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An enthalpy–entropy chart, also known as the ''H''–''S'' chart or Mollier diagram, plots the total heat against entropy, describing the
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 ...
of a thermodynamic system. A typical chart covers a pressure range of 0.01–1000
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, and temperatures up to 800 degrees Celsius. It shows enthalpy H in terms of internal energy U, pressure p and volume V using the relationship H = U + pV \,\! (or, in terms of specific enthalpy,
specific entropy Entropy is a scientific concept, as well as a measurable physical property, that is most commonly associated with a state of disorder, randomness, or uncertainty. The term and the concept are used in diverse fields, from classical thermodynam ...
and specific volume, h = u + pv \! ).


History

The diagram was created in 1904, when
Richard Mollier Richard Mollier (; 30 November 1863, Triest – 13 March 1935, Dresden) was a German professor of Applied Physics and Mechanics in Göttingen and Dresden, a pioneer of experimental research in thermodynamics, particularly for water, steam, and moi ...
plotted the total heat against entropy . 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.


Details

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. Thus, coordinates on the diagram represent
entropy Entropy is a scientific concept, as well as a measurable physical property, that is most commonly associated with a state of disorder, randomness, or uncertainty. The term and the concept are used in diverse fields, from classical thermodyna ...
and
heat In thermodynamics, heat is defined as the form of energy crossing the boundary of a thermodynamic system by virtue of a temperature difference across the boundary. A thermodynamic system does not ''contain'' heat. Nevertheless, the term is ...
. The
work done In physics, work is the energy transferred to or from an object via the application of force along a displacement. In its simplest form, for a constant force aligned with the direction of motion, the work equals the product of the force stren ...
in a process on vapor cycles is represented by length of , so it can be measured directly, whereas in a T–s diagram it has to be computed using thermodynamic relationship between thermodynamic properties. In an isobaric process, the pressure remains constant, so the heat interaction is the change in enthalpy. In an isenthalpic process, the enthalpy is constant. A horizontal line in the diagram represents an
isenthalpic An isenthalpic process or isoenthalpic process is a process that proceeds without any change in enthalpy, ''H''; or specific enthalpy, ''h''. Overview If a steady-state, steady-flow process is analysed using a control volume, everything outside ...
process. A vertical line in the ''h–s'' chart represents an isentropic process. The process 3–4 in a Rankine cycle is isentropic when the
steam turbine A steam turbine is a machine that extracts thermal energy from pressurized steam and uses it to do mechanical work on a rotating output shaft. Its modern manifestation was invented by Charles Parsons in 1884. Fabrication of a modern steam tu ...
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 constant ''dryness fraction'' (''x''), sometimes called the ''quality'', are drawn in the wet region and lines of constant temperature are drawn in the superheated region. ''X'' gives the fraction (by mass) of gaseous substance in the wet region, the remainder being colloidal 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 of specific volumes, 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 A thermal power station is a type of power station in which heat energy is converted to electrical energy. In a steam-generating cycle heat is used to boil water in a large pressure vessel to produce high-pressure steam, which drives a stea ...
. Hence the chart is only useful for enthalpy changes in the expansion process of the steam cycle.


Applications and usage

It can be used in practical applications such as
malt Malt is germinated cereal grain that has been dried in a process known as " malting". The grain is made to germinate by soaking in water and is then halted from germinating further by drying with hot air. Malted grain is used to make beer, w ...
ing, to represent the grain–air–moisture system. The underlying property data for the Mollier diagram is identical to a
psychrometric chart Psychrometrics (or psychrometry, ; also called hygrometry) is the field of engineering concerned with the physical and thermodynamic properties of gas-vapor mixtures. Common applications Although the principles of psychrometry apply to any p ...
. 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.


See also

* Thermodynamic diagrams *
Contour line A contour line (also isoline, isopleth, or isarithm) of a function of two variables is a curve along which the function has a constant value, so that the curve joins points of equal value. It is a plane section of the three-dimensional gr ...
* Phase diagram


References

{{DEFAULTSORT:Enthalpy-entropy chart Thermodynamics Entropy de:Wasserdampf#h-s-Diagramm