Mollier chart

The Mollier chart is routinely used in design works related to power plants (fossil and nuclear), compressors, for steam turbines, refrigeration systems, and air-conditioning equipment. Graphically, it enables the visualization of thermodynamic cycles.

The genesis of Mollier's charts

The diagrams were named after Richard Mollier in 1932 at a conference in Los Angeles.

Richard Mollier (1863-1935) worked as a professor at the University of Dresden. He was the precursor of thermodynamic calculations. Graphic relation between temperature, pressure, enthalpy, entropy and volume of water vapor and humid air. In 1904, for the first time, he published a graph depicting the mentioned relationships for water vapor [Great World Encyclopedia Volume X p. 64]

The air is a mixture of various gases, mainly oxygen, nitrogen and water vapor. The amount of water vapor that may be in the air is limited.

Mollier diagram

Water vapor in the atmosphere is changed, and its behavior is different from the remaining gases (no change of the concentration) - can be so for the purposes of practical treat atmospheric air as a mixture of dry air (consisting only of gas) and water vapor. The amount of water vapor contained in the unit of the volume of air must not exceed a certain maximum value, which is dependent on the temperature. The warmer the air, the more water vapor can be contained in it. The Mollier graph shows the relationship between air temperature, humidity and enthalpy. It is the basic tool for construction engineers and ventilation designers.

Other types of Mollier charts

Currently, many different types of psychometric diagrams are used. The most popular in Europe is "Mollier charts", and Carrier chart in the USA. Both have the same basic format. In short, the difference lies in the position of the axis. In the environment that surrounds us, the air always contains a certain amount of water vapor. Thus, the air is a mixture of dry air and water vapor. The content of water vapor is important in heating, ventilation and air conditioning. Too low or too high air humidity is troublesome for people and gives a feeling of discomfort. In technological processes as well as goods storage, it is also a strictly defined parameter.

In modern buildings, in order to ensure proper comfort in the room, the air must be properly prepared. Depending on the situation, it must be cleaned, heated, cooled, humidified or dried. State changes can be calculated using analytical methods or you can use a simpler way - using a psychometric diagram (Molier's chart or other similar)/

Basic concepts

• unsaturated air - air that at a given temperature can still absorb a certain mass of water vapor,
• saturated air - contains the maximum mass of steam at a given temperature,
• supersaturated air - air in which water has sprinkled in the form of liquid or ice mist
• barometric pressure pb - sum of partial pressures of dry air p1 and steam pw (according to Dalton law)

An oblique coordinate system is used to build the ix graph. On the horizontal axis there is a scale of moisture value x kg / kg - the lines of constant moisture content are vertical. On the left vertical axis there is an enthalpy scale and kJ / kg; solid enthalpy lines, however, run obliquely - usually at an angle of 135 ° from the vertical axis (in a rectangular coordinate system, the area of ​​insufficient air would be too narrow).

Constant relative humidity lines φ = const constitute a system of curves running diagonally from the bottom left corner of the graph upwards. The curve φ = 1 (air saturation state with steam) separates the area of ​​the air which is not saturated (above the curve φ = 1) from the fog area (below the curve φ = 1).

The t = const isotherms are in the area of ​​air that is not saturated, a system of straight parallels, the isotherm of t = 0 ° C in the area of ​​undersaturated air is horizontal. On the saturation line, φ = 1, the isotherms are refracted and in the fog area they are a system of straight lines almost parallel to izentalap.

Because it is assumed that the enthalapa of 1 kg of dry air at 0 ° C is equal to zero, then the lines t = 0 ° C and i = 0kJ / kg intersect on the left vertical axis.

In the Mollier chart, we use the following parameters:

t = air temperature [° C,]

φ = relative humidity [% rh,]

x = water content [g / kg *]

h = enthalpy [kJ / kg *]

• in relation to 1 kg of dry air

Examples of Mollier chart

• The Mollier chart is used to graphically represent the thermodynamic cycle of a steam power plant. The Mollier chart provides a visual representation of the thermal cycle of the steam engine, including the pressure, enthalpy, and entropy of the steam at each point of the cycle. It is also used to calculate the efficiency of the power plant.
• The Mollier chart is also used in the design of air-conditioning and refrigeration systems. It is used to plot the thermodynamic cycle of a refrigeration system, including the temperature and pressure of the refrigerant at each point of the cycle. This allows engineers to optimize the design of the system for maximum efficiency.
• The Mollier chart is used in the design of compressors, such as those used in industrial plants. It is used to graphically represent the thermodynamic cycle of the compressor, including the pressure, enthalpy, and entropy of the gas at each point of the cycle. This allows engineers to optimize the design of the compressor for maximum efficiency.

Advantages of Mollier chart

The Mollier chart is a powerful tool for the visualization of thermodynamic cycles, and its advantages include:

• Its ability to easily plot pressure, enthalpy, entropy, and temperature on a single graph. This enables quick visual comparison of thermodynamic parameters, which is useful in designing efficient systems.
• Its ability to identify different phases of the cycle, such as liquid, vapor, and superheated states. This allows engineers to identify the optimum efficiency points of the cycle.
• Its ability to provide a visual representation of the properties of a given substance, such as its enthalpy, entropy, and temperature, which can be used to optimize the performance of the system.
• Its ability to calculate the efficiency of a given cycle, which can be used to optimize the design for maximum efficiency.

Limitations of Mollier chart

The Mollier chart has several limitations which must be taken into consideration when using it to analyze a system. These include:

• The chart is unable to account for changes in pressure and temperature that occur in a cycle, as it assumes the temperature and pressure remain constant throughout the system.
• It is unable to account for the effects of non-ideal gas behavior, such as friction and compressibility, as the chart assumes ideal gas behavior.
• The chart is unable to predict the exact properties of the system, such as mass flow rate, as it does not account for the properties of the working fluid.
• It is also unable to predict changes in the system due to external influences, such as changes in atmospheric pressure.

Other approaches related to Mollier chart

An introduction to Mollier chart can be extended to other approaches that are related to the visualization of thermodynamic cycles:

• The Temperature-Entropy (T-s) diagram, which plots the temperature and entropy of a substance as it undergoes a thermodynamic process. This diagram is useful for analyzing the changes in temperature, entropy and other thermodynamic properties during a process.
• The Pressure-Enthalpy (P-h) diagram, which plots the pressure and enthalpy of a substance as it undergoes a thermodynamic process. This diagram is useful for analyzing the changes in pressure, enthalpy and other thermodynamic properties during a process.
• The Enthalpy-Entropy (h-s) diagram, which plots the enthalpy and entropy of a substance as it undergoes a thermodynamic process. This diagram is useful for analyzing the changes in enthalpy, entropy and other thermodynamic properties during a process.
• The Exergy diagram, which plots the exergy of a substance as it undergoes a thermodynamic process. This diagram is useful for analyzing the changes in exergy and other thermodynamic properties during a process.

In summary, the Mollier chart is a useful tool for visualizing thermodynamic cycles, and other related approaches can be used to further analyze the changes in thermodynamic properties during a process.

Mollier chart — recommended articles

Markov process — Balanced design — Weep hole — CUSUM chart — Box diagram — Ascii text — Attribute control chart — Cycle time — Network charts

References

• Meyers, C. H., Cragoe, C. S., & Mueller, E. F. (1947). Table and Mollier chart of the thermodynamic properties of 1, 3-butadiene. J Res Natl Bur Stand, 39, 507-507.
• Great Encyclopedia of the World vol, X, Oxford