Talk:Chen-style t'ai chi ch'uan

2014-01-06T23:49:07Z

86.56.151.185:

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Invex function

2013-09-17T09:57:37Z

86.56.1.114:

{{for|the general geometric concept|volume}}
{{Infobox Physical quantity
| bgcolour = {default}
| name = Volume (thermodynamics)
| image =
| caption =
| unit = [[metre|m]]3
| 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]]−1[[mole (unit)|mol]]−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.<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''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]]).

=== 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:
:* ''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, ''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 37 °C, 100 kPa, ''p''''w'' = 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}})]], 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''A – ''P''water S) / ''P''S] * [''T''S / ''T''A]
|-
| BTPS || [(''P''A – ''P''water S)/(''P''A – ''P''water B)] * [''T''B/''T''A] [http://www.dynamicmt.com/btpsform.html online calculator]
|-
| ATPD || (''P''A – ''P''water S)/''P''A
|-
|rowspan=3| ATPD || STPD || (''P''A/''P''S) * (''T''S / ''T''A)
|-
| BTPS || [''P''A/(''P''A – ''P''water B) * (''T''B / ''T''A)
|-
| ATPS || PA/(''P''A – ''P''water S)
|-
| 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| Legend:
*''P''A = Ambient pressure
*''P''S = Standard pressure (100 kPa or 750 mmHg)
*''P''water S = 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''water B = Partial pressure of water in saturated air in 37 °C = 47 mmHg
*''T''S = Standard temperature in [[Kelvin (unit)|kelvins]] (K) = 273 K
*''T''A = Ambient temperature in kelvins = 273 + ''t'' (where ''t'' is ambient temperature in °C)
*''T''B = [[Body temperature]] in kelvins = 310 K
|-
|colspan=3| 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>
:* ''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==
*[[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]]

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Talk:Chen-style t'ai chi ch'uan

Invex function