en>Headbomb: /* References */Various citation cleanup + AWB fixes using AWB (8062)

2012-04-25T05:11:05Z

References: Various citation cleanup + AWB fixes using AWB (8062)

New page

[[File:HS-Wasserdampf engl.png|thumb|The Mollier Enthalpy-Entropy Diagram for water and steam. The "dryness fraction", ''x'', gives the fraction by mass of gaseous water in the wet region, the remainder being droplets of liquid.]]
An '''enthalpy–entropy chart''', also known as the '''h–s chart''' or '''Mollier diagram''', plots the total heat against entropy,<ref name=n1/> describing the [[enthalpy]] of a [[thermodynamic system]].<ref name=rao>{{Citation |title=An Introduction to Thermodynamics |author=Y. V. C. Rao |publisher=Universities Press |year=2004 |isbn=978-81-7371-461-0 |page=70 |accessdate=2010-06-25 |url = http://books.google.co.uk/books?id=bKoUHSxujZIC&pg=PA70&dq=mollier+diagram&hl=en&ei=IIMkTLC5G4Sd_Abwy9XoBA&sa=X&oi=book_result&ct=result&resnum=3&ved=0CDkQ6AEwAg#v=onepage&q=mollier%20diagram&f=false}}</ref> A typical chart covers a pressure range of 0.01 - 1000 [[Bar (unit)|bar]], and temperatures up to 800 degrees [[Celsius]].<ref name=east>{{citation |title=Applied Thermodynamics for Engineering Technologists |format=Paperback |author=T.D. Eastop, A. Mcconkey |publisher=Longman |edition=5 |date=15 Mar 1993 |isbn=978-0-582-09193-1}}</ref> It shows enthalpy <math>h</math> in terms of [[internal energy]] <math>u</math>, pressure <math>P</math> and volume <math>v</math> using the relationship <math>h = u + Pv \,\!</math>.

==History==
The diagram was created in 1904, when [[Richard Mollier]] plotted the total heat against entropy.<ref name=n1>{{citation |title=Engineering Thermodynamics |series=Infinity Science Series / Engineering series |author=R. K. Rajput |edition=3 |publisher=Jones & Bartlett Learning |year=2009 |isbn=978-1-934015-14-8 |page=77 |accessdate=2010-06-25 |url=http://books.google.co.uk/books?id=YnXSHFmPdzMC&pg=PA77&dq=mollier+diagram&hl=en&ei=IIMkTLC5G4Sd_Abwy9XoBA&sa=X&oi=book_result&ct=result&resnum=5&ved=0CEMQ6AEwBA#v=onepage&q=mollier%20diagram&f=false}}</ref> At the 1923 Thermodynamics Conference held in Los Angeles it was decided to name, in his honor, as a “Mollier diagram” any thermodynamic diagram using the Enthalpy h as one of its axes.<ref>Mollier, R. 1923. “Ein neues diagram für dampfluftgemische.” ZVDI 67(9)</ref>

==Details==
[[File:Mollier.pdf|thumb|Mollier Diagram (Chart), IP Units]]
[[File:Mollier enthalpy entropy chart for steam - US units.svg|thumb|Mollier Diagram (Chart), IP Units]]

On the diagram, lines of constant pressure, constant temperature and volume are plotted, so in a two-phase region, the lines of constant pressure and temperature coincide.<ref>{{Citation |title=Thermodynamics |author=Y. V. C. Rao |publisher=Universities Press |year=2001 |isbn=978-81-7371-388-0 | accessdate = 2010-06-25 |page=113 | url = http://books.google.co.uk/books?id=Fv6EpL10gY8C&pg=PA113&dq=mollier+diagram&hl=en&ei=bo8kTIKXO4GC_AbSpcXkBA&sa=X&oi=book_result&ct=result&resnum=10&ved=0CFoQ6AEwCTgK#v=onepage&q=mollier%20diagram&f=false}}</ref> Thus, coordinates on the diagram represent [[entropy]] and [[heat]].<ref name=steam>{{citation |title=The Steam Engine and Turbine - A Text Book for Engineering Colleges |author=Robert C. H. Heck |publisher=Read Books |year=2008 |isbn=978-1-4437-3134-8 |accessdate=2010-06-25 |url=http://books.google.co.uk/books?id=A5RnxZx51eoC&pg=PA138&dq=mollier+diagram&hl=en&ei=IIMkTLC5G4Sd_Abwy9XoBA&sa=X&oi=book_result&ct=result&resnum=10&ved=0CFwQ6AEwCQ#v=onepage&q=mollier%20diagram&f=false}}</ref>

The [[Work (physics)|work done]] on [[vapor cycle]]s is represented by length, so it can be measured directly, whereas in a [[T–s diagram]] it is shown as an area.<ref name=n1/>

In an [[isobaric process]], the pressure remains constant, so the heat interaction is the change in enthalpy.<ref name=rao/>

In an [[isenthalpic process]], the enthalpy is constant.<ref name=rao/>
A vertical line in the h–s chart means an [[isentropic]] process and an horizontal line means an [[isenthalpic]] process. The process 3-4 in a [[rankine cycle]] is [[isentropic]] when the [[steam turbine]] is said to be an ideal one. So the expansion process in a turbine can be easily calculated using the h–s chart when the process is considered to be ideal (which is the case normally when calculating enthalpies, entropies, etc. Later the deviations from the ideal values can be calculated considering the isentropic efficiency of the steam turbine used.)

In a throttling process, the [[Joule–Thomson effect]] means that an adiabatic device uses energy equal to the decrease in the enthalpy of the fluid flowing through the device.<ref name=rao/>

Lines of constant ''dryness fraction'' (''x''), sometimes called the ''quality'' of the steam, are drawn in the wet region and lines of constant temperature are drawn in the superheated region.<ref name=east/> ''X'' gives the fraction (by mass) of gaseous water in the wet region, the remainder being [[colloid]]al liquid droplets. Above the heavy line, the temperature is above the boiling point, and the dry (superheated) steam consists of gas only.

In general such charts do not show the values of [[specific volume]]s, nor do they show the enthalpies of saturated water at pressures which are of the order of those experienced in condensers in a [[thermal power station]].<ref name=east/> Hence the chart is only useful for enthalpy changes in the expansion process of the steam cycle.<ref name=east/>

==Applications and usage==
It can be used in practical applications such as [[malt]]ing, to represent the grain-air-moisture system.<ref>{{Citation |title=Malts and Malting |author=Dennis Edward Briggs |publisher=Springer |year=1998 |isbn=978-0-412-29800-4 |page=499 |accessdate=2010-06-25 |url= http://books.google.co.uk/books?id=s9tf70Wk3bYC&pg=PA499&dq=mollier+diagram&hl=en&ei=bo8kTIKXO4GC_AbSpcXkBA&sa=X&oi=book_result&ct=result&resnum=8&ved=0CFAQ6AEwBzgK#v=onepage&q=mollier%20diagram&f=false}}</ref>

The underlying property data for the Mollier diagram is identical to a [[psychrometric chart]]. At first inspection, there may appear little resemblance between the charts, but if the user rotates a chart ninety degrees and looks at it in a mirror, the resemblance is apparent. The Mollier diagram coordinates are enthalpy ''h'' and humidity ratio ''x''. The enthalpy coordinate is ''skewed'' and the constant enthalpy lines are parallel and evenly spaced.

The Mollier diagram is preferred by many users in Scandinavia, Eastern Europe, and Russia.<ref>Todorovic, B., ASHRAE Transactions DA-07-024 (113-1), 2007</ref>

==See also==
*[[Thermodynamic diagrams]]
*[[Contour line]]
*[[Phase diagram]]

== References ==
{{Commons category|H-S diagrams|H-S diagrams}}
{{reflist}}

{{DEFAULTSORT:Enthalpy-entropy chart}}
[[Category:Thermodynamics]]
[[Category:Entropy]]

[[de:Wasserdampf#h-s-Diagramm]]

Frege system - Revision history

en>Headbomb: /* References */Various citation cleanup + AWB fixes using AWB (8062)