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Table of Nominees
Nominated article Vote
Score		 Supporters Specialist supporters Date created
Tall tale 2 Daniel Mietchen
; Howard C. Berkowitz
' 		9 March 2010
Plane (geometry) 1 Daniel Mietchen Major rewrite on 29 March 2010

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Nominated article Supporters Specialist supporters Dates Score
Developing Article Steam: The vapor (or gaseous) phase of water (H2O). [e]
(PD) Photo: Gretar Ívarsson
Geothermal power plant in Iceland

Steam is the vapor (gaseous) phase of water (H2O) usually generated by the boiling of water. When the steam does not contain any liquid water, it is known as dry steam and it is completely colorless. However, when the steam contains tiny droplets of condensed liquid water, it appears to the eye as a white cloud (see the steam being vented from a geothermal power plant in the adjacent photograph).

What is very often referred to as smoke from cooling towers and other vents in industrial facilities is water vapor which has partially condensed and is mistaken to be white smoke. Water aerosols and mists, such as those created by spray cans for misting house plants or certain types of humidifiers, may also create small visible clouds of water droplets, but aerosols, mists and fogs are not steam. Liquids other than water may also form visible clouds when vaporized, but they are not clouds of steam.

Steam is manufactured in industrial processes by the boiling and vaporization of liquid water. It also occurs naturally by being vented from volcanoes, fumaroles, geysers and other geothermal sources.

Steam has a great many industrial and domestic uses. Probably the most important and by far the largest use of steam is in nuclear, fossil fuel and geothermal power plants.

Types of steam

(CC) Diagram: Milton Beychok

As shown in the adjacent diagram, there are three types of steam:

  • Wet steam: A mixture of water plus steam (liquid plus vapor) at the boiling point temperature of water at a given pressure. Quality of steam refers to the fraction or percentage of gaseous steam in a wet steam mixture.
  • Dry steam: Steam, at the given pressure, that contains no water (also referred to as saturated steam). The steam quality = 100%. At the top of steam generator units for producing saturated steam, there are moisture separators used to remove residual water droplets from outgoing steam.
  • Superheated steam: Dry steam, at the given pressure, that has been heated to a temperature higher than the boiling point of water at that pressure.

Referring to the adjacent drawing again, water is converted into wet, dry saturated or superheated steam in three steps:

  • Water at point 1 is heated to its boiling point at the given pressure of point 2 (the dark blue line). At that point the water is then referred to as saturated water. The amount of heat added between points 1 and 2 is called sensible heat.
  • The water is further heated at constant pressure (the red isobar from point 2 to point 3) to form wet steam. When it is completely vaporized (at point 3), it is then dry saturated steam. The amount of heat required to completely vaporize the water is called the heat of vaporization and denoted as Hv or Hvap.
  • The dry saturated steam is yet further heated at constant pressure (the red isobar from point 3 to point 4). The steam is then referred to as superheated steam. The amount of heat added to superheat the dry saturated steam is also called sensible heat.
  • It should be noted that the points 2 and 3 are at the same boiling point temperature and pressure and also that, at those conditions, the liquid and the steam (whether wet or dry) are in equilibrium with each other.

Production

For more information, see: Steam generator.

Ways of producing steam from water include use of boilers or steam generators. Boilers are pressure vessels in which water is heated to produce pressurized steam, for generally heating houses or buildings, for steam engines, or a variety of other uses. Steam generators are devices or units, often including boilers (the definitions coincide greatly), for producing (generating) steam for power plant, industrial, or other uses. The size of steam generators ranges from bench top to very large units or sections of a thermal power plant. In the field of nuclear power plants, the term steam generator refers specifically to a particular very large heat exchanger used to thermally connect the primary (reactor plant) system to a secondary (steam plant) system in a pressurized water reactor (PWR) plant, which generates steam for the steam plant, of course.

Uses

Electricity generation

For more information, see: Conventional coal-fired power plant, Nuclear power plant, and Steam generator.

The worldwide capacity of electrical power generation by conventional coal-fired power plants currently amounts to about 800,000 MW[1][2][3][4] and the worldwide capacity of nuclear power generation amounts to about 370,000 MW.[5][6] That amounts to a total of 1,170,000 MW of worldwide generation, most of which involves the use of superheated steam to drive the turbines that spin the electrical generators (see the adjacent schematic diagram).[7]

Assuming an overall thermal efficiency of 34%, a steam generator (boiler) efficiency of 75 to 85% and an electrical generator efficiency of 98.5%, a conventional coal-fired power plant would use superheated steam at a rate of 3.47 to 3.93 (t/h) per MW of power output. Thus, a 1000 MW power plant would use 3,470 to 3,930 metric tons (tonnes) of steam per hour and the steam used by the 1,170,000 MW of worldwide power generation by coal-fired and nuclear power plants might be as much as 4,000,000 to 4,600,000 metric tons of steam per hour.

The diagrams below schematically depict the equipment used in a conventional fuel-fired steam to electric power plant as well as the temperature-entropy (T-S) diagram of the corresponding Rankine cycle. A nuclear power plant differs only to the extent that the heat required by the boiler is provided by heat derived from a nuclear reactor.

(PD) Diagram: Milton Beychok
(PD) Image: Milton Beychok
Diagram of a power plant coal-fired steam generator
(PD) Diagram: Milton Beychok

Cogeneration of heat and power

Cogeneration is also referred to as combined heat and power or CHP. In electrical power generation, the turbine exhaust steam is typically condensed and returned to the boiler for re-use. However, in one form of cogeneration, all or part of the turbine exhaust steam is distributed through a district heating system to heat buildings rather than being condensed. The world's biggest steam cogeneration system is the district heating system which distributes steam from seven cogeneration plants to provide heating for 100,000 buildings in the city of New York.[8][9]

Steam engines

As an overall definition, a steam engine is an engine that uses steam to perform mechanical work. By that definition, steam turbines are steam engines. However, this section describes steam engines that use the expansion of steam to move a piston that performs work. Such steam engines were the driving force behind the Industrial Revolution of the 18th century and gained widespread commercial use for driving machinery in factories, powering water pumping stations and transport application such as railway locomotives, steamships and road vehicles. The use of tractors driven by steam engines led to an increase in the land available for agricultural cultivation.

Although largely replaced by steam turbines, stationary reciprocating steam engines are still used in industry and elsewhere for driving pumps, gas compressors and other types of machinery.

Uses in industrial process facilities

A great many processes in petroleum refineries, natural gas processing plants, petrochemical plants and other industrial facilities use steam as:

  • A heat source for distillation column reboilers.
  • A heat source injected directly into various distillation columns known as steam strippers and side-cut strippers to provide the required distillation heat.
  • A heat source flowing through tubular coils installed inside storage tanks to heat certain stored liquids.

Other uses

Sterilization
An autoclave, which uses steam under pressure, is used in microbiology laboratories and similar environments for sterilization; autoclaving is also a major method for industrial and home canning of food
Agricultural
In agriculture, steam is used for soil sterilization to avoid the use of harmful chemical agents and increase soil health.
Commercial and domestic uses
Steam's capability to transfer heat is also used in the home as well as commercial facilities for pressure cookers, steam cleaning of fabrics and carpets, steam ironing and for heating of buildings.
Ship propulsion
Steam is sometimes used to power steam turbines to propel naval ships, ice breakers, and other ships; steam turbines are primarily used in nuclear-powered ships, with other new construction using various combinations of gas turbines, diesel engines, and electric motors

Steam tables and Mollier diagrams

For more information, see: Steam tables and Mollier diagrams.

Steam tables provide tabulated thermodynamic data for the liquid and vapor phases of water. The table below is only an example of the type of data provided. In a complete set of steam tables, the table would provide data in temperature increments of 1 °C. The complete steam tables would also provide a similar "Saturated Steam:Pressure Table" in which the first column would have pressure values and the second column would be temperature values. Most steam tables include tabulated thermodynamic data for superheated steam as well.

Saturated Steam:Temperature Table[10]
T
°C		 P
bar		 P
kPa		 ρL
kg/m3		 ρV
kg/m3 		HL
J/g		 HVap
J/g		 HV
J/g		 SL
J/(g·K) 		SVap
J/(g·K)		 SV
J/(g·K)
10 0.012282 1.2282 999.65 0.00941 42.02 2477.2 2519.2 0.15109 8.7487 8.8998
20 0.023393 2.3393 998.19 0.01731 83.91 2453.5 2537.4 0.29648 8.3695 8.6660
30 0.042470 4.2470 995.61 0.03042 125.73 2429.8 2555.5 0.43675 8.0152 8.4520
40 0.073849 7.3849 992.18 0.05124 167.53 2406.0 2573.5 0.57240 7.6831 8.2555
50 0.12352 12.352 988.00 0.08315 209.34 2381.9 2591.3 0.70381 7.3710 8.0748
100 1.0142 101.42 958.35 0.5982 419.17 2256.4 2675.6 1.3072 6.0469 7.3541
150 4.7616 476.16 917.01 2.5481 632.18 2113.7 2745.9 1.8418 4.9953 6.8371
200 15.549 1554.9 864.66 7.8610 852.27 1939.7 2792.0 2.3305 4.0996 6.4302
250 39.762 3976.2 798.89 19.967 1085.8 1715.2 2800.9 2.7935 3.2785 6.0721
300 85.879 8587.9 712.14 46.168 1345.0 1404.6 2749.6 3.2552 2.4507 5.7059
Symbols:

P = absolute pressure   ρL = liquid density   ρV = vapor density
HL = liquid specific enthalpy   HVap = enthalpy of vaporization   HV = vapor specific enthalpy
SL = liquid specific entropy   SVap = entropy of vaporization   SV = vapor specific entropy

Mollier diagrams are graphical representations of the thermodynamic properties of materials involving "Enthalpy" as one of the coordinates. Mollier diagrams are named after Richard Mollier (1863 - 1935), a professor at Dresden University in Germany, who pioneered the graphical display of the relationship of temperature, pressure, enthalpy, entropy and volume of steam (as well as for moist air) that has aided in the teaching of thermodynamics to many generations of engineers. His enthalpy-entropy (H-S) diagram for steam was first published in 1904.[11][12]

Mollier diagrams are routinely used to visualize the working cycles of thermodynamic systems involved with the chemical engineering process design of power plants (fossil or nuclear), gas compressors, steam turbines, refrigeration systems and air conditioning.

A sample Mollier diagram for steam is presented below and others are available online:[13][14][15]

(GNU) Image: Markus Schweiss
Mollier H-S Diagram for Water-Steam

References

  1. ↑ A megawatt (MW) of electrical power is often denoted as MWe to differentiate it from other forms of power.
  2. ↑ International Energy Agency, 2006, Key Energy Statistics (International Energy Agency)
  3. ↑ International Energy Outlook 2008; Highlights (Energy Information Administration, U.S. DOE)
  4. ↑ International Energy Outlook 2008: Chapter 5 (Energy Information Administration, U.S. DOE)
  5. ↑ Energy, Electricity and Nuclear Power Estimates for the Period up to 2030 2009 Edition, International Atomic Energy Agency
  6. ↑ Nuclear Power Plants, Worldwide European Nuclear Society
  7. ↑ The amount would be even larger if power plants using other fuels were included (i.e., fuel oil, natural gas and biomass, wood, etc).
  8. ↑ Steam Carl Bevelhymer, Gotham Gazette, November 10, 2003
  9. ↑ Newsroom: Steam From the website of the Con Edison company in New York.
  10. ↑ NISTIR 5078, Thermodynamic Properties of Water Tabulation from the IAPWS Formulation 1995 for the Thermodynamic Properties of Ordinary Water Substance for General and Scientific Use (1998), Allan H. Harvey, National Institute of Standards and Technology
  11. ↑ Mollier Charts From the website of the ChemicaLogic Corporation
  12. ↑ R. K. Rajput (2009). Engineering Thermodynamics, 3rd Edition. Jones & Bartlett. ISBN 1-934015-14-8.  Google Books Use the search function for "Mollier diagram" and select page 77.
  13. ↑ Mollier diagram of water-steam From the website of Engineering ToolBox
  14. ↑ H-S Diagram for Water Associate Professor Israel Urieli, Department of Mechanical Engineering, Ohio University.
  15. ↑ Mollier Diagram for Water and the excellent animation video at Mollier Diagram for Water
 (Read more...) 		Meg Ireland Milton Beychok; Howard C. Berkowitz 5


Current Winner (to be selected and implemented by an Administrator)

To change, click edit and follow the instructions, or see documentation at {{Featured Article}}.

Higher mathematics in pre-modern Japan, also known as wasan (和算), flourished during the Edo period from the early 17th to the late 19th centuries. It had its origins in the Chinese mathematical texts which were acquired by the Japanese during their invasions of Korea in the late 16th century.[1] In a fairly isolated state, the Japanese mathematicians were able to make brilliant new discoveries in areas rarely attributed to a non-Western scholarship, sometimes outpacing their Western counterparts.[2]

Studies of Japanese mathematics were prompted by the introduction of Western mathematics to Japan and the subsequent decline of wasan during the latter half of the 19th century. Despite the steady increase in the number of articles published in Japanese since the 1920s, the subject remained at the backstage because of postwar-Japan’s scientific national policy. This changed in the recent years with the revisionist historians who have sought to contradict the Eurocentric historical views by reevaluating the non-Western sciences.[3] In this revisionist discourse, the centerpiece has often consisted of China and Japan, both of which defied the West’s totalitarian portrait of the Orient[4] by building vibrant economies and achieving comparable scientific advances before the mid-1800s.[5]

Mathematics during the Asuka and Nara periods

PD Diagram
Japan's first water clock was built during the Asuka period by Emperor Tenchi.

The oldest known case of mathematics in Japan was a system of exponential notation for high powers of ten, similar to the exponential law , which was in use before Jimmu’s legendary founding of Japan in the seventh century BCE. Findings on the subsequent cases of mathematics in ancient Japan come from the 6th century CE and afterwards when Buddhism was introduced from Korea. During the reign of Empress Suiko, the Chinese chronological system was made known, books on astrology and the calendar were introduced, and the first almanacs came into use. Prince Shotoku was so engaged in these learnings that he was honored as the father of Japanese mathematics. Emperor Tenchi, who ruled from 668 to 671 CE, created a water clock and defined the length of a day as one hundred hours. Around this time, a school of arithmetic and an observatory were also established. In 701, Emperor Monbu established a university system that included mathematical studies based on nine Chinese texts.[6] The most important among them concerned algebra, which enabled the creation of the department of “Arithmetic Intelligence” responsible for land survey and tax collection in 718. Calculations of the period were done with small bamboo sticks known as sangi, which were arranged differently like the Roman numerals to represent different numbers and were placed on paper with prescribed operations.[7]

After this brief period of enthusiasm and progress, Japanese mathematics unfortunately stagnated and stalled for nine hundred years. The nine Chinese texts were eventually forgotten, and mathematics in Japan degenerated into a superstitious body of knowledge that concerned puzzles and fortune telling. It was said that the knowledge of division was lost except in some religious establishments where calendar manuscripts were found.[8] During the Kamakura and the Muromachi periods, occasional references to sangi indicate that its use continued, but no new developments materialized.[9]

Wasan during the Edo period

(PD) Text: Yoshida Mitsuyoshi
Yoshida's Jinkoki discusses the soroban.

The Dark Age for Japanese mathematics ended with Toyotomi Hideyoshi’s invasion of Korea in 1592. A soldier was able to return to the port of Hakata with a Chinese abacus, which existed in China since the 1200s and became known as soroban in Japanese.[10] Its use became widespread after Mori Shigeyoshi published an introductory text regarding the abacus in 1622, although it did not completely replace the sangi that was more convenient for complex algebraic operations.[11] A more extensive text, and also the first complete mathematics book in Japan, was published under the title, Jinkoki, or Large and Small Numbers, in 1627 by Yoshida Mitsuyoshi. It was based on a famous Chinese text that was published in 1593 and dealt mostly with methods of computations such as multiplication, division, and the extraction of square and cube roots on the abacus.[12] Yoshida published at least six new editions of the Jinkoki, and among them the 1641 edition was the beginning of idai,[1] in which open problems are presented to the readers at the end of the book.[13]

Fair Use Photo
Geometry was the most frequent type of problems that appeared on the sangaku tablets.

After this initial takeoff, Japanese mathematics steadily progressed, primarily in areas of geometry and number theory,[14] within an open intellectual dialogue that was initially facilitated and proliferated by the samurai class. At the onset, mathematics was mostly pursued by the samurais as it had military application in surveying, navigation, and calendar making.[15] As the samurais came to work as civil servants with modest stipends, they also taught reading, writing, and arithmetic in small private schools called juku, which comprised much of the educational system in pre-modern Japan. Because of the low attendance fees, juku’s were widely attended by members across all ages and economic strata, and consequently mathematics became widely accessible within the Japanese society. People who could not afford to publish their own books posted their new findings on wooden prayer tablets in temples as offering to the gods. These tablets, which became known as sangaku, allowed the Japanese mathematicians to exchange ideas and identify new problems and thus transformed the temples into intellectual forums facilitating a nationwide dialogue. This open and collaborative discourse also existed in publications through the practice of idai, and it accelerated advances in Japanese mathematics, which took tangible form as wasan by the end of the seventeenth century.[16]

How wasan was expressed

Example of mathematical notations in wasan:

(Fair Use) Diagram: Tsukane Ogawa

The number of vertical lines represent the coefficient; for example, "||" means "".

長 is designated as ; 短, ; and 中, .

巾 means , and 勾 means "/".

How was wasan expressed and solved? It was written vertically in Kanbun, or classical Chinese, that served a similar role in East Asia as Latin in medieval Europe as the written language of higher culture.[17] Because there were only few symbols involved, more complicated equations had to be accompanied by sentences.[18] The traditional Japanese mathematicians did not discriminate between the rational and the irrational numbers, since they did not convert into decimals. This meant that, unlike their Western contemporaries,[19] the Japanese did not automatically assume π to consist of repeating decimals. It is also important to note that there was no concept of the Cartesian plane in wasan, which limited the understanding differential calculus for the Japanese.[20]

Types of problems

In the beginning, wasan included problems dealing with practical concerns, such as the calendar, which stimulated some of the most important findings in the studies of curves.[21] Yoshida introduced the challenge of calculating the value of pi as an idai problem in a later edition of his Jinkoki’s. The first to solve the problem was Muramatsu Shigekiyo, who wrote in 1663 that π = 3.14195264877.[22] He used the same technique that was used by Archimedes nineteen hundred years earlier, in which the value of pi is approximated on a regular polygon with a very large number of sides (in Muramatsu’s case, 32,768). Seki Takakazu, Japan’s most celebrated mathematician, calculated a much more accurate value of pi to be 355/113, which was correct to the eleventh digit.[23] He first used Muramatsu’s method to calculate the perimeters of three polygons with 215, 216, and 217 sides respectively. Then he posited that the perimeter of an infinite-sided polygon, a.k.a. the circle, is the sum of a geometric series ( a + ar + ar2 + ar3…), which equals to a/(1 - r) with infinite number of terms:

P(∞) = P(15) + a/(1-r) = P(16) + a1 a2 /( a1 - a2 ) = P(16) +[ P(16) - P(15) ][ P(17) - P(16) ] /{[ P(16) - P(15) ] - [ P(17) - P(16) ]}

(PD) Diagram: Seki Takakazu
Seki's square matrices from his 1633 manuscript Kaifuku Dai.

He let a1 equal the difference in the perimeters of 215 and 216-sided polygons, a2 equal the difference in the perimeters of 216 and 217-sided polygons, and r equal the ratio of the differences, a2 and a1.

Seki evidently took great interest in the number theory, as his other achievements include discovering the theory of determinants, the Bernoulli numbers, and Horner’s method for extracting irrational roots before the European mathematicians who are given credit for originating them.[24] He also devoted one of his seven books to the magic squares.

(CC) Image: Chunbum Park
Construction of Seki's magic square.

In one example, Seki drew a filled 3 by 3 square and a blank 7 by 7 (which is 2n + 1, in which n = 3) square. Then he started numbering to the right from the cell to the left of the upper right-hand corner until he reached n (in this case, number 3). Then he numbered left from the cell left of 1 until he reached the 2n-1 (in this case, number 5). Then he numbered down the right side to the cell preceding the lower right-hand one. Then he numbered along the top row until he reached the upper left-hand corner. Then he filled the left-hand column and the bottom row by subtracting from (2n + 1)2 + 1 the respective numbers on the opposite side. Then he switched n (in this case, 3) figures to the left of the upper right-hand corner with the corresponding ones in the lower row, and likewise for the n figures above the lower right hand corner, resulting in a square shown in fig. 11. Finally he filled the inner cells by repeating the procedure with number 13, resulting in the square shown in fig. 12, which includes all numbers from 1 to 49, which paired at opposite ends equal to 50 (11 + 39 = 50 ; 34 + 16 = 50 ; 12 + 38 = 50), and features consecutive patterns at intervals of 3 (10, 11, 12; 23, 25, 27; 43, 42, 41; 8, 18, 28; 24, 34, 44..).[25]

Outside the published works, Japanese mathematics was usually limited to geometry problems that were found on the sangaku tablets. Geometry problems sometimes concerned beautiful arrangement of shapes, such as a fan, and solving them were considered as a type of art in itself.[21] Some geometric problems related to more practical concerns of architecture and woodcraft. One such case involved the lotus decorations of the Japanese temples from the Asuka and the Nara periods (538-794). As the lotus fruits were usually arranged in densest packaging within the receptacle, a practical artistic concern was the densest packing of circles within circles. The Japanese may also have had an interest in the densest packing problems because they addressed the practical issues of economical cutting and arrangement of objects.[26] Geometry problems continued to evolve in more complex forms, until they eventually involved intersecting solids and surface areas.[27]

Wasan's decline and conclusion

Despite its substantial achievements, mathematics in Japan never led to a discovery of mechanical or physical laws as it has in the West. This was partly because mathematics was considered as more of a recreational art rather than science. The Japanese mathematicians also refused to denigrate their works as those of the artisans by solving problems relating to practical issues. Instead they focused on abstract problems, which made inevitable the displacement of wasan by western mathematics by the late Tokugawa period.[28]

notes

  1. ↑ 1.0 1.1 Okumura, 2009. pp. 79
  2. ↑ Ruttkay, 2008. pp. 1
  3. ↑ Ogawa, 2001.pp. 146-147
  4. ↑ Hobson, 2004. pp. 226
  5. ↑ Hanley, 1999. pp. 13
  6. ↑ Smith and Mikami, 1914. pp. 4-9
  7. ↑ Hideotshi and Rothman, 2008. pp. 10-12
  8. ↑ Smith and Mikami, 1914. pp. 14-15
  9. ↑ Hideotshi and Rothman, 2008. pp. 14
  10. ↑ Palmer
  11. ↑ Hideotshi and Rothman, 2008. pp. 19
  12. ↑ Smith and Mikami, 1914. pp. 38
  13. ↑ Hideotshi and Rothman, 2008. pp. 13-16
  14. ↑ Okumura, 2009. pp. 80
  15. ↑ Bartholomew, 1989. pp. 21
  16. ↑ Hideotshi and Rothman, 2008. pp. 19-21
  17. ↑ Hideotshi and Rothman, 2008. pp. 9
  18. ↑ Ogawa, 2001.pp. 140
  19. ↑ Hideotshi and Rothman, 2008. pp. 75
  20. ↑ Morimoto, 2009. pp. 132-133
  21. ↑ 21.0 21.1 Ogawa, 2001.pp. 145
  22. ↑ "Japanese mathematics in the Edo period (1600-1868) (Science networks. Historical studies)." Lavoisier Librairie. Web. 07 Dec. 2009. <http://www.lavoisier.fr>.
  23. ↑ Hideotshi and Rothman, 2008. pp. 16
  24. ↑ Hideotshi and Rothman, 2008. pp. 69-71
  25. ↑ Smith and Mikami, 1914. pp. 116-118
  26. ↑ Tarnai and Miyazaki, 2003. pp. 145-149
  27. ↑ Okumura, 2009. pp. 81
  28. ↑ Ravina, 1993. pp. 205-207

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