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Enthalpy–entropy chart

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(Redirected fromMollier diagram)
Chart describing internal energy of thermodynamic systems
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.

Anenthalpy–entropy chart, also known as theHS chart orMollier diagram, plots the total heat against entropy,[1] describing theenthalpy of athermodynamic system.[2] A typical chart covers a pressure range of 0.01–1000bar, and temperatures up to 800 degreesCelsius.[3] It shows enthalpyH{\displaystyle H} in terms ofinternal energyU{\displaystyle U}, pressurep{\displaystyle p} and volumeV{\displaystyle V} using the relationshipH=U+pV{\displaystyle H=U+pV\,\!} (or, in terms ofspecific enthalpy,specific entropy andspecific volume,h=u+pv{\displaystyle h=u+pv\!} ).

History

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The diagram was created in 1904, whenRichard Mollier plotted the total heat[4]H against entropyS.[5][1]

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 as one of its axes.[6]

Details

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Mollier diagram (chart), I–P units
Mollier diagram (chart), US 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.[7] Thus, coordinates on the diagram represententropy andheat.[8]

Thework done in a process onvapor cycles is represented by length ofh, so it can be measured directly, whereas in aT–s diagram it has to be computed using thermodynamic relationship between thermodynamic properties.[1]

In anisobaric process, the pressure remains constant, so the heat interaction is the change in enthalpy.[2]

In anisenthalpic process, the enthalpy is constant.[2] A horizontal line in the diagram represents anisenthalpic process.

A vertical line in theh–s chart represents anisentropic process. The process 3–4 in aRankine cycle isisentropic when thesteam 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 and they can be calculated considering the isentropic efficiency of the steam turbine used.)

Lines of constantdryness fraction (x), sometimes called thequality, are drawn in the wet region and lines of constant temperature are drawn in the superheated region.[3]X gives the fraction (by mass) of gaseous substance in the wet region, the remainder beingcolloidal liquid droplets. Above the heavy line, the temperature is above the boiling point, and the dry (superheated) substance is gas only.

In general such charts do not show the values ofspecific volumes, nor do they show the enthalpies of saturated water at pressures which are of the order of those experienced in condensers in athermal power station.[3] Hence the chart is only useful for enthalpy changes in the expansion process of the steam cycle.[3]

Applications and usage

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It can be used in practical applications such asmalting, to represent the grain–air–moisture system.[9]

The underlying property data for the Mollier diagram is identical to apsychrometric 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 enthalpyh and humidity ratiox. The enthalpy coordinate isskewed and the constant enthalpy lines are parallel and evenly spaced.

See also

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References

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Wikimedia Commons has media related toEnthalpy-entropy diagrams.
  1. ^abcR. K. Rajput (2009),Engineering Thermodynamics, Infinity Science Series / Engineering series (3 ed.), Jones & Bartlett Learning, p. 77,ISBN 978-1-934015-14-8, retrieved2010-06-25
  2. ^abcY. V. C. Rao (2004),An Introduction to Thermodynamics, Universities Press, p. 70,ISBN 978-81-7371-461-0, retrieved2010-06-25
  3. ^abcdT. D. Eastop, A. Mcconkey (15 Mar 1993),Applied Thermodynamics for Engineering Technologists (5 ed.), Longman,ISBN 978-0-582-09193-1
  4. ^"total heat" is used equivalently with "enthalpy", a term coined only after 1904, and in wider use from c. the 1920s.
  5. ^Mollier, R. (20 February 1904)."Neue Diagramme zur technischen Wärmelehre" [New charts for engineering thermodynamics].Zeitschrift des Vereines Deutscher Ingenieure (in German).48 (8):271–275.
  6. ^See:
    • Mollier, R. (8 September 1923). "Ein neues Diagramm für Dampfluftgemische" [A new diagram for water vapor-air mixtures].Zeitschrift des Vereines Deutscher Ingenieure (in German).67:869–872.
    • English translation:Mollier, Richard (December 1923). "A new diagram for water vapor-air mixtures".Mechanical Engineering.45:703–705.
  7. ^Y. V. C. Rao (2001),Thermodynamics, Universities Press, p. 113,ISBN 978-81-7371-388-0, retrieved2010-06-25
  8. ^Robert C. H. Heck (2008),The Steam Engine and Turbine – A Text Book for Engineering Colleges, Read Books,ISBN 978-1-4437-3134-8, retrieved2010-06-25
  9. ^Dennis Edward Briggs (1998),Malts and Malting, Springer, p. 499,ISBN 978-0-412-29800-4, retrieved2010-06-25
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