frontcover#PPA113,M1 Page 113 in: Exercise Physiology: Basis of Human Movement in Health and Disease] | |||
By Stanley P Brown, Wayne C Miller, Jane M Eason | |||
Edition: illustrated | |||
Published by Lippincott Williams & Wilkins, 2006 | |||
ISBN 0-7817-7730-5, 978-0-7817-7730-8 | |||
672 pages</ref> | |||
|} | |||
===Partial volume=== | |||
{{see also|Partial pressure#Partial volume|l1=Partial pressure}} | |||
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:<ref name=biophysics200>Page 200 in: Medical biophysics. Flemming Cornelius. 6th Edition, 2008.</ref> | |||
:<math>V_x = V_{tot} \times \frac{P_x}{P_{tot}} = V_{tot} \times \frac{n_x}{n_{tot}}</math> | |||
:* ''V<sub>x</sub>'' is the partial volume of any individual gas component (X) | |||
:* ''V<sub>tot</sub>'' is the total volume in gas mixture | |||
:* ''P<sub>x</sub>'' is the [[partial pressure]] of gas X | |||
:* ''P<sub>tot</sub>'' is the total pressure in gas mixture | |||
:* ''n<sub>x</sub>'' is the [[amount of substance]] of a gas (X) | |||
:* ''n<sub>tot</sub>'' is the total amount of substance in gas mixture | |||
==See also== | |||
*[[Volumetric flow rate]] | |||
==References== | |||
{{reflist}} | |||
{{DEFAULTSORT:Volume (Thermodynamics)}} | |||
[[Category:Atmospheric thermodynamics]] | |||
[[Category:Gases]] | |||
[[Category:Physical chemistry]] | |||
[[Category:Standards]] | |||
[[Category:Thermodynamics]] | |||
[[Category:Volume]] | |||
[[Category:State functions]] | |||
[[Category:Concepts in physics]] | |||
[[Category:Physical quantities]] | |||
[[ca:Volum (termodinàmica)#Volum específic]] |
Revision as of 10:57, 17 September 2013
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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 interdependent with other thermodynamic properties such as pressure and temperature. For example, volume is related to the pressure and temperature of an ideal gas by the ideal gas law.
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, 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 is the tendency of matter to change in volume in response to a change in temperature.
Many thermodynamic cycles 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 :
where is the internal energy of the system.
The second law of thermodynamics 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; and in systems where the volume is not held constant, the measure of useful work attainable is the Gibbs free energy.
Similarly, the appropriate value of heat capacity 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
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Specific volume () is the volume occupied by a unit of mass of a material.[1] 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. 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 and decreases inversely proportionally to pressure, approximately according to the ideal gas law:
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−1mol−1
- T is the absolute temperature
To simplify, a volume of gas may be expressed as the volume it would have in standard conditions for temperature and pressure, which are 0 °C and 100 kPa.[2]
Humidity exclusion
In contrast to other gas components, water content in air, or humidity, 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: Vd (volume dry). This fraction more accurately follows the ideal gas law. On the contrary Vs (volume saturated) is the volume a gas mixture would have if humidity was added to it until saturation (or 100% relative humidity).
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:
- pw 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, pw = 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 37 °C, 100 kPa, pw = 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 (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 conditions for temperature and pressure|Standard temperature (0 °C or 273 K) and pressure (Template:Convert or Template:Convert)]], dry (no humidity)
Conversion factors
To convert from | To | Multiply by |
---|---|---|
ATPS | STPD | [(PA – Pwater S) / PS] * [TS / TA] |
BTPS | [(PA – Pwater S)/(PA – Pwater B)] * [TB/TA] online calculator | |
ATPD | (PA – Pwater S)/PA | |
ATPD | STPD | (PA/PS) * (TS / TA) |
BTPS | [PA/(PA – Pwater B) * (TB / TA) | |
ATPS | PA/(PA – Pwater S) | |
BTPS | [1] | |
STPD | [2] | |
Legend:
| ||
Unless else specified in table, then reference is:[3] |
Partial volume
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In 12 months 2013, c ommercial retails, shoebox residences and mass market properties continued to be the celebrities of the property market. Models are snapped up in report time and at document breaking prices. Builders are having fun with overwhelming demand and patrons need more. We feel that these segments of the property market are booming is a repercussion of the property cooling measures no.6 and no. 7. With additional buyer's stamp responsibility imposed on residential properties, buyers change their focus to commercial and industrial properties. I imagine every property purchasers need their property funding to understand in value.
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:[4]
-
- Vx is the partial volume of any individual gas component (X)
- Vtot is the total volume in gas mixture
- Px is the partial pressure of gas X
- Ptot is the total pressure in gas mixture
- nx is the amount of substance of a gas (X)
- ntot is the total amount of substance in gas mixture
See also
References
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ca:Volum (termodinàmica)#Volum específic
- ↑ 20 year-old Real Estate Agent Rusty from Saint-Paul, has hobbies and interests which includes monopoly, property developers in singapore and poker. Will soon undertake a contiki trip that may include going to the Lower Valley of the Omo.
My blog: http://www.primaboinca.com/view_profile.php?userid=5889534 - ↑ 20 year-old Real Estate Agent Rusty from Saint-Paul, has hobbies and interests which includes monopoly, property developers in singapore and poker. Will soon undertake a contiki trip that may include going to the Lower Valley of the Omo.
My blog: http://www.primaboinca.com/view_profile.php?userid=5889534 - ↑ Page 113 in: Exercise Physiology: Basis of Human Movement in Health and Disease By Stanley P Brown, Wayne C Miller, Jane M Eason Edition: illustrated Published by Lippincott Williams & Wilkins, 2006 ISBN 0-7817-7730-5, 978-0-7817-7730-8 672 pages
- ↑ Page 200 in: Medical biophysics. Flemming Cornelius. 6th Edition, 2008.