The thermodynamic square (also known as the thermodynamic wheel, Guggenheim scheme or Born square) is a mnemonic diagram attributed to Max Born and used to help determine thermodynamic relations. Born presented the thermodynamic square in a 1929 lecture. The symmetry of thermodynamics appears in a paper by F.O. Koenig. The corners represent common conjugate variables while the sides represent thermodynamic potentials. The placement and relation among the variables serves as a key to recall the relations they constitute.
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| - Guggenheim-Quadrat (de)
- Carré thermodynamique de Born (fr)
- Quadrato termodinamico (it)
- Kwadrat termodynamiczny (pl)
- Thermodynamic square (en)
- 熱力學方格 (zh)
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| - Das Guggenheim-Quadrat oder Guggenheim-Schema (nach Edward Guggenheim) ist ein Hilfsmittel, um einige einfache, aber grundlegende Beziehungen der Thermodynamik, wie die charakteristischen Funktionen oder die Maxwell-Beziehungen, aus dem Gedächtnis heraus aufzustellen. Verknüpft werden die thermodynamischen Potentiale
* innere Energie
* Enthalpie
* freie Energie
* Gibbs-Energie an den Kantenmitten mit den Zustandsgrößen
* Entropie
* Volumen
* Druck
* Temperatur an den Ecken des Quadrats. (de)
- 熱力學方格（英語：thermodynamic square），又稱為熱力輪（thermodynamic wheel）、古根海姆圖（Guggenheim scheme）或玻恩方格（Born square），是由馬克斯·玻恩提出的一種記憶術，用於快速建構熱力學關係式。1929年，玻恩在課堂中提出熱力學方格。F·O·柯尼希（Koenig）的論文中曾提及熱力學的對稱性。方格角落為共軛變數，而四邊則是熱動力位能。變數之間的放置和關係是記憶它們構成關係的關鍵。 (zh)
- The thermodynamic square (also known as the thermodynamic wheel, Guggenheim scheme or Born square) is a mnemonic diagram attributed to Max Born and used to help determine thermodynamic relations. Born presented the thermodynamic square in a 1929 lecture. The symmetry of thermodynamics appears in a paper by F.O. Koenig. The corners represent common conjugate variables while the sides represent thermodynamic potentials. The placement and relation among the variables serves as a key to recall the relations they constitute. (en)
- Il quadrato termodinamico (o quadrato di Born) è un diagramma mnemonico utilizzato per facilitare la determinazione di relazioni termodinamiche. Gli angoli rappresentano variabili coniugate comuni mentre i lati rappresentano i . Il posizionamento e il rapporto tra le variabili fornisce una chiave per richiamare alla mente le relazioni che costituiscono. Per ovviare a questo problema esiste anche la frase "Good Physicists Have Studied Under Very Ambitious Teachers". In italiano può essere ricordato come: "Una Volta Facevo Tanti Giochi, Poi Ho Smesso" (it)
- En thermodynamique, le carré thermodynamique de Born est un moyen mnémotechnique permettant de retrouver les relations de Maxwell. Les côtés du carré comportent les potentiels thermodynamiques et les coins opposent les variables conjuguées. Les variables situées sur le côté gauche du carré sont affectées d'un signe négatif. Les Anglais utilisent des phrases pour retenir l'ordre des lettres, telle « Good Physicists Have Studied Under Very Fine Teachers » (en français : « Les bons physiciens ont eu de très bons professeurs »). De manière similaire, la phrase « Seule Une Vraie Fonction Thermodynamique Génère Parfaite Harmonie » est parfois utilisée dans la littérature scientifique francophone. (fr)
- Kwadrat termodynamiczny (także Kwadrat Guggenheima) jest mnemotechnicznym sposobem ułatwiającym zapamiętanie wzorów łączących ze sobą różne funkcje termodynamiczne. Jego stworzenie przypisywane jest Maxowi Bornowi. W zapamiętaniu kolejności (początek w prawym górnym rogu; kierunek poruszania się przeciwny do ruchu wskazówek zegara) pomaga zdanie: Vicekonsul Urugwaju Stary Hrabia Pafnucy Gryzł Twarde Fistaszki (pl)
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| - Das Guggenheim-Quadrat oder Guggenheim-Schema (nach Edward Guggenheim) ist ein Hilfsmittel, um einige einfache, aber grundlegende Beziehungen der Thermodynamik, wie die charakteristischen Funktionen oder die Maxwell-Beziehungen, aus dem Gedächtnis heraus aufzustellen. Verknüpft werden die thermodynamischen Potentiale
* innere Energie
* Enthalpie
* freie Energie
* Gibbs-Energie an den Kantenmitten mit den Zustandsgrößen
* Entropie
* Volumen
* Druck
* Temperatur an den Ecken des Quadrats. (de)
- En thermodynamique, le carré thermodynamique de Born est un moyen mnémotechnique permettant de retrouver les relations de Maxwell. Les côtés du carré comportent les potentiels thermodynamiques et les coins opposent les variables conjuguées. Les variables situées sur le côté gauche du carré sont affectées d'un signe négatif. Les Anglais utilisent des phrases pour retenir l'ordre des lettres, telle « Good Physicists Have Studied Under Very Fine Teachers » (en français : « Les bons physiciens ont eu de très bons professeurs »). De manière similaire, la phrase « Seule Une Vraie Fonction Thermodynamique Génère Parfaite Harmonie » est parfois utilisée dans la littérature scientifique francophone. Cette méthode a été développée par Max Born sous une forme un peu différente. Il existe des variantes qui généralisent ce procédé. (fr)
- Il quadrato termodinamico (o quadrato di Born) è un diagramma mnemonico utilizzato per facilitare la determinazione di relazioni termodinamiche. Gli angoli rappresentano variabili coniugate comuni mentre i lati rappresentano i . Il posizionamento e il rapporto tra le variabili fornisce una chiave per richiamare alla mente le relazioni che costituiscono. Un espediente mnemonico utilizzato dagli studenti anglofoni per ricordare le relazioni di Maxwell della termodinamica è "Good Physicists Have Studied Under Very Fine Teachers" che permette loro di ricordare l'ordine delle variabili all'interno del quadrato in senso orario; un'altra frase è "Valid Facts and Theoretical Understanding Generate Solutions to Hard Problems" le cui iniziali rappresentano sia le variabili che i potenziali, ordinati secondo il verso di scrittura da sinistra a destra. In entrambi i casi l'energia libera di Helmholtz è identificata dalla lettera F anziché dalla lettera A, come vorrebbero le convenzioni IUPAC. Per ovviare a questo problema esiste anche la frase "Good Physicists Have Studied Under Very Ambitious Teachers". In italiano può essere ricordato come: "Una Volta Facevo Tanti Giochi, Poi Ho Smesso" Il quadrato termodinamico è anche chiamato "quadrato di Born" in quanto la sua creazione è stata attribuita al fisico Max Born. (it)
- The thermodynamic square (also known as the thermodynamic wheel, Guggenheim scheme or Born square) is a mnemonic diagram attributed to Max Born and used to help determine thermodynamic relations. Born presented the thermodynamic square in a 1929 lecture. The symmetry of thermodynamics appears in a paper by F.O. Koenig. The corners represent common conjugate variables while the sides represent thermodynamic potentials. The placement and relation among the variables serves as a key to recall the relations they constitute. A mnemonic used by students to remember the Maxwell relations (in thermodynamics) is "Good Physicists Have Studied Under Very Fine Teachers", which helps them remember the order of the variables in the square, in clockwise direction. Another mnemonic used here is "Valid Facts and Theoretical Understanding Generate Solutions to Hard Problems", which gives the letter in the normal left-to-right writing direction. Both times A has to be identified with F, another common symbol for Helmholtz free energy. To prevent the need for this switch the following mnemonic is also widely used:"Good Physicists Have Studied Under Very Ambitious Teachers"; another one is Good Physicists Have SUVAT, in reference to the equations of motion. One other useful variation of the mnemonic when the symbol E is used for internal energy instead of U is the following: "Some Hard Problems Go To Finish Very Easy". (en)
- Kwadrat termodynamiczny (także Kwadrat Guggenheima) jest mnemotechnicznym sposobem ułatwiającym zapamiętanie wzorów łączących ze sobą różne funkcje termodynamiczne. Jego stworzenie przypisywane jest Maxowi Bornowi. W zapamiętaniu kolejności (początek w prawym górnym rogu; kierunek poruszania się przeciwny do ruchu wskazówek zegara) pomaga zdanie: Vicekonsul Urugwaju Stary Hrabia Pafnucy Gryzł Twarde Fistaszki Relację znajdujemy poprzez ułożenie stosunku zmiennych znajdujących się w narożach kwadratu, będących w tej samej płaszczyźnie (pionowo lub poziomo), do stosunku zmiennych w narożach równoległych. Na przykład, poprzez stosunek zmiennych lewego boku kwadratu (pionowo) S/p oraz równoległy do niego prawy bok, gdzie odpowiadają tym zmiennym zmienne V/T otrzymujemy czwartą relację Maxwella (pamiętamy o znaku "-" po lewej stronie). (pl)
- 熱力學方格（英語：thermodynamic square），又稱為熱力輪（thermodynamic wheel）、古根海姆圖（Guggenheim scheme）或玻恩方格（Born square），是由馬克斯·玻恩提出的一種記憶術，用於快速建構熱力學關係式。1929年，玻恩在課堂中提出熱力學方格。F·O·柯尼希（Koenig）的論文中曾提及熱力學的對稱性。方格角落為共軛變數，而四邊則是熱動力位能。變數之間的放置和關係是記憶它們構成關係的關鍵。 (zh)
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