document_title: Barry Lyndon

question_text: who played the title role in barry lindon

text: Barry Lyndon

text: Plot[edit]

text: Act I[edit]

text: An omniscient (though possibly unreliable)[3] narrator relates that in 1750s Ireland, the father of Redmond Barry is killed in a duel over a sale of some horses. The widow, disdaining offers of marriage, devotes herself to her only son.

text: As a despondent young man, Barry becomes infatuated with his older cousin, Nora Brady. Though she charms him during a card game, she later shows interest in a well-off British Army captain, John Quin, much to Barry's dismay. Nora and her family plan to leverage their finances through marriage, while Barry holds Quin in contempt and escalates the situation until a fateful duel beside a river when Barry shoots Quin. In the aftermath, Barry is urged to flee from incoming police and head through the countryside towards Dublin, but along the way he is robbed of purse, pistol, and horse by Captain Feeney, an infamous highwayman.

text: Dejected, Barry carries on to the next town, where he hears a promotional spiel to join the British Army, offering the chance at fame and glory (and a lifelong pension) in return for good service. Barry enlists. Some time after joining the regiment, Barry encounters Captain Grogan, a warm-hearted family friend. Grogan informs him that Barry did not in fact kill Quin, his dueling pistol having only been loaded with tow. The duel was staged by Nora's family to be rid of Barry so that their finances would be secured through a lucrative marriage.

text: Barry’s regiment is sent to Germany to fight in the Seven Years' War, where Captain Grogan is fatally wounded by the French in a skirmish at the Battle of Minden. Fed up with the war, Barry deserts the army, stealing an officer courier's uniform, horse, and identification papers. En route to neutral Holland he encounters the Prussian Captain Potzdorf, who, seeing through his disguise, offers him the choice of being turned back over to the British where he will be shot as a deserter, or enlisting in the Prussian Army. Barry enlists in his second army and later receives a special commendation from Frederick the Great for saving Potzdorf's life in a battle.

text: Two years later, after the war ends in 1763, Barry is employed by Captain Potzdorf's uncle in the Prussian Ministry of Police to become the servant of the Chevalier de Balibari, an expatriate Irishman and professional gambler. The Prussians suspect he is a spy and send Barry as an undercover agent to verify this. Barry reveals himself to the Chevalier right away and they become confederates at the card table, where Barry and his fine eyesight relay information to his partner. After he and the Chevalier cheat the Prince of Tübingen at the card table, the Prince accuses the Chevalier (without proof) and refuses to pay his debt and demands satisfaction. When Barry relays this to his Prussian handlers, they (still suspecting that the Chevalier is a spy) are wary of allowing another meeting between the Chevalier and the Prince. So, the Prussians arrange for the Chevalier to be expelled from the country. Barry conveys this plan to the Chevalier, who flees in the night. The next morning, Barry, under disguise as the Chevalier, is escorted from Prussian territory by Prussian army officers.

text: Over the next few years, Barry and the Chevalier travel the spas and parlors of Europe, profiting from their gambling with Barry forcing payment from reluctant debtors with sword duels. Seeing that his life is going nowhere, Barry decides to marry into wealth. At a gambling table in Spa, he encounters the beautiful and wealthy Countess of Lyndon. He seduces and later marries her after the death of her elderly husband, Sir Charles Lyndon. Because Lyndon is frail, sickly, and old, Barry's goading and verbal repartee ultimately send him into a fit of convulsions that ends with his death. Barry's coup-de-grace is the assertion that "he who laughs last, wins".

text: Act II[edit]

text: In 1773, Barry takes the Countess' last name in marriage and settles in England to enjoy her wealth, still with no money of his own. Lord Bullingdon, Lady Lyndon's ten-year-old son by Sir Charles, does not approve of the marriage and quickly comes to despise Barry, calling him a "common opportunist" who does not truly love his mother. Barry retaliates by subjecting Bullingdon to systematic physical abuse.

text: The Countess bears Barry a son, Bryan Patrick, but the marriage is unhappy: Barry is openly unfaithful and enjoys spending his wife's money on self-indulgent luxuries, while keeping his wife in seclusion.

text: Some years later, Barry's mother comes to live with him at the Lyndon estate. She warns her son that if Lady Lyndon were to die, all her wealth would go to her first-born son Lord Bullingdon, leaving Barry and his son Bryan penniless. Barry's mother advises him to obtain a noble title to protect himself. To further this goal, he cultivates the acquaintance of the influential Lord Wendover and begins to expend even larger sums of money to ingratiate himself to high society. All this effort is wasted, however, during a birthday party for Lady Lyndon. A now young adult Lord Bullingdon crashes the event where he publicly enumerates the reasons that he detests his stepfather so dearly, declaring it his intent to leave the family estate for as long as Barry remains there and married to his mother. Seething with hatred, Barry savagely assaults Bullingdon until he is pulled off by the guests. This loses Barry all the wealthy and powerful friends he has worked so hard to entreat and he is cast out of polite society. Nevertheless, Bullingdon makes good on his word by leaving the estate and England itself for parts unknown.

text: In contrast to his mistreatment of his stepson, Barry proves an overindulgent and doting father to Bryan, with whom he spends all his time after Bullingdon's departure. He cannot refuse his son anything, and succumbs to Bryan's insistence on receiving a full-grown horse for his ninth birthday. Defying his parents' direct instructions that he ride the horse only in the presence of his father, the spoiled Bryan is thrown from the horse, paralyzed, and dies a few days later from his injuries.

text: The grief-stricken Barry turns to alcohol, while Lady Lyndon seeks solace in religion, assisted by the Reverend Samuel Runt, who had been tutor first to Lord Bullingdon and then to Bryan. Left in charge of the families' affairs while Barry and Lady Lyndon grieve, Barry's mother dismisses the Reverend, both because the family no longer needs (nor can afford, due to Barry's spending debts) a tutor and for fear that his influence worsens Lady Lyndon's condition. Plunging even deeper into grief, Lady Lyndon later attempts suicide (though she ingests only enough poison to make herself ill). The Reverend and the family's accountant Graham then seek out Lord Bullingdon. Upon hearing of these events, Lord Bullingdon returns to England where he finds Barry drunk in a gentlemen's club, mourning the loss of his son rather than being with Lady Lyndon. Bullingdon demands satisfaction for Barry's public assault, challenging him to a duel.

text: The duel with pistols is held in a tithe barn.[4] A coin toss gives Bullingdon the right of first fire, but he nervously misfires his pistol as he prepares to shoot. Barry, reluctant to shoot Bullingdon, magnanimously fires into the ground, but the unmoved Bullingdon refuses to let the duel end, claiming he has not received "satisfaction". In the second round, Bullingdon shoots Barry in his left leg. At a nearby inn, a surgeon informs Barry that the leg will need to be amputated below the knee if he is to survive.

text: While Barry is recovering, Bullingdon re-takes control of the Lyndon estate. A few days later, Lord Bullingdon sends a very nervous Graham to the inn with a proposition: Lord Bullingdon will grant Barry an annuity of five hundred guineas a year on the condition that he leave England, with payments ending the moment should Barry ever return. Otherwise, with his credit and bank accounts exhausted, Barry's creditors and bill collectors will assuredly see that he is jailed. Defeated in mind and body, Barry accepts.

text: The narrator states that Barry went first back to Ireland with his mother, then to the European continent to resume his former profession of gambler (though without his former success). Barry kept his word and never returned to England or ever saw Lady Lyndon again. The final scene (set in December 1789) shows a middle-aged Lady Lyndon signing Barry's annuity cheque as her son looks on.

text: Epilogue[edit]

text: Cast[edit]

text:
Michael Hordern (voice) as Narrator
Ryan O'Neal as Redmond Barry (later Redmond Barry Lyndon)
Marisa Berenson as Lady Lyndon
Patrick Magee as the Chevalier du Balibari
Hardy Krüger as Captain Potzdorf
Gay Hamilton as Nora Brady
Godfrey Quigley as Captain Grogan
Steven Berkoff as Lord Ludd
Wolf Kahler as Prince of Tübingen
Marie Kean as Belle, Barry's mother
Murray Melvin as Reverend Samuel Runt
Frank Middlemass as Sir Charles Reginald Lyndon
Leon Vitali as Lord Bullingdon
Dominic Savage as young Bullingdon
Leonard Rossiter as Captain John Quin
André Morell as Lord Wendover
Anthony Sharp as Lord Hallam
Philip Stone  as Graham
David Morley as Bryan Patrick Lyndon
Diana Koerner as Lieschen (German Girl)
Arthur O'Sullivan as Captain Feeney
Billy Boyle as Seamus Feeney
Roger Booth as King George III

tag: ul

text: Critic Tim Robey suggests that the film "makes you realise that the most undervalued aspect of Kubrick's genius could well be his way with actors."[5] He adds that the supporting cast is a "glittering procession of cameos, not from star names but from vital character players."[5]

text: The cast featured Leon Vitali as the older Lord Bullingdon, who would then become Kubrick's personal assistant, working as the casting director on his following films, and supervising film-to-video transfers for Kubrick. Their relationship lasted until Kubrick's death. The film's cinematographer, John Alcott, appears at the men's club in the non-speaking role of the man asleep in a chair near the title character when Lord Bullingdon challenges Barry to a duel. Kubrick's daughter Vivian also appears (in an uncredited role) as a guest at Bryan's birthday party.

text: Other Kubrick stalwarts to appear were Leonard Rossiter (2001: A Space Odyssey), Steven Berkoff, Patrick Magee and Anthony Sharp (A Clockwork Orange). Philip Stone, who plays Graham, also appeared in A Clockwork Orange and would go on to feature in The Shining.

text: Production[edit]

text: Development[edit]

text: After completing post production 2001: A Space Odyssey, Kubrick resumed planning a film about Napoleon. During pre-production,  Sergei Bondarchuk and Dino De Laurentiis' Waterloo was released, and failed at the box office. Reconsidering, Kubrick's financiers pulled funding, and he turned his attention towards an adaptation of Anthony Burgess's 1962 novel A Clockwork Orange. Subsequently, Kubrick showed an interest in Thackeray's Vanity Fair but dropped the project when a serialised version for television was produced. He told an interviewer, "At one time, Vanity Fair interested me as a possible film but, in the end, I decided the story could not be successfully compressed into the relatively short time-span of a feature film...as soon as I read Barry Lyndon I became very excited about it."[6]

text: Having garnered Oscar nominations for Dr. Strangelove, 2001: A Space Odyssey and A Clockwork Orange, Kubrick's reputation in the early 1970s was that of "a perfectionist auteur who loomed larger over his movies than any concept or star."[5] His studio—Warner Bros.—was therefore "eager to bankroll" his next project, which Kubrick kept "shrouded in secrecy" from the press partly due to the furor surrounding the controversially violent A Clockwork Orange (particularly in the UK) and partly due to his "long-standing paranoia about the tabloid press."[5]

text: Having felt compelled to set aside his plans for a film about Napoleon Bonaparte, Kubrick set his sights on Thackeray's 1844 "satirical picaresque about the fortune-hunting of an Irish rogue," Barry Lyndon, the setting of which allowed Kubrick to take advantage of the copious period research he had done for the now-aborted Napoleon.[5] At the time, Kubrick merely announced that his next film would star Ryan O'Neal (deemed "a seemingly un-Kubricky choice of leading man"[5]) and Marisa Berenson, a former Vogue and Time magazine cover model, and be shot largely in Ireland.[5] So heightened was the secrecy surrounding the film that "Even Berenson, when Kubrick first approached her, was told only that it was to be an 18th-century costume piece [and] she was instructed to keep out of the sun in the months before production, to achieve the period-specific pallor he required."[5]

text: Principal photography[edit]

text:
Principal photography took 300 days, from spring 1973 through early 1974, with a break for Christmas.[7] The crew arrived in Dublin, Ireland in May 1973. Jan Harlan recalls that Kubrick "loved his time in Ireland - he rented a lovely house west of Dublin, he loved the scenery and the culture and the people".
[8]

text: Many of the exteriors were shot in Ireland, playing "itself, England, and Prussia during the Seven Years' War."[5] Drawing inspiration from "the landscapes of Watteau and Gainsborough," Kubrick and cinematographer Alcott also relied on the "scrupulously researched art direction" of Ken Adam and Roy Walker.[5] Alcott, Adam and Walker were among those who would win Oscars for their "amazing work" on the film.[5]

text: Several of the interior scenes were filmed in Powerscourt House, an 18th-century mansion in County Wicklow, Republic of Ireland. The house was destroyed in an accidental fire several months after filming (November 1974), so the film serves as a record of the lost interiors, particularly the "Saloon" which was used for more than one scene. The Wicklow Mountains are visible, for example, through the window of the saloon during a scene set in Berlin. Other locations included Kells Priory (the English Redcoat encampment)[9] Blenheim Palace, Castle Howard (exteriors of the Lyndon estate), Huntington Castle, Clonegal (exterior), Corsham Court (various interiors and the music room scene), Petworth House (chapel), Stourhead (lake and temple), Longleat, and Wilton House (interior and exterior) in England, Dunrobin Castle (exterior and garden as Spa) in Scotland, Dublin Castle in Ireland (the chevalier's home), Ludwigsburg Palace near Stuttgart and Frederick the Great's Neues Palais at Potsdam near Berlin (suggesting Berlin's main street Unter den Linden as construction in Potsdam had just begun in 1763). Some exterior shots were also filmed at Waterford Castle (now a luxury hotel and golf course) and Little Island, Waterford. Moorstown Castle in Tipperary also featured. Several scenes were filmed at Castletown House outside Carrick-on-Suir, Co. Tipperary, and at Youghal, Co. Cork.

text: The filming took place in the backdrop of some of the most intense years of the Troubles in Ireland, during which the Provisional Irish Republican Army (Provisional IRA) was waging an armed campaign in order to bring about a United Ireland.

text: On 30 January 1974 while filming in Dublin City's Phoenix Park shooting had to be canceled due to the chaos caused by 14 bomb threats.[10]

text:
One day a phone call was received and Kubrick was given 24 hours to leave the country, he left within 12 hours. The phone call was alleged that Provisional IRA had him on a hit list and Harlan recalls "Whether the threat was a hoax or it was real, almost doesn't matter...Stanley was not willing to take the risk. He was threatened, and he packed his bag and went home
[11][12]

text: Cinematography[edit]

text: The film—as with "almost every Kubrick film"—is a "showcase for [a] major innovation in technique."[5] While 2001: A Space Odyssey had featured "revolutionary effects," and The Shining would later feature heavy use of the Steadicam, Barry Lyndon saw a considerable number of sequences shot "without recourse to electric light."[5] Cinematography was overseen by director of photography John Alcott (who won an Oscar for his work), and is particularly noted for the technical innovations that made some of its most spectacular images possible. To achieve photography without electric lighting "[f]or the many densely furnished interior scenes... meant shooting by candlelight," which is known to be difficult in still photography, "let alone with moving images."[5]

text: Kubrick was "determined not to reproduce the set-bound, artificially lit look of other costume dramas from that time."[5] After "tinker[ing] with different combinations of lenses and film stock," the production obtained three super-fast 50mm lenses (Carl Zeiss Planar 50mm f/0.7) developed by Zeiss for use by NASA in the Apollo moon landings, which Kubrick had discovered.[5][13] These super-fast lenses "with their huge aperture (the film actually features the lowest f-stop in film history) and fixed focal length" were problematic to mount, and were extensively modified into three versions by Cinema Products Corp. for Kubrick so to gain a wider angle of view, with input from optics expert Richard Vetter of Todd-AO.[5][13] The rear element of the lens had to be 2.5 mm away from the film plane, requiring special modification to the rotating camera shutter.[14] This allowed Kubrick and Alcott to shoot scenes lit with actual candles to an average lighting volume of only three candela, "recreating the huddle and glow of a pre-electrical age."[5] In addition, Kubrick had the entire film push-developed by one stop.[13]

text: Although Kubrick's express desire was to avoid electric lighting where possible, most shots were achieved with conventional lenses and lighting, but were lit to deliberately mimic natural light rather than for compositional reasons. In addition to potentially seeming more realistic, these methods also gave a particular period look to the film which has often been likened to 18th-century paintings (which were, of course, depicting a world devoid of electric lighting), in particular owing "a lot to William Hogarth, with whom Thackeray had always been fascinated."[5]

text: The film is widely regarded as having a stately, static, painterly quality,[5] mostly due to its lengthy wide angle long shots. To illuminate the more notable interior scenes, artificial lights were placed outside and aimed through the windows, which were covered in a diffuse material to scatter the light evenly through the room rather than being placed inside for maximum use as most conventional films do. An example of this method occurs in the scene where Barry duels Lord Bullingdon. Though it appears to be lit entirely with natural light, one can see that the light coming in through the cross-shaped windows in the tithe barn appears blue in color, while the main lighting of the scene coming in from the side is not. This is because the light through the cross-shaped windows is daylight from the sun, which when recorded on the film stock used by Kubrick showed up as blue-tinted compared to the incandescent electric light coming in from the side.[citation needed]

text: Despite such slight tinting effects, this method of lighting not only gave the look of natural daylight coming in through the windows, but it also protected the historic locations from the damage caused by mounting the lights on walls or ceilings and the heat from the lights. This helped the film "fit... perfectly with Kubrick's gilded-cage aesthetic – the film is consciously a museum piece, its characters pinned to the frame like butterflies."[5]

text: Music[edit]

text:
Barry LyndonSoundtrack album by variousReleased
December 27, 1975 (1975-12-27)Genre
classical, march, folkLength
49:48Label
Warner Bros.Producer
Leonard Rosenman

tag: table

text: The film's period setting allowed Kubrick to indulge his penchant for classical music, and the film score uses pieces by Bach, Vivaldi, Paisiello, Mozart, and Schubert.[note 1] The piece most associated with the film, however, is the main title music, Handel's Sarabande from the Keyboard suite in D minor (HWV 437). Originally for solo harpsichord, the versions for the main and end titles are performed with orchestral strings, harpsichord, and timpani. The score also includes Irish folk music, including Seán Ó Riada's song Women of Ireland, arranged by Paddy Moloney and performed by The Chieftains. The British Grenadiers also features in scenes with Redcoats marching.

text: No.TitleWriter(s)Performer/conductor/arrangerLength1."Sarabande–Main Title"George Frideric HandelNational Philharmonic Orchestra2:382."Women of Ireland"Peadar Ó Doirnín, Seán Ó RiadaThe Chieftains4:083."Piper's Maggot Jig"traditionalThe Chieftains1:394."The Sea-Maiden"traditionalThe Chieftains2:025."Tin Whistles"Ó RiadaPaddy Moloney & Seán Potts3:416."The British Grenadiers"traditionalFifes & Drums2:127."Hohenfriedberger March"Frederick the GreatFifes & Drums1:128."Lillibullero"traditionalFifes & Drums1:069."Women of Ireland"Ó RiadaDerek Bell0:5210."March from Idomeneo"Wolfgang Amadeus MozartNational Philharmonic Orchestra1:2911."Sarabande–Duel"HandelNational Philharmonic Orchestra3:1112."Lillibullero"traditionalLeslie Pearson0:5213."German Dance no. 1 in C major"Franz SchubertNational Philharmonic Orchestra2:1214."Sarabande–Duel"HandelNational Philharmonic Orchestra0:4815."Film Adaptation of the Cavatina from Il barbiere di Siviglia"Giovanni PaisielloNational Philharmonic Orchestra4:2816."Cello Concerto in E minor"Antonio VivaldiLucerne Festival Strings/Pierre Fournier/Rudolf Baumgartner3:4917."Adagio from Concerto for two harpsichords in C minor"Johann Sebastian BachMünchener Bach-Orchester/Hedwig Bilgram/Karl Richter5:1018."Film Adaptation of Piano Trio in E-flat, Op. 100 (second movement)"SchubertMoray Welsh/Anthony Goldstone/Ralph Holmes4:1219."Sarabande–End Title"HandelNational Philharmonic Orchestra4:07Total length:49:48

text: Reception[edit]

text: The film "was not the commercial success Warner Bros. had been hoping for" within the United States,[5] although it fared better in Europe. This mixed reaction saw the film (in the words of one retrospective review) "greeted, on its release, with dutiful admiration – but not love. Critics... rail[ed] against the perceived coldness of Kubrick's style, the film's self-conscious artistry and slow pace. Audiences, on the whole, rather agreed..."[5] This "air of disappointment"[5] factored into Kubrick's decision for his next film –  Stephen King's The Shining – a project that would not only please him artistically, but also be more likely to succeed financially. Still, several other critics, including Gene Siskel, praised the film's technical quality and strong narrative, and Siskel himself counted it as one of the five best films of the year.

text: In recent years, the film has gained a more positive reaction. As of  April 2018[update] it holds a 94% "Certified Fresh" rating on Rotten Tomatoes based on 64 reviews, nine of which are from the site's "top critics."[15] Roger Ebert added the film to his 'Great Movies' list on 9 September 2009, writing, "It defies us to care, it asks us to remain only observers of its stately elegance", and it "must be one of the most beautiful films ever made."[16]

text: Director Martin Scorsese has named Barry Lyndon as his favorite Kubrick film,[17] and it is also one of Lars von Trier's favorite films.[18] Quotations from its script have also appeared in such disparate works as Ridley Scott's The Duellists, Scorsese's The Age of Innocence, and Wes Anderson's Rushmore.[citation needed]

text: Awards[edit]

text: In 1976, at the 48th Academy Awards, the film won four awards, for Best Art Direction (Ken Adam, Roy Walker, Vernon Dixon), Best Cinematography (John Alcott), Best Costume Design (Milena Canonero, Ulla-Britt Söderlund) and Best Musical Score (Leonard Rosenman, "for his arrangements of Schubert and Handel".)[5] Kubrick was nominated three times, for Best Director, Best Picture, and Best Adapted Screenplay.[19]

text: Kubrick won the British Academy of Film and Television Arts Award for Best Direction. John Alcott won for Best Cinematography. Barry Lyndon was also nominated for Best Film, Art Direction, and Costume Design.

text: Source novel[edit]

text: Kubrick based his adapted screenplay on William Makepeace Thackeray's The Luck of Barry Lyndon (republished as the novel Memoirs of Barry Lyndon, Esq.), a picaresque tale written and published in serial form in 1844.

text: The film departs from the novel in several ways. In Thackeray's writings, events are related in the first person by Barry himself. A comic tone pervades the work, as Barry proves both a raconteur and an unreliable narrator. Kubrick's film, by contrast, presents the story objectively. Though the film contains voice-over (by actor Michael Hordern), the comments expressed are not Barry's, but those of an omniscient narrator.  Kubrick felt that using a first-person narrative would not be useful in a film adaptation:[20]

text: I believe Thackeray used Redmond Barry to tell his own story in a deliberately distorted way because it made it more interesting. Instead of the omniscient author, Thackeray used the imperfect observer, or perhaps it would be more accurate to say the dishonest observer, thus allowing the reader to judge for himself, with little difficulty, the probable truth in Redmond Barry's view of his life. This technique worked extremely well in the novel but, of course, in a film you have objective reality in front of you all of the time, so the effect of Thackeray's first-person story-teller could not be repeated on the screen. It might have worked as comedy by the juxtaposition of Barry’s version of the truth with the reality on the screen, but I don’t think that Barry Lyndon should have been done as a comedy.

text: Kubrick made several changes to the plot, including the addition of the final duel.


document_title: Nilgiri tahr

question_text: nilgiri himalayan and arabian are types of which of the animals

root

text: Nilgiri tahr

text: Etymology[edit]

text: In the Tamil language it is called varaiaadu (வரையாடு), the term being composed of two Tamil words, wurrai a precipice, and aadu, a goat.In Malayalam it is pronounced as "Varayaadu" (വരയാട്).[2] The ancient word in classical Tamil was "varudai" (வருடை: Natrinai, 359; Ainkurunuru, 287; Pattinappalai, 139). It was previously named Capra warryato by Gray.[3]

tag: p

text: Taxonomy[edit]

text: Its closest relatives are sheep (genus Ovis). Until 2005, it was placed with the Himalayan tahr (Hemitragus jemlahicus) and the Arabian tahr (Arabitragus jayakari) in the genus Hemitragus. However, it has recently been transferred to a new genus Nilgiritragus because it is genetically more similar to members of the genus Ovis than to other tahrs.[4]

text: Description[edit]

text: The Nilgiri tahr is a stocky goat with short, coarse fur and a bristly mane. Males are larger than females and of darker color when mature. Both sexes have curved horns, reaching up to 40 centimetres (16 in) for males and 30 centimetres (12 in) for females. Adult males weigh 80 to 100 kilograms (180 to 220 lb) and stand about 100 centimetres (39 in) tall at the shoulder. Adult males develop a light grey area on their backs and are thus called "saddlebacks".[2]

text: Habitat and distribution[edit]

text: The Nilgiri tahr inhabits the open montane grassland habitat of the South Western Ghats montane rain forests ecoregion. At elevations from 1,200 to 2,600 metres (3,900 to 8,500 ft), the forests open into grasslands interspersed with pockets of stunted forests, locally known as sholas. These grassland habitats are surrounded by dense forests at the lower elevations. The Nilgiri tahrs formerly ranged over these grasslands in large herds, before but hunting and poaching in the nineteenth century reduced their population.[1][5]

text: Conservation[edit]

text: As few as 100 Nilgiri tahrs were left in the wild by the early 20th century. Since that time their numbers have inceased somewhat; in a comprehensive study of the Nilgiri tahr population in Western Ghats, the WWF-India has put the population at 3,122.[6] Their range extends over 400 kilometres (250 mi) from north to south, and Eravikulam National Park is home to the largest population. As per the Wildlife census conducted by Kerala forest department in association with volunteers from College of Forestry & Veterinary Science under Kerala Agricultural University, from April 24-28, 2014, number of animals in Eravikulam National Park has increased to 894 individuals. This is the highest ever count recorded in the national park, with the first census in 1996 finding only 640 tahrs.[5] The other significant concentration is in the Nilgiri Hills, with smaller populations in the Anamalai Hills, Periyar National Park, Palni Hills and other pockets in the Western Ghats south of Eravikulam, almost to India's southern tip. A small populations of tahr numbering around 200 are known to inhabit the Boothapandi, Azhakiyapandipuram, Velimalai, Kulasekaram and Kaliyal Ranges in the Kanyakumari district of Tamil Nadu [7] and another small herd of less than 30 animals is known to inhibit Ponmudi hills in Trivandrum district of Kerala [8]

text: Gallery[edit]

text:
In Rajamala, Munnar

Nilgiri tahrs making their way down the mountain

An adult male Nilgiri tahr, with a pallid harrier (female)


document_title: Daddy's Home 2

question_text: who plays will ferrell's dad in daddy's home 2

question_tokens: who plays will ferrell 's dad in daddy 's home 2

text: Daddy's Home 2

text: Plot[edit]

text: After finally becoming friends at the end of the first film, Brad Whittaker and Dusty Mayron have a co-dad system where their two children, Megan and Dylan, take turns at each father's house. Dusty has also remarried, this time to Karen, a writer, and is stepdad to Adrianna, Karen's daughter.

text: Brad and his wife, Sara, along with Dusty and Karen, attend a school play for Megan, where she announces to the whole audience that she doesn't like the fact that she has to go back and forth to different houses all the time. Back at the house, after the play, Brad and Dusty decide to do away with having two separate Christmases and instead do one "together Christmas". Dusty, however, finds out his tough fighter pilot/astronaut father Kurt (Mel Gibson) is coming for Christmas.

text: At the airport the next day, Dusty tells Brad that his father is going to make fun of them since he won't understand their co-dad arrangement. When Kurt arrives, he mistakes Brad for a chauffeur. When Dusty explains that Brad is the stepdad to his children, Kurt doesn't like it. Brad's overbearing and over-cheerful dad, Don, arrives next, unnerving Kurt. Don tells Brad that his mother didn't come along, because she is taking care of Brad's Uncle who isn't feeling well.

text: Back at the house, Megan and Dylan warmly embrace Don, since he is very present in their lives, while Kurt hasn't seen the children since they were toddlers. Through jealousy of the affection the children show to Don, Kurt rents a large cabin through Airbnb, to house all of them through the holiday week. As Brad and Dusty pack the bags into the car, Dusty tells Brad that Kurt thinks the two men are harboring bad feelings for each other, but are just hiding it from everyone by pretending to be friends. When Kurt walks to the car, they change the subject.

text: Throughout the week, Brad and Dusty's co-dad relationship is put to the test by Kurt's meddling. It is revealed that Kurt has never really had a good father-son relationship with Dusty either. Dusty gets angry, and Brad tells him to set a good example for his children, and the only person who could ruin the vacation for him was himself. Meanwhile, Dusty tries to get close to his stepdaughter, Adrianna, but she doesn't like him and repeatedly tells him that he isn't her father. Sara also tries to bond with Karen but is taken aback by some of Karen's actions, like shoplifting clothes from a store. Dylan develops a crush on a little girl staying in the cabin next door. Brad gives him some “advice” but it only made Dylan more afraid. He gets made fun of by Megan and Adrianna. Finding the trees to small in a farm they illegally went onto private property to cut one down. Brad mistakes a power line for a tree, and is electrocuted. The men come home with a $20,000 tree.

text: The next day, the entire family goes bowling, And Dylan throws a fit after his ball keeps getting stuck in the gutter. Grandpa Kurt motivates him, and the entire bowling arena cheers as Dylan knocks down a single pin. After bowling, the family goes out to take the kids to see Santa. While there, Kurt convinces Dylan to ask Santa for a shotgun, which he does ask for. Don tells Dylan that a shotgun for hunting means that a poor innocent animal will lose its life. This convinces Dylan to change his mind, but when it is Megan turn to ask for something, she decides she wants to go hunting after hearing Grandpa Kurt saying that women can’t shoot. While out hunting the next day, Megan accidentally shoots Kurt in the shoulder, sending him to the hospital. While Kurt’s disablement, she managed to shoot two turkeys to Grandpa Kurt’s surprise. When day ends, Brad is outside clearing snow. Sara comes outside and asks about Brad’s dad’s relationship with his mom. Brad is confused and tells her they love each other more then his dad loves him. While he is talking to Sara, his snow plowed reels in Christmas lights, which drops onto Dusty’s car.

text: At the hospital, Dusty and Kurt begin to bond after they almost begin fighting when Kurt tries to leave the hospital. That night, Brad, Dusty, Don & Kurt go to an improv comedy club where the four men are relaxing and having a good time watching the show. Kurt gets up to go get another drink at the bar. Dusty sees Kurt picking up a woman at the bar and leaves with her. Brad enters Don into the improv show, and Dusty chooses a topic of a husband confronting his cheating wife as the subject of an improv skit. As the skit progresses, it is revealed that Don has separated from his wife in real life. The audience believes that this is all part of the show, even when Brad tries to tell the audience that it is not.

text: The next day, Brad confronts Dusty. After Dusty reveals that he chose the infidelity subject for the improv game because he wanted to get back at Brad, because of how Brad has a good relationship with Don. Inside Sara comforts Don about his divorce in front of an eggnog bowl. When they leave, Meagan and Adrianna fill cups of alcoholic eggnog to drink. Brad says he knows that is why Dusty chose that particular topic and to get back at Dusty; Brad has invited Adrianna's real dad, Roger, to the cabin for Christmas.

text: That evening, the entire family takes part in a Christmas manger representation. Brad gets into a fight with Dusty after Brad wants to play Joseph, which Dusty is currently playing. When Megan begins to swear, and Adrianna fell from being drunk the crowd breaks up. Instead of Dusty fighting Brad, he almost comes to blows with Roger.

text: The next morning, Christmas Day, the families all pack up to leave. On their way out of town, the families are forced back to town on account of a blizzard. They are forced to take shelter at a movie theater. With every other movie being sold out, due to the huge influx of business from other families seeking shelter at the theater, both families go to see the last movie available: Missile Tow, a fictitious Liam Neeson holiday action film.

text: When the power cuts off during the movie, the families go to the lobby where each man confronts their father about the secrets, lies, and attitudes. Don confronts Brad about not telling him the truth about his divorce, while Dusty tries to talk to Kurt. When Dylan sees the girl he has a crush on, is also there at the theater, he is teased again by Megan and Adrianna. After remembering some advice given to him by Kurt, Dylan walks toward her to kiss her. All of a sudden, he doesn't kiss her, but instead kisses Adrianna, his stepsister. Roger gets freaked out and attempts to leave with Adrianna, but is confronted by Dusty. He deduces that the reason why Adrianna hasn't warmed up to him is that he has never told her that he loves her, which he does. He also tells Roger that loving Adrianna means loving her real father as well since he is also part of the family. Roger almost leaves without Adrianna, but has a change of heart after everyone breaks out into a song of Do They Know It's Christmas? and decides to stay. Don and Brad also reconcile.

text: Sometime later, at the airport, Don and Kurt are preparing to leave to head back to their respective homes. Kurt heads with Don up the terminal escalators, where he reveals to Don that he switched out the tickets and they're going to spend New Years in Las Vegas.

text: As Brad's mom's flight arrives, Dusty and Brad discover that Brad's new stepdad is Chesley "Sully" Sullenberger, the pilot of the "Miracle on the Hudson" flight. Brad and Dusty remember that they watched the film "Sully" together not too long ago and Brad appears to be welcoming towards him. Brad runs down the terminal and says that Sully will never replace his father, because Sully has only one great personal story, whereas his father has thousands of stories.

text: Cast[edit]

text:
Will Ferrell as Brad Whitaker
Mark Wahlberg as Dusty Mayron
Mel Gibson as Kurt Mayron
John Lithgow as Don Whitaker
Linda Cardellini as Sara Whitaker
John Cena as Roger
Scarlett Estevez as Megan Mayron
Owen Vaccaro as Dylan Mayron
Alessandra Ambrosio as Karen Mayron
Didi Costine as Adrianna
Chesley Sullenberger as himself
Liam Neeson as himself
Bill Burr as Jerry

text: Production[edit]

text: In April 2016, the sequel was announced, with Will Ferrell and Mark Wahlberg reprising their roles, Sean Anders and John Morris writing the script, and Anders directing.[3] In January 2017, it was reported that Mel Gibson and John Lithgow were being sought to play the main characters' fathers in the film.[4] The two were later confirmed to star, along with Linda Cardellini, John Cena, Owen Vaccaro and Scarlett Estevez, reprising their roles.[5][6]

text: Filming[edit]

text: Principal photography began on March 20, 2017.[7] Scenes were filmed in Concord, Massachusetts, Framingham, Massachusetts, and Great Barrington, Massachusetts.

text: Release[edit]

text: The film was released in the United States on November 10, 2017.[8]

text: Home media[edit]

text: Daddy's Home 2 was released on Digital HD on February 6, 2018, and was released on Blu-ray and DVD on February 20, 2018.[9][10]

text: Reception[edit]

text: Box office[edit]

text: Daddy's Home 2 grossed $103.8 million in the United States and Canada, and $76.6 million in other territories, for a worldwide total of $180.4 million, against a production budget of $69 million.[2]

text: In the United States and Canada, Daddy's Home 2 opened alongside Murder on the Orient Express, and was projected to gross around $20 million from 3,575 theaters in its opening weekend.[11] The film made $10.7 million on its first day, including $1.5 million from Thursday night previews at 2,500 theaters, up from the $1.2 million made by the first film. It went on to debut to $29.7 million, finishing second at the box office, behind holdover Thor: Ragnarok ($57 million).[12] In its second weekend the film made $14.4 million (a drop of 51.3%), finishing 4th behind Justice League, Wonder and Thor: Ragnarok.[13]

text: Critical response[edit]

text: On Rotten Tomatoes, the film holds an approval rating of 19% based on 111 reviews, and an average rating of 3.8/10. The site's critical consensus reads, "A formulaic comedy that's unlikely to spread much yuletide merriment, Daddy's Home 2 can only muster a few stray yuks from its talented cast."[14] On Metacritic, the film has a weighted average score of 30 out of 100 based on 26 critics, indicating "generally unfavorable reviews".[15] Audiences polled by CinemaScore gave the film an average grade of "A−" on an A+ to F scale.[12]

text: Alonso Duralde of TheWrap was critical of what he described as the film's sloppiness and laziness, saying, "Director Sean Anders and his co-writer John Morris execute what are supposed to be the laughs with blunt force. The jokes announce themselves with heavy footsteps, and almost none of them land, stranding a talented cast with terrible material that they’re straining to sell."[16] Richard Roeper of the Chicago Sun-Times gave the film 1 out of 4 stars, saying: "After enduring last week’s lousy and lazy A Bad Moms Christmas, I would have bet it would be many a year before we’d see another holiday comedy more sour and cynical and profoundly unfunny. I sit corrected."[17]

text: Glenn Kenny of RogerEbert.com gave the film 2.5 out of 4 stars, writing, "I found the sequel better than the original—the writing sharper, the jokes fresher and smarter, the comic interaction between the lead characters consistently engaging. I mentioned this to my incredulous wife, who said, 'So you’re saying it's the Godfather, Part 2 of the Daddy’s Home series'."[18]

text: Accolades[edit]

text:
Year
Award
Category
Subject
Result

2018
Golden Raspberry Awards
Worst Actor
Mark Wahlberg
Nominated

Worst Supporting Actor
Mel Gibson
Won


document_title: Temperature

question_text: who invented the standard unit of measuring temperature

question_tokens: who invented the standard unit of measuring temperature

text: Temperature

text: Effects[edit]

text: This section needs additional citations for verification. Please help improve this article by adding citations to reliable sources. Unsourced material may be challenged and removed. (January 2013) (Learn how and when to remove this template message)

text: Many physical processes are affected by temperature, such as

text:
physical properties of materials including the phase (solid, liquid, gaseous or plasma), density, solubility, vapor pressure, electrical conductivity
rate and extent to which chemical reactions occur[1]
the amount and properties of thermal radiation emitted from the surface of an object
speed of sound is a function of the square root of the absolute temperature[2]

text: Scales[edit]

text: This section needs additional citations for verification. Please help improve this article by adding citations to reliable sources. Unsourced material may be challenged and removed. (August 2012) (Learn how and when to remove this template message)

text: Temperature scales differ in two ways: the point chosen as zero degrees, and the magnitudes of incremental units or degrees on the scale.

text: The Celsius scale (°C) is used for common temperature measurements in most of the world. It is an empirical scale that was developed by a historical progress, which led to its zero point 7002273149999999999♠0 °C being defined by the freezing point of water, and additional degrees defined so that 7002373150000000000♠100 °C was the boiling point of water, both at sea-level atmospheric pressure. Because of the 100-degree interval, it was called a centigrade scale.[3] Since the standardization of the kelvin in the International System of Units, it has subsequently been redefined in terms of the equivalent fixing points on the Kelvin scale, and so that a temperature increment of one degree Celsius is the same as an increment of one kelvin, though they differ by an additive offset of 273.15.

text: The United States commonly uses the Fahrenheit scale, on which water freezes at 7002273149999999999♠32 °F and boils at 7002373150000000000♠212 °F at sea-level atmospheric pressure.

text: Many scientific measurements use the Kelvin temperature scale (unit symbol: K), named in honor of the Scots-Irish physicist who first defined it. It is a thermodynamic or absolute temperature scale. Its zero point, 5000000000000000000♠0 K, is defined to coincide with the coldest physically-possible temperature (called absolute zero). Its degrees are defined through thermodynamics.  The temperature of absolute zero occurs at  5000000000000000000♠0 K = 5000000000000000000♠−273.15 °C (or 5000000000000000000♠−459.67 °F), and the freezing point of water at sea-level atmospheric pressure occurs at 7002273149999999999♠273.15 K = 7002273149999999999♠0 °C.

text: The International System of Units (SI) defines a scale and unit for the kelvin or thermodynamic temperature by using the reliably reproducible temperature of the triple point of water as a second reference point (the first reference point being 5000000000000000000♠0 K at absolute zero). The triple point is a singular state with its own unique and invariant temperature and pressure, along with, for a fixed mass of water in a vessel of fixed volume, an autonomically and stably self-determining partition into three mutually contacting phases, vapour, liquid, and solid, dynamically depending only on the total internal energy of the mass of water. For historical reasons, the triple point temperature of water is fixed at 273.16 units of the measurement increment.

text: Types[edit]

text: There is a variety of kinds of temperature scale. It may be convenient to classify them as empirically and theoretically based. Empirical temperature scales are historically older, while theoretically based scales arose in the middle of the nineteenth century.[4][5]

text: Empirically-based[edit]

text: Empirically based temperature scales rely directly on measurements of simple physical properties of materials. For example, the length of a column of mercury, confined in a glass-walled capillary tube, is dependent largely on temperature, and is the basis of the very useful mercury-in-glass thermometer. Such scales are valid only within convenient ranges of temperature. For example, above the boiling point of mercury, a mercury-in-glass thermometer is impracticable. Most materials expand with temperature increase, but some materials, such as water, contract with temperature increase over some specific range, and then they are hardly useful as thermometric materials. A material is of no use as a thermometer near one of its phase-change temperatures, for example its boiling-point.

text: In spite of these restrictions, most generally used practical thermometers are of the empirically based kind. Especially, it was used for calorimetry, which contributed greatly to the discovery of thermodynamics. Nevertheless, empirical thermometry has serious drawbacks when judged as a basis for theoretical physics. Empirically based thermometers, beyond their base as simple direct measurements of ordinary physical properties of thermometric materials, can be re-calibrated, by use of theoretical physical reasoning, and this can extend their range of adequacy.

text: Theoretically-based[edit]

text: Theoretically based temperature scales are based directly on theoretical arguments, especially those of thermodynamics, kinetic theory and quantum mechanics. They rely on theoretical properties of idealized devices and materials. They are more or less comparable with practically feasible physical devices and materials. Theoretically based temperature scales are used to provide calibrating standards for practical empirically based thermometers.

text: The accepted fundamental thermodynamic temperature scale is the Kelvin scale, based on an ideal cyclic process envisaged for a Carnot heat engine.

text: An ideal material on which a temperature scale can be based is the ideal gas. The pressure exerted by a fixed volume and mass of an ideal gas is directly proportional to its temperature. Some natural gases show so nearly ideal properties over suitable temperature ranges that they can be used for thermometry; this was important during the development of thermodynamics and is still of practical importance today.[6][7] The ideal gas thermometer is, however, not theoretically perfect for thermodynamics. This is because the entropy of an ideal gas at its absolute zero of temperature is not a positive semi-definite quantity, which puts the gas in violation of the third law of thermodynamics. The physical reason is that the ideal gas law, exactly read, refers to the limit of infinitely high temperature and zero pressure.[8][9][10]

text: Measurement of the spectrum of electromagnetic radiation from an ideal three-dimensional black body can provide an accurate temperature measurement because the frequency of maximum spectral radiance of black-body radiation is directly proportional to the temperature of the black body; this is known as Wien's displacement law and has a theoretical explanation in Planck's law and the Bose–Einstein law.

text: Measurement of the spectrum of noise-power produced by an electrical resistor can also provide an accurate temperature measurement. The resistor has two terminals and is in effect a one-dimensional body. The Bose-Einstein law for this case indicates that the noise-power is directly proportional to the temperature of the resistor and to the value of its resistance and to the noise band-width. In a given frequency band, the noise-power has equal contributions from every frequency and is called Johnson noise. If the value of the resistance is known then the temperature can be found.[11][12]

text: If molecules, or atoms, or electrons,[13][14] are emitted from a material and their velocities are measured, the spectrum of their velocities often nearly obeys a theoretical law called the Maxwell–Boltzmann distribution, which gives a well-founded measurement of temperatures for which the law holds.[15] There have not yet been successful experiments of this same kind that directly use the Fermi–Dirac distribution for thermometry, but perhaps that will be achieved in future.[16]

text: Thermodynamic approach[edit]

text: Temperature is one of the principal quantities in the study of thermodynamics.

text: Kelvin scale and absolute thermodynamic definitions[edit]

text: The Kelvin scale is called absolute for two reasons. One is that its formal character is independent of the properties of particular materials. The other reason is that its zero is in a sense absolute, in that it indicates absence of microscopic classical motion of the constituent particles of matter, so that they have a limiting specific heat of zero for zero temperature, according to the third law of thermodynamics. Nevertheless, a Kelvin temperature does in fact have a definite numerical value that has been arbitrarily chosen by tradition and is dependent on the property of a particular materials; it is simply less arbitrary than relative "degrees" scales such as Celsius and Fahrenheit.  Being an absolute scale with one fixed point (zero), there is only one degree of freedom left to arbitrary choice, rather than two as in relative scales. For the Kelvin scale in modern times, this choice of convention is made to be that of setting the gas–liquid–solid triple point of water, a point which can be reliably reproduced as a standard experimental phenomenon, at a numerical value of 273.16 kelvins. The Kelvin scale is also called the thermodynamic scale. However, to demonstrate that its numerical value is indeed arbitrary, it is useful to point out that an alternate, less widely used absolute temperature scale exists called the Rankine scale, made to be aligned with the Fahrenheit scale as Kelvin is with Celsius.

text: The thermodynamic definition of temperature is due to Kelvin.

text: It is framed in terms of an idealized device called a Carnot engine, imagined to define a continuous cycle of states of its working body. The cycle is imagined to run so slowly that at each point of the cycle the working body is in a state of thermodynamic equilibrium. There are four limbs in such a Carnot cycle. The engine consists of four bodies. The main one is called the working body. Two of them are called heat reservoirs, so large that their respective non-deformation variables are not changed by transfer of energy as heat through a wall permeable only to heat to the working body. The fourth body is able to exchange energy with the working body only through adiabatic work; it may be called the work reservoir. The substances and states of the two heat reservoirs should be chosen so that they are not in thermal equilibrium with one another. This means that they must be at different fixed temperatures, one, labeled here with the number 1, hotter than the other, labeled here with the number 2. This can be tested by connecting the heat reservoirs successively to an auxiliary empirical thermometric body that starts each time at a convenient fixed intermediate temperature. The thermometric body should be composed of a material that has a strictly monotonic relation between its chosen empirical thermometric variable and the amount of adiabatic isochoric work done on it. In order to settle the structure and sense of operation of the Carnot cycle, it is convenient to use such a material also for the working body; because most materials are of this kind, this is hardly a restriction of the generality of this definition. The Carnot cycle is considered to start from an initial condition of the working body that was reached by the completion of a reversible adiabatic compression. From there, the working body is initially connected by a wall permeable only to heat to the heat reservoir number 1, so that during the first limb of the cycle it expands and does work on the work reservoir. The second limb of the cycle sees the working body expand adiabatically and reversibly, with no energy exchanged as heat, but more energy being transferred as work to the work reservoir. The third limb of the cycle sees the working body connected, through a wall permeable only to heat, to the heat reservoir 2, contracting and accepting energy as work from the work reservoir. The cycle is closed by reversible adiabatic compression of the working body, with no energy transferred as heat, but energy being transferred to it as work from the work reservoir.

text: With this set-up, the four limbs of the reversible Carnot cycle are characterized by amounts of energy transferred, as work from the working body to the work reservoir, and as heat from the heat reservoirs to the working body. The amounts of energy transferred as heat from the heat reservoirs are measured through the changes in the non-deformation variable of the working body, with reference to the previously known properties of that body, the amounts of work done on the work reservoir, and the first law of thermodynamics. The amounts of energy transferred as heat respectively from reservoir 1 and from reservoir 2 may then be denoted respectively Q1 and Q2. Then the absolute or thermodynamic temperatures, T1 and T2,  of the reservoirs are defined so that to be such that

text:
T

1

/

T

2

=
−

Q

1

/

Q

2

.

{\displaystyle T_{1}/T_{2}=-Q_{1}/Q_{2}.}

(1)

text: Kelvin's original work postulating absolute temperature was published in 1848. It was based on the work of Carnot, before the formulation of the first law of thermodynamics. Kelvin wrote in his 1848 paper that his scale was absolute in the sense that it was defined "independently of the properties of any particular kind of matter". His definitive publication, which sets out the definition just stated, was printed in 1853, a paper read in 1851.[17][18][19][20]

text: This definition rests on the physical assumption that there are readily available walls permeable only to heat. In his detailed definition of a wall permeable only to heat, Carathéodory includes several ideas. The non-deformation state variable of a closed system is represented as a real number. A state of thermal equilibrium between two closed systems connected by a wall permeable only to heat means that a certain mathematical relation holds between the state variables, including the respective non-deformation variables, of those two systems (that particular mathematical relation is regarded by Buchdahl as a preferred statement of the zeroth law of thermodynamics).[21] Also, referring to thermal contact equilibrium, "whenever each of the systems S1 and S2 is made to reach equilibrium with a third system S3 under identical conditions, the systems S1 and S2 are in mutual equilibrium."[22] It may be viewed as a re-statement of the principle stated by Maxwell in the words: "All heat is of the same kind."[23] This physical idea is also expressed by Bailyn as a possible version of the zeroth law of thermodynamics: "All diathermal walls are equivalent."[24] Thus the present definition of thermodynamic temperature rests on the zeroth law of thermodynamics. Explicitly, this present definition of thermodynamic temperature also rests on the first law of thermodynamics, for the determination of amounts of energy transferred as heat.

text: Implicitly for this definition, the second law of thermodynamics provides information that establishes the virtuous character of the temperature so defined. It provides that any working substance that complies with the requirement stated in this definition will lead to the same ratio of thermodynamic temperatures, which in this sense is universal, or absolute. The second law of thermodynamics also provides that the thermodynamic temperature defined in this way is positive, because this definition requires that the heat reservoirs not be in thermal equilibrium with one another, and the cycle can be imagined to operate only in one sense if net work is to be supplied to the work reservoir.

text: Numerical details are settled by making one of the heat reservoirs a cell at the triple point of water, which is defined to have an absolute temperature of 273.16 K.[25]  The zeroth law of thermodynamics allows this definition to be used to measure the absolute or thermodynamic temperature of an arbitrary body of interest, by making the other heat reservoir have the same temperature as the body of interest.

text: Intensive variability[edit]

text: In thermodynamic terms, temperature is an intensive variable because it is equal to a differential coefficient of one extensive variable with respect to another, for a given body. It thus has the dimensions of a ratio of two extensive variables. In thermodynamics, two bodies are often considered as connected by contact with a common wall, which has some specific permeability properties. Such specific permeability can be referred to a specific intensive variable. An example is a diathermic wall that is permeable only to heat; the intensive variable for this case is temperature. When the two bodies have been in contact for a very long time, and have settled to a permanent steady state, the relevant intensive variables are equal in the two bodies; for a diathermal wall, this statement is sometimes called the zeroth law of thermodynamics.[26][27][28]

text: In particular, when the body is described by stating its internal energy U, an extensive variable, as a function of its entropy S, also an extensive variable, and other state variables V, N, with U = U (S, V, N), then the temperature is equal to the partial derivative of the internal energy with respect to the entropy:[27][28][29]

text:
T
=

(

∂
U

∂
S

)

V
,
N

.

{\displaystyle T=\left({\frac {\partial U}{\partial S}}\right)_{V,N}.}

(2)

text: Likewise, when the body is described by stating its entropy S as a function of its internal energy U, and other state variables V, N, with S = S (U, V, N), then the reciprocal of the temperature is equal to the partial derivative of the entropy with respect to the internal energy:[27][29][30]

text:
1
T

=

(

∂
S

∂
U

)

V
,
N

.

{\displaystyle {\frac {1}{T}}=\left({\frac {\partial S}{\partial U}}\right)_{V,N}.}

(3)

text: The above definition, equation (1), of the absolute temperature is due to Kelvin. It refers to systems closed to transfer of matter, and has special emphasis on directly experimental procedures. A presentation of thermodynamics by Gibbs starts at a more abstract level and deals with systems open to the transfer of matter; in this development of thermodynamics, the equations (2) and (3) above are actually alternative definitions of temperature.[31]

text: Local thermodynamic equilibrium[edit]

text: Real world bodies are often not in thermodynamic equilibrium and not homogeneous. For study by methods of classical irreversible thermodynamics, a body is usually spatially and temporally divided conceptually into 'cells' of small size. If classical thermodynamic equilibrium conditions for matter are fulfilled to good approximation in such a 'cell', then it is homogeneous and a temperature exists for it. If this is so for every 'cell' of the body, then local thermodynamic equilibrium is said to prevail throughout the body.[32][33][34][35][36]

text: It makes good sense, for example, to say of the extensive variable U, or of the extensive variable S, that it has a density per unit volume, or a quantity per unit mass of the system, but it makes no sense to speak of density of temperature per unit volume or quantity of temperature per unit mass of the system. On the other hand, it makes no sense to speak of the internal energy at a point, while when local thermodynamic equilibrium prevails, it makes good sense to speak of the temperature at a point. Consequently, temperature can vary from point to point in a medium that is not in global thermodynamic equilibrium, but in which there is local thermodynamic equilibrium.

text: Thus, when local thermodynamic equilibrium prevails in a body, temperature can be regarded as a spatially varying local property in that body, and this is because temperature is an intensive variable.

text: Kinetic theory approach[edit]

text: A more thorough account of this is below at Theoretical foundation.

text: Kinetic theory provides a microscopic explanation of temperature, based on macroscopic systems' being composed of many microscopic particles, such as molecules and ions of various species, the particles of a species being all alike. It explains macroscopic phenomena through the classical mechanics of the microscopic particles. The equipartition theorem of kinetic theory asserts that each classical degree of freedom of a freely moving particle has an average kinetic energy of kBT/2 where kB denotes Boltzmann's constant. The translational motion of the particle has three degrees of freedom, so that, except at very low temperatures where quantum effects predominate, the average translational kinetic energy of a freely moving particle in a system with temperature T will be 3kBT/2.

text: It is possible to measure the average kinetic energy of constituent microscopic particles if they are allowed to escape from the bulk of the system. The spectrum of velocities has to be measured, and the average calculated from that. It is not necessarily the case that the particles that escape and are measured have the same velocity distribution as the particles that remain in the bulk of the system, but sometimes a good sample is possible.

text: Molecules, such as oxygen (O2), have more degrees of freedom than single spherical atoms: they undergo rotational and vibrational motions as well as translations. Heating results in an increase in temperature due to an increase in the average translational kinetic energy of the molecules. Heating will also cause, through equipartitioning, the energy associated with vibrational and rotational modes to increase. Thus a diatomic gas will require more energy input to increase its temperature by a certain amount, i.e. it will have a greater heat capacity than a monatomic gas.

text: The process of cooling involves removing internal energy from a system. When no more energy can be removed, the system is at absolute zero, though this cannot be achieved experimentally. Absolute zero is the null point of the thermodynamic temperature scale, also called absolute temperature. If it were possible to cool a system to absolute zero, all classical motion of its particles would cease and they would be at complete rest in this classical sense. Microscopically in the description of quantum mechanics, however, matter still has zero-point energy even at absolute zero, because of the uncertainty principle.

text: Basic theory[edit]

text:
Conjugate variablesof thermodynamics

Pressure
Volume

(Stress)
(Strain)

Temperature
Entropy

Chemical potential
Particle number

text: Temperature is a measure of a quality of a state of a material.[37]  The quality may be regarded as a more abstract entity than any particular temperature scale that measures it, and is called hotness by some writers.[38] The quality of hotness refers to the state of material only in a particular locality, and in general, apart from bodies held in a steady state of thermodynamic equilibrium, hotness varies from place to place. It is not necessarily the case that a material in a particular place is in a state that is steady and nearly homogeneous enough to allow it to have a well-defined hotness or temperature. Hotness may be represented abstractly as a one-dimensional manifold. Every valid temperature scale has its own one-to-one map into the hotness manifold.[39][40]

text: When two systems in thermal contact are at the same temperature no heat transfers between them. When a temperature difference does exist heat flows spontaneously from the warmer system to the colder system until they are in thermal equilibrium. Heat transfer occurs by conduction or by thermal radiation.[41][42][43][44][45][46][47][48]

text: Experimental physicists, for example Galileo and Newton,[49] found that there are indefinitely many empirical temperature scales. Nevertheless, the zeroth law of thermodynamics says that they all measure the same quality.

text: Bodies in thermodynamic equilibrium[edit]

text: For experimental physics, hotness means that, when comparing any two given bodies in their respective separate thermodynamic equilibria, any two suitably given empirical thermometers with numerical scale readings will agree as to which is the hotter of the two given bodies, or that they have the same temperature.[50] This does not require the two thermometers to have a linear relation between their numerical scale readings, but it does require that the relation between their numerical readings shall be strictly monotonic.[51][52] A definite sense of greater hotness can be had, independently of calorimetry, of thermodynamics, and of properties of particular materials, from Wien's displacement law of thermal radiation: the temperature of a bath of thermal radiation is proportional, by a universal constant, to the frequency of the maximum of its frequency spectrum; this frequency is always positive, but can have values that tend to zero. Thermal radiation is initially defined for a cavity in thermodynamic equilibrium. These physical facts justify a mathematical statement that hotness exists on an ordered one-dimensional manifold. This is a fundamental character of temperature and thermometers for bodies in their own thermodynamic equilibrium.[4][39][40][53][54]

text: Except for a system undergoing a first-order phase change such as the melting of ice, as a closed system receives heat, without change in its volume and without change in external force fields acting on it, its temperature rises. For a system undergoing such a phase change so slowly that departure from thermodynamic equilibrium can be neglected, its temperature remains constant as the system is supplied with latent heat. Conversely, a loss of heat from a closed system, without phase change, without change of volume, and without change in external force fields acting on it, decreases its temperature.[55]

text: Bodies in a steady state but not in thermodynamic equilibrium[edit]

text: While for bodies in their own thermodynamic equilibrium states, the notion of temperature requires that all empirical thermometers must agree as to which of two bodies is the hotter or that they are at the same temperature, this requirement is not safe for bodies that are in steady states though not in thermodynamic equilibrium. It can then well be that different empirical thermometers disagree about which is the hotter, and if this is so, then at least one of the bodies does not have a well defined absolute thermodynamic temperature. Nevertheless, any one given body and any one suitable empirical thermometer can still support notions of empirical, non-absolute, hotness and temperature, for a suitable range of processes. This is a matter for study in non-equilibrium thermodynamics.

text: Bodies not in a steady state[edit]

text: When a body is not in a steady state, then the notion of temperature becomes even less safe than for a body in a steady state not in thermodynamic equilibrium. This is also a matter for study in non-equilibrium thermodynamics.

text: Thermodynamic equilibrium axiomatics[edit]

text: For axiomatic treatment of thermodynamic equilibrium, since the 1930s, it has become customary to refer to a zeroth law of thermodynamics. The customarily stated minimalist version of such a law postulates only that all bodies, which when thermally connected would be in thermal equilibrium, should be said to have the same temperature by definition, but by itself does not establish temperature as a quantity expressed as a real number on a scale. A more physically informative version of such a law views empirical temperature as a chart on a hotness manifold.[39][54][56] While the zeroth law permits the definitions of many different empirical scales of temperature, the second law of thermodynamics selects the definition of a single preferred, absolute temperature, unique up to an arbitrary scale factor, whence called the thermodynamic temperature.[4][39][57][58][59][60] If internal energy is considered as a function of the volume and entropy of a homogeneous system in thermodynamic equilibrium, thermodynamic absolute temperature appears as the partial derivative of internal energy with respect the entropy at constant volume. Its natural, intrinsic origin or null point is absolute zero at which the entropy of any system is at a minimum. Although this is the lowest absolute temperature described by the model, the third law of thermodynamics postulates that absolute zero cannot be attained by any physical system.

text: Heat capacity[edit]

text: When an energy transfer to or from a body is only as heat, the state of the body changes. Depending on the surroundings and the walls separating them from the body, various changes are possible in the body. They include chemical reactions, increase of pressure, increase of temperature, and phase change. For each kind of change under specified conditions, the heat capacity is the ratio of the quantity of heat transferred to the magnitude of the change. For example, if the change is an increase in temperature at constant volume, with no phase change and no chemical change, then the temperature of the body rises and its pressure increases. The quantity of heat transferred, ΔQ, divided by the observed temperature change, ΔT, is the body's heat capacity at constant volume:

text: If heat capacity is measured for a well defined amount of substance, the specific heat is the measure of the heat required to increase the temperature of such a unit quantity by one unit of temperature. For example, to raise the temperature of water by one kelvin (equal to one degree Celsius) requires 4186 joules per kilogram (J/kg).

text: Measurement[edit]

text: Temperature measurement using modern scientific thermometers and temperature scales goes back at least as far as the early 18th century, when Gabriel Fahrenheit adapted a thermometer (switching to mercury) and a scale both developed by Ole Christensen Rømer. Fahrenheit's scale is still in use in the United States for non-scientific applications.

text: Temperature is measured with thermometers that may be calibrated to a variety of temperature scales. In most of the world (except for Belize, Myanmar, Liberia and the United States), the Celsius scale is used for most temperature measuring purposes. Most scientists measure temperature using the Celsius scale and thermodynamic temperature using the Kelvin scale, which is the Celsius scale offset so that its null point is 5000000000000000000♠0 K = 5000000000000000000♠−273.15 °C, or absolute zero. Many engineering fields in the U.S., notably high-tech and US federal specifications (civil and military), also use the Kelvin and Celsius scales. Other engineering fields in the U.S. also rely upon the Rankine scale (a shifted Fahrenheit scale) when working in thermodynamic-related disciplines such as combustion.

text: Units[edit]

text: The basic unit of temperature in the International System of Units (SI) is the kelvin. It has the symbol K.

text: For everyday applications, it is often convenient to use the Celsius scale, in which 7002273149999999999♠0 °C corresponds very closely to the freezing point of water and 7002373150000000000♠100 °C is its boiling point at sea level. Because liquid droplets commonly exist in clouds at sub-zero temperatures, 7002273149999999999♠0 °C is better defined as the melting point of ice. In this scale a temperature difference of 1 degree Celsius is the same as a 1kelvin increment, but the scale is offset by the temperature at which ice melts (7002273149999999999♠273.15 K).

text: By international agreement[61] the Kelvin and Celsius scales are defined by two fixing points: absolute zero and the triple point of Vienna Standard Mean Ocean Water, which is water specially prepared with a specified blend of hydrogen and oxygen isotopes. Absolute zero is defined as precisely 5000000000000000000♠0 K and 5000000000000000000♠−273.15 °C. It is the temperature at which all classical translational motion of the particles comprising matter ceases and they are at complete rest in the classical model. Quantum-mechanically, however, zero-point motion remains and has an associated energy, the zero-point energy.  Matter is in its ground state,[62] and contains no thermal energy. The triple point of water is defined as 7002273160000000000♠273.16 K and 7002273159999999999♠0.01 °C. This definition serves the following purposes: it fixes the magnitude of the kelvin as being precisely 1 part in 273.16 parts of the difference between absolute zero and the triple point of water; it establishes that one kelvin has precisely the same magnitude as one degree on the Celsius scale; and it establishes the difference between the null points of these scales as being 7002273149999999999♠273.15 K (5000000000000000000♠0 K = 5000000000000000000♠−273.15 °C and 7002273160000000000♠273.16 K = 7002273159999999999♠0.01 °C).

text: In the United States, the Fahrenheit scale is widely used. On this scale the freezing point of water corresponds to 7002273149999999999♠32 °F and the boiling point to 7002373150000000000♠212 °F. The Rankine scale, still used in fields of chemical engineering in the U.S., is an absolute scale based on the Fahrenheit increment.

text: Conversion[edit]

text: The following table shows the temperature conversion formulas for conversions to and from the Celsius scale.

text:
Temperature conversions

from Celsius

to Celsius

Fahrenheit

[°F] = [°C] × 9⁄5 + 32

[°C] = ([°F] − 32) × 5⁄9

Kelvin

[K] = [°C] + 273.15

[°C] = [K] − 273.15

Rankine

[°R] = ([°C] + 273.15) × 9⁄5

[°C] = ([°R] − 491.67) × 5⁄9

Delisle

[°De] = (100 − [°C]) × 3⁄2

[°C] = 100 − [°De] × 2⁄3

Newton

[°N] = [°C] × 33⁄100

[°C] = [°N] × 100⁄33

Réaumur

[°Ré] = [°C] × 4⁄5

[°C] = [°Ré] × 5⁄4

Rømer

[°Rø] = [°C] × 21⁄40 + 7.5

[°C] = ([°Rø] − 7.5) × 40⁄21

text: Plasma physics[edit]

text:
The field of plasma physics deals with phenomena of electromagnetic nature that involve very high temperatures. It is customary to express temperature as energy in units of electronvolts (eV) or kiloelectronvolts (keV). The energy, which has a different dimension from temperature, is then calculated as the product of the Boltzmann constant and temperature,

E
=

k

B

T

{\displaystyle E=k_{B}T}

. Then, 1 eV corresponds to 7004116050000000000♠11605 K. In the study of QCD matter one routinely encounters temperatures of the order of a few hundred MeV, equivalent to about 7012100000000000000♠1012 K.

text: Theoretical foundation[edit]

text: Historically, there are several scientific approaches to the explanation of temperature: the classical thermodynamic description based on macroscopic empirical variables that can be measured in a laboratory; the kinetic theory of gases which relates the macroscopic description to the probability distribution of the energy of motion of gas particles; and a microscopic explanation based on statistical physics and quantum mechanics. In addition, rigorous and purely mathematical treatments have provided an axiomatic approach to classical thermodynamics and temperature.[63] Statistical physics provides a deeper understanding by describing the atomic behavior of matter, and derives macroscopic properties from statistical averages of microscopic states, including both classical and quantum states. In the fundamental physical description, using natural units, temperature may be measured directly in units of energy. However, in the practical systems of measurement for science, technology, and commerce, such as the modern metric system of units, the macroscopic and the microscopic descriptions are interrelated by the Boltzmann constant, a proportionality factor that scales temperature to the microscopic mean kinetic energy.

text: The microscopic description in statistical mechanics is based on a model that analyzes a system into its fundamental particles of matter or into a set of classical or quantum-mechanical oscillators and considers the system as a statistical ensemble of microstates. As a collection of classical material particles, temperature is a measure of the mean energy of motion, called kinetic energy, of the particles, whether in solids, liquids, gases, or plasmas. The kinetic energy, a concept of classical mechanics, is half the mass of a particle times its speed squared. In this mechanical interpretation of thermal motion, the kinetic energies of material particles may reside in the velocity of the particles of their translational or vibrational motion or in the inertia of their rotational modes. In monatomic perfect gases and, approximately, in most gases, temperature is a measure of the mean particle kinetic energy. It also determines the probability distribution function of the energy. In condensed matter, and particularly in solids, this purely mechanical description is often less useful and the oscillator model provides a better description to account for quantum mechanical phenomena. Temperature determines the statistical occupation of the microstates of the ensemble. The microscopic definition of temperature is only meaningful in the thermodynamic limit, meaning for large ensembles of states or particles, to fulfill the requirements of the statistical model.

text: In the context of thermodynamics, the kinetic energy is also referred to as thermal energy. The thermal energy may be partitioned into independent components attributed to the degrees of freedom of the particles or to the modes of oscillators in a thermodynamic system. In general, the number of these degrees of freedom that are available for the equipartitioning of energy depend on the temperature, i.e. the energy region of the interactions under consideration. For solids, the thermal energy is associated primarily with the vibrations of its atoms or molecules about their equilibrium position. In an ideal monatomic gas, the kinetic energy is found exclusively in the purely translational motions of the particles. In other systems, vibrational and rotational motions also contribute degrees of freedom.

text: Kinetic theory of gases[edit]

text:
Maxwell and Boltzmann developed a kinetic theory that yields a fundamental understanding of temperature in gases.[64]
This theory also explains the ideal gas law and the observed heat capacity of monatomic  (or 'noble') gases.[65][66][67]

text: The ideal gas law is based on observed empirical relationships between pressure (p), volume (V), and temperature (T), and was recognized long before the kinetic theory of gases was developed (see Boyle's and Charles's laws).  The ideal gas law states:[68]

text: where n is the number of moles of gas and R = 7000831445980000000♠8.3144598(48) J⋅mol−1⋅K−1[69]  is the gas constant.

text: This relationship gives us our first hint that there is an absolute zero on the temperature scale, because it only holds if the temperature is measured on an absolute scale such as Kelvin's. The ideal gas law allows one to measure temperature on this absolute scale using the gas thermometer.  The temperature in kelvins can be defined as the pressure in pascals of one mole of gas in a container of one cubic meter, divided by the gas constant.

text: Although it is not a particularly convenient device, the gas thermometer provides an essential theoretical basis by which all thermometers can be calibrated.  As a practical matter it is not possible to use a gas thermometer to measure absolute zero temperature since the gases tend to condense into a liquid long before the temperature reaches zero. It is possible, however, to extrapolate to absolute zero by using the ideal gas law, as shown in the figure.

text: The kinetic theory assumes that pressure is caused by the force associated with individual atoms striking the walls, and that all energy is translational kinetic energy.  Using a sophisticated symmetry argument,[70] Boltzmann deduced what is now called the Maxwell–Boltzmann probability distribution function for the velocity of particles in an ideal gas.  From that probability distribution function, the average kinetic energy (per particle) of a monatomic ideal gas is[66][71]

text:
where the Boltzmann constant k is the ideal gas constant divided by the Avogadro number, and

v

rms

=

⟨

v

2

⟩

{\displaystyle v_{\text{rms}}={\sqrt {\langle v^{2}\rangle }}}

 is the root-mean-square speed. Thus the ideal gas law states that internal energy is directly proportional to temperature.[72] This direct proportionality between temperature and internal energy is a special case of the equipartition theorem, and holds only in the classical limit of an ideal gas. It does not hold for most substances, although it is true that temperature is a monotonic (non-decreasing) function of internal energy.

text: Zeroth law of thermodynamics[edit]

text: When two otherwise isolated bodies are connected together by a rigid physical path impermeable to matter, there is spontaneous transfer of energy as heat from the hotter to the colder of them. Eventually they reach a state of mutual thermal equilibrium, in which heat transfer has ceased, and the bodies' respective state variables have settled to become unchanging.

text: One statement of the zeroth law of thermodynamics is that if two systems are each in thermal equilibrium with a third system, then they are also in thermal equilibrium with each other.

text: This statement helps to define temperature but it does not, by itself, complete the definition. An empirical temperature is a numerical scale for the hotness of a thermodynamic system. Such hotness may be defined as existing on a one-dimensional manifold, stretching between hot and cold. Sometimes the zeroth law is stated to include the existence of a unique universal hotness manifold, and of numerical scales on it, so as to provide a complete definition of empirical temperature.[56] To be suitable for empirical thermometry, a material must have a monotonic relation between hotness and some easily measured state variable, such as pressure or volume, when all other relevant coordinates are fixed. An exceptionally suitable system is the ideal gas, which can provide a temperature scale that matches the absolute Kelvin scale. The Kelvin scale is defined on the basis of the second law of thermodynamics.

text: Second law of thermodynamics[edit]

text: In the previous section certain properties of temperature were expressed by the zeroth law of thermodynamics. It is also possible to define temperature in terms of the second law of thermodynamics which deals with entropy. The second law states that any process will result in either no change or a net increase in the entropy of the universe. This can be understood in terms of probability.

text: For example, in a series of coin tosses, a perfectly ordered system would be one in which either every toss comes up heads or every toss comes up tails. This means that for a perfectly ordered set of coin tosses, there is only one set of toss outcomes possible: the set in which 100% of tosses come up the same. On the other hand, there are multiple combinations that can result in disordered or mixed systems, where some fraction are heads and the rest tails. A disordered system can be 90% heads and 10% tails, or it could be 98% heads and 2% tails, et cetera. As the number of coin tosses increases, the number of possible combinations corresponding to imperfectly ordered systems increases. For a very large number of coin tosses, the combinations to ~50% heads and ~50% tails dominates and obtaining an outcome significantly different from 50/50 becomes extremely unlikely. Thus the system naturally progresses to a state of maximum disorder or entropy.

text: It has been previously stated that temperature governs the transfer of heat between two systems and it was just shown that the universe tends to progress so as to maximize entropy, which is expected of any natural system. Thus, it is expected that there is some relationship between temperature and entropy. To find this relationship, the relationship between heat, work and temperature is first considered. A heat engine is a device for converting thermal energy into mechanical energy, resulting in the performance of work, and analysis of the Carnot heat engine provides the necessary relationships. The work from a heat engine corresponds to the difference between the heat put into the system at the high temperature, qH and the heat ejected at the low temperature, qC. The efficiency is the work divided by the heat put into the system:

text:
efficiency

=

w

c
y

q

H

=

q

H

−

q

C

q

H

=
1
−

q

C

q

H

,

{\displaystyle {\text{efficiency}}={\frac {w_{cy}}{q_{H}}}={\frac {q_{H}-q_{C}}{q_{H}}}=1-{\frac {q_{C}}{q_{H}}},}

(4)

text: where wcy is the work done per cycle. The efficiency depends only on qC/qH. Because qC and qH correspond to heat transfer at the temperatures TC and TH respectively, qC/qH should be some function of these temperatures:

text:
q

C

q

H

=
f
(

T

H

,

T

C

)
.

{\displaystyle {\frac {q_{C}}{q_{H}}}=f(T_{H},T_{C}).}

(5)

text: Carnot's theorem states that all reversible engines operating between the same heat reservoirs are equally efficient. Thus, a heat engine operating between T1 and T3 must have the same efficiency as one consisting of two cycles, one between T1 and T2, and the second between T2 and T3. This can only be the case if

text: which implies

text: Since the first function is independent of T2, this temperature must cancel on the right side, meaning f(T1,T3) is of the form g(T1)/g(T3) (i.e. f(T1,T3) = f(T1,T2)f(T2,T3) = g(T1)/g(T2)· g(T2)/g(T3) = g(T1)/g(T3)), where g is a function of a single temperature. A temperature scale can now be chosen with the property that

text:
q

C

q

H

=

T

C

T

H

.

{\displaystyle {\frac {q_{C}}{q_{H}}}={\frac {T_{C}}{T_{H}}}.}

(6)

text: Substituting (4) back into (2) gives a relationship for the efficiency in terms of temperature:

text:
efficiency

=
1
−

q

C

q

H

=
1
−

T

C

T

H

.

{\displaystyle {\text{efficiency}}=1-{\frac {q_{C}}{q_{H}}}=1-{\frac {T_{C}}{T_{H}}}.}

(7)

text: For TC = 0 K the efficiency is 100% and that efficiency becomes greater than 100% below 0 K. Since an efficiency greater than 100% violates the first law of thermodynamics, this implies that 0 K is the minimum possible temperature. In fact the lowest temperature ever obtained in a macroscopic system was 20 nK, which was achieved in 1995 at NIST. Subtracting the right hand side of Equation 5 from the middle portion and rearranging gives

text: where the negative sign indicates heat ejected from the system. This relationship suggests the existence of a state function, S, defined by

text:
d
S
=

d

q

rev

T

,

{\displaystyle dS={\frac {dq_{\text{rev}}}{T}},}

(8)

text: where the subscript indicates a reversible process. The change of this state function around any cycle is zero, as is necessary for any state function.  This function corresponds to the entropy of the system, which was described previously. Rearranging Equation 6 gives a new definition for temperature in terms of entropy and heat:

text:
T
=

d

q

rev

d
S

.

{\displaystyle T={\frac {dq_{\text{rev}}}{dS}}.}

(9)

text: For a system, where entropy S(E) is a function of its energy E, the temperature T is given by

text:
T

−
1

=

d

d
E

S
(
E
)
,

{\displaystyle T^{-1}={\frac {d}{dE}}S(E),}

(10)

text: i.e. the reciprocal of the temperature is the rate of increase of entropy with respect to energy.

text: Definition from statistical mechanics[edit]

text: Statistical mechanics defines temperature based on a system's fundamental degrees of freedom.  Eq.(10) is the defining relation of temperature. Eq. (9) can be derived from the principles underlying the fundamental thermodynamic relation.

text: Generalized temperature from single-particle statistics[edit]

text:
It is possible to extend the definition of temperature even to systems of few particles, like in a quantum dot. The generalized temperature is obtained by considering time ensembles instead of configuration-space ensembles given in statistical mechanics in the case of thermal and particle exchange between a small system of fermions (N even less than 10) with a single/double-occupancy system. The finite quantum grand canonical ensemble,[73] obtained under the hypothesis of ergodicity and orthodicity,[74] allows expressing the generalized temperature from the ratio of the average time of occupation

τ

1

{\displaystyle \tau _{1}}

 and

τ

2

{\displaystyle \tau _{2}}

 of the single/double-occupancy system:[75]

text: where EF is the Fermi energy. This generalized temperature tends to the ordinary temperature when N goes to infinity.

text: Negative temperature[edit]

text: On the empirical temperature scales, which are not referenced to absolute zero, a negative temperature is one below the zero-point of the scale used. For example, dry ice has a sublimation temperature of 7002194649999999999♠−78.5 °C which is equivalent to 7002194649999999999♠−109.3 °F. On the absolute Kelvin scale, however, this temperature is 7002194600000000000♠194.6 K. On the absolute scale of thermodynamic temperature no material can have a temperature smaller than or equal to 0 K, both of which are forbidden by the third law of thermodynamics.

text: Temperature is basically defined for a body in its own state of internal thermodynamic equilibrium, and in this definition, on an absolute scale, it is always positive. In an apparent contradiction of this reliable and valid rule, a so-called negative absolute "temperature" may be approximately defined for a component of a body that is not in its own state of internal thermodynamic equilibrium: a component may have a negative approximate "temperature" while the rest of the components of the body have positive approximate temperatures. Such a non-equilibrium situation is either transient in time or is maintained by external factors that drive a flow of energy through the body of interest. An example of such a component is a spin system within a body, as follows.

text: In the quantum mechanical description of electron and nuclear spin systems that have a limited number of possible states, and therefore a discrete upper limit of energy they can attain, it is possible to obtain a negative temperature, which is numerically indeed less than absolute zero. However, this is not the macroscopic temperature of the material, but instead the temperature of only very specific degrees of freedom, that are isolated from others and do not exchange energy by virtue of the equipartition theorem.

text: A negative temperature is experimentally achieved with suitable radio frequency techniques that cause a population inversion of spin states from the ground state. As the energy in the system increases upon population of the upper states, the entropy increases as well, as the system becomes less ordered, but attains a maximum value when the spins are evenly distributed among ground and excited states, after which it begins to decrease, once again achieving a state of higher order as the upper states begin to fill exclusively. At the point of maximum entropy, the temperature function shows the behavior of a singularity, because the slope of the entropy function decreases to zero at first and then turns negative. Since temperature is the inverse of the derivative of the entropy, the temperature formally goes to infinity at this point, and switches to negative infinity as the slope turns negative. At energies higher than this point, the spin degree of freedom therefore exhibits formally a negative thermodynamic temperature. As the energy increases further by continued population of the excited state, the negative temperature approaches zero asymptotically.[76]  As the energy of the system increases in the population inversion, a system with a negative temperature is not colder than absolute zero, but rather it has a higher energy than at positive temperature, and may be said to be in fact hotter at negative temperatures. When brought into contact with a system at a positive temperature, energy will be transferred from the negative temperature regime to the positive temperature region.

text: Examples[edit]

text:
Temperature

Peak emittance wavelength[77] of black-body radiation

Kelvin

Celsius

Absolute zero(precisely by definition)

5000000000000000000♠0 K

5000000000000000000♠−273.15 °C

cannot be defined

Coldest temperatureachieved[78]

100 pK

6989999875737761613♠−273.149999999900 °C

7007290000000000000♠29000 km

Coldest Bose–Einstein condensate[79]

450 pK

6990449972503702156♠−273.14999999955 °C

7006640000000000000♠6400 km

One millikelvin(precisely by definition)

6997100000000000000♠0.001 K

6996999999999976353♠−273.149 °C

7000289777000000000♠2.89777 m(radio, FM band)[80]

Cosmic microwave background(2013 measurement)

7000272600000000000♠2.7260 K

7000272599999999999♠−270.424 °C

6997106301000000000♠0.00106301 m(millimeter-wavelength microwave)

Water triple point(precisely by definition)

7002273160000000000♠273.16 K

7002273159999999999♠0.01 °C

6995106083000000000♠10608.3 nm(long-wavelength IR)

Water boiling point[A]

7002373133900000000♠373.1339 K

7002373133900000000♠99.9839 °C

6994776603000000000♠7766.03 nm(mid-wavelength IR)

Iron melting point

7003181100000000000♠1811 K

7003181115000000000♠1538 °C

6994160000000000000♠1600 nm(far infrared)

Incandescent lamp[B]

7003250000000000000♠2500 K

≈7003247315000000000♠2200 °C

6994116000000000000♠1160 nm(near infrared)[C]

Sun's visible surface[D][81]

7003577800000000000♠5778 K

7003577815000000000♠5505 °C

6993501500000000000♠501.5 nm(green-blue light)

Lightning boltchannel[E]

28 kK

7004282731500000000♠28000 °C

6993100000000000000♠100 nm(far ultraviolet light)

Sun's core[E]

16 MK

16 million °C

6990180000000000000♠0.18 nm (X-rays)

Thermonuclear weapon(peak temperature)[E][82]

350 MK

350 million °C

8.3×10−3 nm(gamma rays)

Sandia National Labs'Z machine[E][83]

2 GK

2 billion °C

1.4×10−3 nm(gamma rays)[F]

Core of a high-massstar on its last day[E][84]

3 GK

3 billion °C

1×10−3 nm(gamma rays)

Merging binary neutronstar system[E][85]

350 GK

350 billion °C

6985800000000000000♠8×10−6 nm(gamma rays)

Relativistic HeavyIon Collider[E][86]

1 TK

1 trillion °C

6985300000000000000♠3×10−6 nm(gamma rays)

CERN's proton vs nucleus collisions[E][87]

10 TK

10 trillion °C

6984300000000000000♠3×10−7 nm(gamma rays)

Universe 6956539099999999999♠5.391×10−44 safter the Big Bang[E]

7032141700000000000♠1.417×1032 K(Planck temperature)

7032141700000000000♠1.417×1032 °C

6964161600000000000♠1.616×10−27 nm(Planck length)[88]

text:
A  For Vienna Standard Mean Ocean Water at one standard atmosphere (101.325 kPa) when calibrated strictly per the two-point definition of thermodynamic temperature.
B  The 7003250000000000000♠2500 K value is approximate. The 7002273149999999999♠273.15 K difference between K and °C is rounded to 7002300000000000000♠300 K to avoid false precision in the Celsius value.
C  For a true black-body (which tungsten filaments are not). Tungsten filament emissivity is greater at shorter wavelengths, which makes them appear whiter.
D  Effective photosphere temperature. The 7002273149999999999♠273.15 K difference between K and °C is rounded to 7002273000000000000♠273 K to avoid false precision in the Celsius value.
E  The 7002273149999999999♠273.15 K difference between K and °C is within the precision of these values.
F  For a true black-body (which the plasma was not). The Z machine's dominant emission originated from 40 MK electrons (soft x-ray emissions) within the plasma.