Perpetual motion

نوشته شده در موضوع تولید انرژی رایگان در 25 اکتبر 2016

Perpetual motion is suit of bodies that continues indefinitely. This is unfit given of attrition and other energy-dissipating processes.[2][3][4] A perpetual suit machine is a suppositious appurtenance that can do work indefinitely though an appetite source. This kind of appurtenance is impossible, as it would violate a initial or second law of thermodynamics.[3][4][5]

These laws of thermodynamics request even during unequivocally grand scales. For example, a motions and rotations of astronomical bodies such as planets might seem perpetual, though are indeed thesis to many processes that solemnly waste their kinetic energy, such as solar wind, interstellar middle resistance, gravitational deviation and thermal radiation, so they will not keep relocating forever.[6][7]

Thus, machines that mislay appetite from calculable sources will not work indefinitely, given they are driven by a appetite stored in a source, that will eventually be exhausted. A common instance is inclination powered by sea currents, whose appetite is eventually subsequent from a Sun, that itself will eventually bake out. Machines powered by some-more problematic sources have been proposed, though are thesis to a same inevitable laws, and will eventually breeze down.


The story of incessant suit machines dates behind to a Middle Ages. For millennia, it was not transparent possibly incessant suit inclination were probable or not, though a growth of complicated theories of thermodynamics has shown that they are impossible. Despite this, many attempts have been finished to erect such machines, stability into complicated times. Modern designers and proponents mostly use other terms, such as “over unity”, to report their inventions.

Basic principles[edit]

Oh ye seekers after incessant motion, how many vain chimeras have we pursued? Go and take your place with a alchemists.

There is a systematic accord that incessant suit in an private complement violates possibly a initial law of thermodynamics, a second law of thermodynamics, or both. The initial law of thermodynamics is a chronicle of a law of charge of energy. The second law can be phrased in several opposite ways, a many discerning of that is that feverishness flows casually from hotter to colder places; applicable here is that a law observes that in each perceivable process, there is attrition or something tighten to it; another matter is that no feverishness engine (an engine that produces work while relocating feverishness from a high feverishness to a low temperature) can be some-more fit than a Carnot feverishness engine.

In other words:

  1. In any private system, one can't emanate new appetite (law of charge of energy)
  2. The outlay work appetite of feverishness engines is always smaller than a submit heating power. The rest of a feverishness appetite postulated is squandered as feverishness to a ambient surroundings. The potency (this is a constructed work appetite divided by a submit heating power) has a maximum, given by a Carnot efficiency. It is always reduce than one.
  3. The potency of genuine feverishness engines is even reduce than a Carnot potency due to irreversibility outset from a speed of processes, including friction.

Statements 2 and 3 request to feverishness engines. Other forms of engines that modify e.g. automatic into electromagnetic energy, can't work with 100% efficiency, given it unfit to pattern any complement that is giveaway of appetite dissipation.

Machines that approve with both laws of thermodynamics by accessing appetite from radical sources are infrequently referred to as incessant suit machines, nonetheless they do not accommodate a customary criteria for a name. By proceed of example, clocks and other low-power machines, such as Cox’s timepiece, have been designed to run on a differences in barometric vigour or feverishness between night and day. These machines have a source of energy, despite one that is not straightforwardly apparent so that they customarily seem to violate a laws of thermodynamics.

Even machines that mislay appetite from permanent sources – such as sea currents – will run down when their appetite sources fundamentally do. They are not incessant suit machines given they are immoderate appetite from an outmost source and are not private systems.


One sequence of incessant suit machines refers to a sold law of thermodynamics a machines outcome to violate:[10]

  • A perpetual suit appurtenance of a initial kind produces work though a submit of energy. It so violates a initial law of thermodynamics: a law of charge of energy.
  • A perpetual suit appurtenance of a second kind is a appurtenance that casually translates thermal appetite into automatic work. When a thermal appetite is homogeneous to a work done, this does not violate a law of charge of energy. However, it does violate a some-more pointed second law of thermodynamics (see also entropy). The signature of a incessant suit appurtenance of a second kind is that there is customarily one feverishness fountainhead involved, that is being casually cooled though involving a send of feverishness to a cooler reservoir. This acclimatisation of feverishness into useful work, though any side effect, is impossible, according to a second law of thermodynamics.
  • A perpetual suit appurtenance of a third kind, is customarily (but not always)[11] tangible as one that totally eliminates attrition and other dissipative forces, to say suit perpetually (due to a mass inertia). (Third in this box refers usually to a position in a above sequence scheme, not a third law of thermodynamics.) It is unfit to make such a machine,[12][13] as abolition can never be totally separated in a automatic system, no matter how tighten a complement gets to this ideal (see examples in a Low Friction section).


“Epistemic impossibility” describes things that positively can't start within a current plan of a earthy laws. This interpretation of a word “impossible” is what is dictated in discussions of a stupidity of incessant suit in a sealed system.[14]

The charge laws are quite strong from a mathematical perspective. Noether’s theorem, that was proven mathematically in 1915, states that any charge law can be subsequent from a analogous continual balance of a transformation of a earthy system.[15] For example, if a loyal laws of production sojourn immutable over time afterwards a charge of appetite follows. On a other hand, if a charge laws are invalid, afterwards a foundations of production would need to change.[16]

Scientific investigations as to possibly a laws of production are immutable over time use telescopes to inspect a star in a apart past to discover, to a boundary of a measurements, possibly ancient stars were matching to stars today. Combining opposite measurements such as spectroscopy, proceed dimensions of a speed of light in a past and matching measurements demonstrates that production has remained roughly a same, if not identical, for all of understandable time travelling billions of years.[17]

The beliefs of thermodynamics are so good established, both theoretically and experimentally, that proposals for incessant suit machines are zodiacally met with dishonesty on a prejudiced of physicists. Any due incessant suit pattern offers a potentially exegetic plea to physicists: one is certain that it can't work, so one contingency explain how it fails to work. The problem (and a value) of such an use depends on a refinement of a proposal; a best ones tend to arise from physicists’ possess suspicion experiments and mostly strew light on certain aspects of physics. So, for example, a suspicion hearing of a Brownian ratchet as a incessant suit appurtenance was initial discussed by Gabriel Lippmann in 1900 though it was not until 1912 that Marian Smoluchowski gave an adequate reason for given it can't work.[18] However, during that twelve-year duration scientists did not trust that a appurtenance was possible. They were merely unknowingly of a accurate apparatus by that it would fundamentally fail.

The law that entropy always increases, holds, we think, a autarchic position among a laws of Nature. If someone points out to we that your pet speculation of a star is in feud with Maxwell’s equations — afterwards so many a worse for Maxwell’s equations. If it is found to be contradicted by regard — well, these experimentalists do wreck things sometimes. But if your speculation is found to be opposite a second law of thermodynamics we can give we no hope; there is zero for it though to tumble in deepest humiliation.

In a midst 19th-century Henry Dircks investigated a story of incessant suit experiments, essay a sarcastic conflict on those who continued to try what he believed to be impossible:

“There is something lamentable, degrading, and roughly violent in posterior a idealist schemes of past ages with stubborn determination, in paths of training that have been investigated by higher minds, and with that such brave persons are totally unacquainted. The story of Perpetual Motion is a story of a fool-hardiness of possibly half-learned, or totally ignorant persons.”[19]


This territory needs additional citations for verification. Please assistance urge this essay by adding citations to arguable sources. Unsourced element might be challenged and removed. (August 2010) (Learn how and when to mislay this template message)

Some common ideas recover regularly in incessant suit appurtenance designs. Many ideas that continue to seem currently were settled as early as 1670 by John Wilkins, Bishop of Chester and an central of a Royal Society. He summarized 3 intensity sources of appetite for a incessant suit machine, “Chymical [sic] Extractions”, “Magnetical Virtues” and “the Natural Affection of Gravity”.[1]

The clearly puzzling ability of magnets to change suit during a stretch though any apparent appetite source has prolonged appealed to inventors. One of a beginning examples of a captivating engine was due by Wilkins and has been widely copied since: it consists of a ramp with a magnet during a top, that pulled a steel round adult a ramp. Near a magnet was a tiny hole that was ostensible to concede a round to dump underneath a ramp and lapse to a bottom, where a strap authorised it to lapse to a tip again. The device simply could not work. Faced with this problem, some-more complicated versions typically use a array of ramps and magnets, positioned so a round is to be handed off from one magnet to another as it moves. The problem stays a same.

Gravity also acts during a distance, though an apparent appetite source, though to get appetite out of a gravitational margin (for instance, by dropping a complicated object, producing kinetic appetite as it falls) one has to put appetite in (for instance, by lifting a intent up), and some appetite is always dissolute in a process. A standard focus of sobriety in a incessant suit appurtenance is Bhaskara’s circle in a 12th century, whose pivotal suspicion is itself a repeated theme, mostly called a overbalanced wheel: relocating weights are trustworthy to a circle in such a proceed that they tumble to a position serve from a wheel’s core for one half of a wheel’s rotation, and closer to a core for a other half. Since weights serve from a core request a larger torque, it was suspicion that a circle would stagger forever. However, given a side with weights serve from a core has fewer weights than a other side, during that moment, a torque is offset and incessant transformation is not achieved.[20] The relocating weights might be hammers on pivoted arms, or rolling balls, or mercury in tubes; a element is a same.

Another fanciful appurtenance involves a frictionless sourroundings for motion. This involves a use of diamagnetic or electromagnetic levitation to boyant an object. This is finished in a opening to discharge atmosphere attrition and attrition from an axle. The levitated intent is afterwards giveaway to stagger around a core of sobriety though interference. However, this appurtenance has no unsentimental purpose given a rotated intent can't do any work as work requires a levitated intent to means suit in other objects, bringing attrition into a problem. Furthermore, a perfect opening is an unattainable idea given both a enclosure and a intent itself would solemnly vaporize, thereby spiritless a vacuum.

To mislay work from heat, so producing a incessant suit appurtenance of a second kind, a many common proceed (dating behind during slightest to Maxwell’s demon) is unidirectionality. Only molecules relocating quick adequate and in a right instruction are authorised by a demon’s trap door. In a Brownian ratchet, army given to spin a ratchet one proceed are means to do so while army in a other instruction are not. A diode in a feverishness bath allows by currents in one instruction and not a other. These schemes typically destroy in dual ways: possibly progressing a unidirectionality costs appetite (requiring Maxwell’s demon to perform some-more thermodynamic work to sign a speed of a molecules than a volume of appetite gained by a disproportion of feverishness caused) or a unidirectionality is an apparition and occasional vast violations make adult for a visit tiny non-violations (the Brownian ratchet will be thesis to inner Brownian army and therefore will infrequently spin a wrong way).

Buoyancy is another frequently misunderstood phenomenon. Some due perpetual-motion machines skip a fact that to pull a volume of atmosphere down in a potion takes a same work as to lift a analogous volume of potion adult opposite gravity. These forms of machines might engage dual chambers with pistons, and a apparatus to fist a atmosphere out of a tip cover into a bottom one, that afterwards becomes expansive and floats to a top. The squeezing apparatus in these designs would not be means to do adequate work to pierce a atmosphere down, or would leave no additional work accessible to be extracted.


Proposals for such inoperable machines have spin so common that a United States Patent and Trademark Office (USPTO) has finished an central process of refusing to extend patents for incessant suit machines though a operative model. The USPTO Manual of Patent Examining Practice states:

With a difference of cases involving incessant motion, a indication is not usually compulsory by a Office to denote a operability of a device. If operability of a device is questioned, a applicant contingency settle it to a compensation of a examiner, though he or she might name his or her possess proceed of so doing.[21]

And, further, that:

A rejecting [of a obvious application] on a belligerent of miss of focus includes a some-more specific drift of inoperativeness, involving incessant motion. A rejecting underneath 35 U.S.C. 101 for miss of focus should not be formed on drift that a invention is frivolous, fake or opposite open policy.[22]

The filing of a obvious focus is a ecclesiastic task, and a USPTO will not exclude filings for incessant suit machines; a focus will be filed and afterwards many substantially deserted by a obvious examiner, after he has finished a grave examination.[23] Even if a obvious is granted, it does not meant that a invention indeed works, it usually means that a investigator believes that it works, or was incompetent to figure out given it would not work.[23]

The USPTO maintains a collection of Perpetual Motion Gimmicks.

The United Kingdom Patent Office has a specific use on incessant motion; Section 4.05 of a UKPO Manual of Patent Practice states:

Processes or articles purported to work in a demeanour that is clearly discordant to timeless earthy laws, such as incessant suit machines, are regarded as not carrying industrial application.[24]

Examples of decisions by a UK Patent Office to exclude obvious applications for incessant suit machines include:[25]

Decision BL O/044/06, John Frederick Willmott’s focus no. 0502841[26]
Decision BL O/150/06, Ezra Shimshi’s focus no. 0417271[27]

The European Patent Classification (ECLA) has classes including obvious applications on incessant suit systems: ECLA classes “F03B17/04: Alleged perpetua mobilia …” and “F03B17/00B: [… machines or engines] (with sealed loop dissemination or similar : … Installations wherein a potion circulates in a sealed loop; Alleged perpetua mobilia of this or matching kind …”.[28]

Apparent incessant suit machines[edit]

As “perpetual motion” can customarily exist in private systems, and loyal private systems do not exist, there are not any genuine “perpetual motion” devices. However, there are concepts and technical drafts that introduce “perpetual motion”, though on closer research it is suggested that they indeed “consume” some arrange of healthy apparatus or implicit energy, such as a proviso changes of H2O or other fluids or tiny healthy feverishness gradients, or simply can't means unfixed operation. In general, extracting work from these inclination is impossible.

Resource consuming[edit]

Some examples of such inclination include:

  • The celebration bird fondle functions regulating tiny ambient feverishness gradients and evaporation. It runs until all H2O is evaporated.
  • A capillary action-based H2O siphon functions regulating tiny ambient feverishness gradients and effluvium vigour differences. With a “Capillary Bowl”, it was suspicion that a capillary transformation would keep a H2O issuing in a tube, though given a congruity force that draws a potion adult a tube in a initial place binds a drop from releasing into a bowl, a upsurge is not perpetual.
  • A Crookes radiometer consists of a prejudiced opening potion enclosure with a lightweight propeller changed by (light-induced) feverishness gradients.
  • Any device picking adult minimal amounts of appetite from a healthy electromagnetic deviation around it, such as a solar powered motor.
  • Any device powered by changes in atmosphere pressure, such as some clocks (Cox’s timepiece, Beverly Clock). The suit leeches appetite from relocating atmosphere that in spin gained a appetite from being acted on.
  • The Atmos time uses changes in a fog vigour of ethyl chloride with feverishness to breeze a time spring.
  • A device powered by hot spoil from an isotope with a comparatively prolonged half-life; such a device could plausibly work for hundreds or thousands of years.
  • The Oxford Electric Bell and Karpen Pile driven by dry raise batteries.

Low friction[edit]

  • In flywheel appetite storage, “modern flywheels can have a zero-load outline time quantifiable in years”.[29]
  • Once spun up, objects in a opening of space—stars, black holes, planets, moons, spin-stabilized satellites, etc.—dissipate appetite unequivocally slowly, permitting them to spin for prolonged periods. Tides on Earth are dissipating a gravitational appetite of a Moon/Earth complement during an normal rate of about 3.75 terawatts.[30][31]
  • In certain quantum-mechanical systems (such as superfluidity and superconductivity), unequivocally low attrition transformation is possible. However, a suit stops when a complement reaches an balance state (e.g. all a potion helium arrives during a same level.) Similarly, clearly entropy-reversing effects like superfluids climbing a walls of containers work by typical capillary action.

Thought experiments[edit]

In some cases a suspicion (or gedanken) hearing appears to advise that incessant suit might be probable by supposed and accepted earthy processes. However, in all cases, a smirch has been found when all of a applicable production is considered. Examples include:

  • Maxwell’s Demon: This was creatively due to uncover that a Second Law of Thermodynamics practical in a statistical clarity only, by postulating a “demon” that could name enterprising molecules and mislay their energy. Subsequent research (and experiment) have shown there is no proceed to physically exercise such a complement that does not outcome in an altogether boost in entropy.
  • Brownian Ratchet: In this suspicion experiment, one imagines a paddle circle connected to a ratchet. Brownian suit would means surrounding gas molecules to strike a paddles, though a ratchet would customarily concede it to spin in one direction. A some-more consummate research showed that when a earthy ratchet was deliberate during this molecular scale, Brownian suit would also impact a ratchet and means it to incidentally destroy ensuing in no net gain. Thus, a device would not violate a Laws of thermodynamics.
  • Vacuum appetite and Zero-point energy: In sequence to explain effects such as practical particles and a Casimir effect, many formulations of quantum production embody a credentials appetite that pervades dull space, famous as opening or zero-point energy. The ability to strap zero-point appetite for useful work is deliberate pseudoscience by a systematic village during large.[32][33] Inventors have due several methods for extracting useful work from zero-point energy, though nothing have been found to be viable,[32][34] no claims for descent of zero-point appetite have ever been certified by a systematic community,[35] and there is no justification that zero-point appetite can be used in defilement of charge of energy.[36]

See also[edit]

  • Physics portal
  • Energy portal
  • Incredible utility
  • Pathological science
  • Pseudoscience
  • Johann Bessler


  1. ^ a b Angrist, Stanley (January 1968). “Perpetual Motion Machines”. Scientific American. 218 (1): 115–122. doi:10.1038/scientificamerican0168-114. 
  2. ^ Oxlade, Chris (2006). Friction And Resistance. Heinemann-Raintree Library. p. 27. ISBN 1403481717. 
  3. ^ a b Derry, Gregory N. What Science Is and How It Works. Princeton University Press. p. 167. ISBN 1400823110. 
  4. ^ a b Roy, Bimalendu Narayan (2002). Fundamentals of Classical and Statistical Thermodynamics. John Wiley Sons. p. 58. ISBN 0470843136. 
  5. ^ “Definition of incessant motion”. 2012-11-22. Retrieved 2012-11-27. 
  6. ^ Taylor, J. H.; Weisberg, J. M. (1989). “Further initial tests of relativistic sobriety regulating a binary pulsar PSR 1913 + 16”. Astrophysical Journal. 345: 434–450. Bibcode:1989ApJ…345..434T. doi:10.1086/167917. 
  7. ^ Weisberg, J. M.; Nice, D. J.; Taylor, J. H. (2010). “Timing Measurements of a Relativistic Binary Pulsar PSR B1913+16”. Astrophysical Journal. 722: 1030–1034. arXiv:1011.0718v1. Bibcode:2010ApJ…722.1030W. doi:10.1088/0004-637X/722/2/1030. 
  8. ^ Simanek, Donald E. (2012). “Perpetual Futility: A brief story of a hunt for incessant motion”. The Museum of Unworkable Devices. Donald Simanek’s website, Lock Haven University. Retrieved 3 October 2013.  External couple in |publisher=, |work= (help)
  9. ^ quote creatively from Leonardo’s notebooks, South Kensington Museum MS ii p. 92 McCurdy, Edward (1906). Leonardo da Vinci’s note-books. US: Charles Scribner’s Sons. p. 64. 
  10. ^ Rao, Y. V. C. (2004). An Introduction to Thermodynamics. Hyderabad, India: Universities Press (India) Private Ltd. ISBN 81-7371-461-4. Retrieved Aug 2010.  Check date values in: |access-date= (help)
  11. ^ An choice clarification is given, for example, by Schadewald, who defines a “perpetual suit appurtenance of a third kind” as a appurtenance that violates a third law of thermodynamics. See Schadewald, Robert J. (2008), Worlds of Their Own – A Brief History of Misguided Ideas: Creationism, Flat-Earthism, Energy Scams, and a Velikovsky Affair, Xlibris, ISBN 978-1-4363-0435-1. pp55–56
  12. ^ Wong, Kau-Fui Vincent (2000). Thermodynamics for Engineers. CRC Press. p. 154. ISBN 978-0-84-930232-9. 
  13. ^ Akshoy, Ranjan Paul; Sanchayan, Mukherjee; Pijush, Roy (2005). Mechanical Sciences: Engineering Thermodynamics and Fluid Mechanics. Prentice-Hall India. p. 51. ISBN 978-8-12-032727-6. 
  14. ^ Barrow, John D. (1998). Impossibility: The Limits of Science and a Science of Limits. Oxford University Press. ISBN 978-0-19-851890-7. 
  15. ^ Goldstein, Herbert; Poole, Charles; Safko, John (2002). “Classical Mechanics (3rd edition)”. San Francisco: Addison Wesley: 589–598. ISBN 0-201-65702-3. 
  16. ^ “The incessant parable of giveaway energy”. BBC News. 9 Jul 2007. Retrieved 16 August 2010. In short, law states that appetite can't be combined or destroyed. Denying a effect would criticise not usually small pieces of scholarship – a whole edifice would be no more. All of a record on that we built a complicated universe would distortion in ruins. 
  17. ^ “CE410: Are constants constant?”, talkorigins
  18. ^ Harmor, Greg; Derek Abbott (2005). “The Feynman-Smoluchowski ratchet”. Parrondo’s Paradox Research Group. School of Electrical Electronic Engineering, Univ. of Adelaide. Retrieved 2010-01-15.  External couple in |publisher= (help)
  19. ^ Dircks, Henry (1861). Perpetuum Mobile: Or, A History of a Search for Self-motive. p. 354. Retrieved 17 August 2012. 
  20. ^ Jenkins, Alejandro (2013). “Self-oscillation”. Physics Reports. 525 (2): 167–222. arXiv:1109.6640. Bibcode:2013PhR…525..167J. doi:10.1016/j.physrep.2012.10.007. 
  21. ^ “600 Parts, Form, and Content of Application – 608.03 Models, Exhibits, Specimens”. Manual of Patent Examining Procedure (8 ed.). Aug 2001. 
  22. ^ “700 Examination of Applications II. UTILITY – 706.03(a) Rejections Under 35 U.S.C. 101”. Manual of Patent Examining Procedure (8 ed.). Aug 2001. 
  23. ^ a b Pressman, David (2008). Nolo, ed. Patent It Yourself (13, illustrated, revised ed.). Nolo. p. 99. ISBN 1-4133-0854-6. 
  24. ^ “Manual of Patent Practice, Section 4” (PDF). United Kingdom Patent Office. 
  25. ^ See also, for some-more examples of refused obvious applications during a United Kingdom Patent Office (UK-IPO), UK-IPO gets worse on incessant motion, IPKat, 12 Jun 2008. Consulted on Jun 12, 2008.
  26. ^ “Patents Ex parte preference (O/044/06)” (PDF). Retrieved 2013-03-04. 
  27. ^
  28. ^ ECLA classes F03B17/04 and F03B17/00B. Consulted on Jun 12, 2008.
  29. ^ WO focus 2008037004, Kwok, James, “An appetite storage device and process of use”, published 2008-04-03 
  30. ^ Munk, W.; Wunsch, C (1998). “Abyssal recipes II: energetics of tidal and breeze mixing”. Deep-Sea Research Part I: Oceanographic Research Papers. 45 (12): 1977. Bibcode:1998DSRI…45.1977M. doi:10.1016/S0967-0637(98)00070-3. 
  31. ^ Ray, R. D.; Eanes, R. J.; Chao, B. F. (1996). “Detection of tidal abolition in a plain Earth by satellite tracking and altimetry”. Nature. 381 (6583): 595. Bibcode:1996Natur.381..595R. doi:10.1038/381595a0. 
  32. ^ a b Amber M. Aiken, Ph.D. “Zero-Point Energy: Can We Get Something From Nothing?” (PDF). U.S. Army National Ground Intelligence Center. Forays into “free energy” inventions and perpetual-motion machines regulating ZPE are deliberate by a broader systematic village to be pseudoscience. 
  33. ^ Perpetual motion, on deteriorate 8 , part 2 of Scientific American Frontiers.
  34. ^ Martin Gardner, “‘Dr’ Bearden’s Vacuum Energy”, Skeptical Inquirer, January/February 2007
  35. ^ Matt Visser (3 Oct 1996). “What is a ‘zero-point energy’ (or ‘vacuum energy’) in quantum physics? Is it unequivocally probable that we could strap this energy?”. Phlogistin / Scientific American Magazine. Archived from the original on Aug 18, 1997. Retrieved 31 May 2013. 
  36. ^ “FOLLOW-UP: What is a ‘zero-point energy’ (or ‘vacuum energy’) in quantum physics? Is it unequivocally probable that we could strap this energy?”. Scientific American. 18 Aug 1997. 

External links[edit]

Definitions from Wiktionary

Media from Commons

News from Wikinews

Quotations from Wikiquote

Texts from Wikisource

Textbooks from Wikibooks

Learning resources from Wikiversity

Wikisource has a content of a 1911 Encyclopædia Britannica essay Perpetual Motion.

Article source:

دیدگاهتان را بنویسید

نشانی ایمیل شما منتشر نخواهد شد. بخش‌های موردنیاز علامت‌گذاری شده‌اند *