{"id":6337,"date":"2021-07-07T15:39:27","date_gmt":"2021-07-07T13:39:27","guid":{"rendered":"https:\/\/www.mathweb.fr\/euclide\/?p=6337"},"modified":"2021-07-07T15:39:30","modified_gmt":"2021-07-07T13:39:30","slug":"taux-devolution-dune-temperature-esbroufe-ou-legitime","status":"publish","type":"post","link":"https:\/\/www.mathweb.fr\/euclide\/2021\/07\/07\/taux-devolution-dune-temperature-esbroufe-ou-legitime\/","title":{"rendered":"Taux d&rsquo;\u00e9volution d&rsquo;une temp\u00e9rature: esbroufe ou l\u00e9gitime ?"},"content":{"rendered":"\n<p class=\"wp-block-paragraph\">Au DNB 2021, en m\u00e9tropole, il \u00e9tait question de taux d&rsquo;\u00e9volution d&rsquo;une temp\u00e9rature exprim\u00e9e en degr\u00e9 Celsius.<\/p>\n\n\n\n<div class=\"wp-block-image is-style-default\"><figure class=\"aligncenter size-large\"><img loading=\"lazy\" decoding=\"async\" width=\"649\" height=\"393\" src=\"https:\/\/www.mathweb.fr\/euclide\/wp-content\/uploads\/2021\/07\/DNB2021-Metropole.png\" alt=\"taux \u00e9volution temp\u00e9rature\" class=\"wp-image-6338\" srcset=\"https:\/\/www.mathweb.fr\/euclide\/wp-content\/uploads\/2021\/07\/DNB2021-Metropole.png 649w, https:\/\/www.mathweb.fr\/euclide\/wp-content\/uploads\/2021\/07\/DNB2021-Metropole-300x182.png 300w, https:\/\/www.mathweb.fr\/euclide\/wp-content\/uploads\/2021\/07\/DNB2021-Metropole-600x363.png 600w\" sizes=\"auto, (max-width: 649px) 100vw, 649px\" \/><\/figure><\/div>\n\n\n\n<p class=\"wp-block-paragraph\">Il s&rsquo;agit en l&rsquo;occurrence de la question 5.<\/p>\n\n\n\n<p class=\"wp-block-paragraph\">Bien que cela ne soit pas r\u00e9ellement probl\u00e9matique au niveau coll\u00e8ge, nous sommes en droit de nous demander s&rsquo;il \u00e9tait p\u00e9dagogiquement correct de proposer une telle question&#8230; Pourquoi ?<\/p>\n\n\n\n<!--more-->\n\n\n\n<div id=\"ez-toc-container\" class=\"ez-toc-v2_0_85 counter-hierarchy ez-toc-counter ez-toc-white ez-toc-container-direction\">\n<div class=\"ez-toc-title-container\">\n<p class=\"ez-toc-title\" style=\"cursor:inherit\">Au menu sur cette page...<\/p>\n<span class=\"ez-toc-title-toggle\"><a href=\"#\" class=\"ez-toc-pull-right ez-toc-btn ez-toc-btn-xs ez-toc-btn-default ez-toc-toggle\" aria-label=\"Toggle Table of Content\"><span class=\"ez-toc-js-icon-con\"><span class=\"\"><span class=\"eztoc-hide\" style=\"display:none;\">Toggle<\/span><span class=\"ez-toc-icon-toggle-span\"><svg style=\"fill: #999;color:#999\" xmlns=\"http:\/\/www.w3.org\/2000\/svg\" class=\"list-377408\" width=\"20px\" height=\"20px\" viewBox=\"0 0 24 24\" fill=\"none\"><path d=\"M6 6H4v2h2V6zm14 0H8v2h12V6zM4 11h2v2H4v-2zm16 0H8v2h12v-2zM4 16h2v2H4v-2zm16 0H8v2h12v-2z\" fill=\"currentColor\"><\/path><\/svg><svg style=\"fill: #999;color:#999\" class=\"arrow-unsorted-368013\" xmlns=\"http:\/\/www.w3.org\/2000\/svg\" width=\"10px\" height=\"10px\" viewBox=\"0 0 24 24\" version=\"1.2\" baseProfile=\"tiny\"><path d=\"M18.2 9.3l-6.2-6.3-6.2 6.3c-.2.2-.3.4-.3.7s.1.5.3.7c.2.2.4.3.7.3h11c.3 0 .5-.1.7-.3.2-.2.3-.5.3-.7s-.1-.5-.3-.7zM5.8 14.7l6.2 6.3 6.2-6.3c.2-.2.3-.5.3-.7s-.1-.5-.3-.7c-.2-.2-.4-.3-.7-.3h-11c-.3 0-.5.1-.7.3-.2.2-.3.5-.3.7s.1.5.3.7z\"\/><\/svg><\/span><\/span><\/span><\/a><\/span><\/div>\n<nav><ul class='ez-toc-list ez-toc-list-level-1 ' ><li class='ez-toc-page-1 ez-toc-heading-level-2'><a class=\"ez-toc-link ez-toc-heading-1\" href=\"https:\/\/www.mathweb.fr\/euclide\/2021\/07\/07\/taux-devolution-dune-temperature-esbroufe-ou-legitime\/#Taux_devolution_dune_temperature_les_differentes_echelles\" >Taux d&rsquo;\u00e9volution d&rsquo;une temp\u00e9rature: les diff\u00e9rentes \u00e9chelles<\/a><ul class='ez-toc-list-level-3' ><li class='ez-toc-heading-level-3'><a class=\"ez-toc-link ez-toc-heading-2\" href=\"https:\/\/www.mathweb.fr\/euclide\/2021\/07\/07\/taux-devolution-dune-temperature-esbroufe-ou-legitime\/#Le_kelvin_K\" >Le kelvin (K)<\/a><ul class='ez-toc-list-level-4' ><li class='ez-toc-heading-level-4'><a class=\"ez-toc-link ez-toc-heading-3\" href=\"https:\/\/www.mathweb.fr\/euclide\/2021\/07\/07\/taux-devolution-dune-temperature-esbroufe-ou-legitime\/#Le_point_triple_de_leau\" >Le point triple de l&rsquo;eau<\/a><\/li><\/ul><\/li><li class='ez-toc-page-1 ez-toc-heading-level-3'><a class=\"ez-toc-link ez-toc-heading-4\" href=\"https:\/\/www.mathweb.fr\/euclide\/2021\/07\/07\/taux-devolution-dune-temperature-esbroufe-ou-legitime\/#Le_degre_Celsius_%C2%B0C\" >Le degr\u00e9 Celsius (\u00b0C)<\/a><\/li><li class='ez-toc-page-1 ez-toc-heading-level-3'><a class=\"ez-toc-link ez-toc-heading-5\" href=\"https:\/\/www.mathweb.fr\/euclide\/2021\/07\/07\/taux-devolution-dune-temperature-esbroufe-ou-legitime\/#Le_degre_Fahrenheit_%C2%B0F\" >Le degr\u00e9 Fahrenheit (\u00b0F)<\/a><\/li><\/ul><\/li><li class='ez-toc-page-1 ez-toc-heading-level-2'><a class=\"ez-toc-link ez-toc-heading-6\" href=\"https:\/\/www.mathweb.fr\/euclide\/2021\/07\/07\/taux-devolution-dune-temperature-esbroufe-ou-legitime\/#Taux_devolution_dune_temperature_un_calcul_simple\" >Taux d&rsquo;\u00e9volution d&rsquo;une temp\u00e9rature: un calcul simple<\/a><\/li><\/ul><\/nav><\/div>\n<h2 class=\"wp-block-heading\"><span class=\"ez-toc-section\" id=\"Taux_devolution_dune_temperature_les_differentes_echelles\"><\/span>Taux d&rsquo;\u00e9volution d&rsquo;une temp\u00e9rature: les diff\u00e9rentes \u00e9chelles<span class=\"ez-toc-section-end\"><\/span><\/h2>\n\n\n\n<p class=\"wp-block-paragraph\">Pour mesure une temp\u00e9rature, on a le choix entre:<\/p>\n\n\n\n<ul class=\"wp-block-list\"><li>le Kelvin,<\/li><li>le degr\u00e9 Celsius,<\/li><li>le degr\u00e9 Fahrenheit.<\/li><\/ul>\n\n\n\n<h3 class=\"wp-block-heading\"><span class=\"ez-toc-section\" id=\"Le_kelvin_K\"><\/span>Le kelvin (K)<span class=\"ez-toc-section-end\"><\/span><\/h3>\n\n\n\n<p class=\"wp-block-paragraph\">Le Kelvin doit son nom au physicien britannique <a href=\"https:\/\/fr.wikipedia.org\/wiki\/William_Thomson_(Lord_Kelvin)\" target=\"_blank\" rel=\"noreferrer noopener\">William Thomson (Lord Kelvin)<\/a>. C&rsquo;est l&rsquo;unit\u00e9 de temp\u00e9rature thermodynamique (c&rsquo;est-\u00e0-dire d\u00e9finie uniquement \u00e0 partir des deux premiers principes de la thermodynamique). Elle ne d\u00e9pend donc pas des thermom\u00e8tre utilis\u00e9s. C&rsquo;est une temp\u00e9rature absolue ne n\u00e9cessitant qu&rsquo;un seul point de r\u00e9f\u00e9rence\u00a0: le point triple de l&rsquo;eau.<\/p>\n\n\n\n<h4 class=\"wp-block-heading\"><span class=\"ez-toc-section\" id=\"Le_point_triple_de_leau\"><\/span>Le point triple de l&rsquo;eau<span class=\"ez-toc-section-end\"><\/span><\/h4>\n\n\n\n<p class=\"wp-block-paragraph\">Le <em>diagramme de phase<\/em> est le graphique repr\u00e9sentant l&rsquo;\u00e9tat dans lequel se trouve un certain corps en fonction de la temp\u00e9rature et de la pression.<\/p>\n\n\n\n<p class=\"wp-block-paragraph\">Le <em>point triple<\/em> de l&rsquo;eau est le point du diagramme de phase de l&rsquo;eau en lequel l&rsquo;eau se trouve dans les trois \u00e9tats simultan\u00e9ment: liquide, solide et gazeux. Il se trouve \u00e0 environ 610,6 Pa et 273,16 K. Au point triple, l&rsquo;eau commence \u00e0 bouillir et \u00e0 former des gla\u00e7ons tout en restant liquide.<\/p>\n\n\n\n<p class=\"wp-block-paragraph\">Le Kelvin est alors d\u00e9fini comme \u00e9tant le 1\/273,16 du point triple de l&rsquo;eau.<\/p>\n\n\n\n<h3 class=\"wp-block-heading\"><span class=\"ez-toc-section\" id=\"Le_degre_Celsius_%C2%B0C\"><\/span>Le degr\u00e9 Celsius (\u00b0C)<span class=\"ez-toc-section-end\"><\/span><\/h3>\n\n\n\n<p class=\"wp-block-paragraph\">Le degr\u00e9 Celsius doit son nom au physicien su\u00e9dois <a href=\"https:\/\/fr.wikipedia.org\/wiki\/Anders_Celsius\" target=\"_blank\" rel=\"noreferrer noopener\">Anders Celsius<\/a>. Par d\u00e9finition, 0\u00b0C = 273,16 K.<\/p>\n\n\n\n<p class=\"wp-block-paragraph\">Quant \u00e0 la variation de 1\u00b0C, on la d\u00e9finit comme \u00e9tant \u00e9gale \u00e0 1 K.<\/p>\n\n\n\n<h3 class=\"wp-block-heading\"><span class=\"ez-toc-section\" id=\"Le_degre_Fahrenheit_%C2%B0F\"><\/span>Le degr\u00e9 Fahrenheit (\u00b0F)<span class=\"ez-toc-section-end\"><\/span><\/h3>\n\n\n\n<p class=\"wp-block-paragraph\">Le degr\u00e9 Fahrenheint doit son nom au physicien allemand Gabriel Fahrenheit. Par d\u00e9finition, <\/p>\n\n\n\n<blockquote class=\"wp-block-quote is-layout-flow wp-block-quote-is-layout-flow\"><p>Historiquement, dans cette \u00e9chelle, le point z\u00e9ro \u00e9tait la temp\u00e9rature de solidification d&rsquo;un m\u00e9lange eutectique de chlorure d&rsquo;ammonium et d&rsquo;eau, et le point 96 \u00e9tait la temp\u00e9rature du corps humain. Fahrenheit v\u00e9rifia que le point de solidification de l\u2019eau \u00e9tait de 32\u00a0degr\u00e9s et son point d\u2019\u00e9bullition de 212\u00a0degr\u00e9s.<\/p><cite><a href=\"https:\/\/fr.wikipedia.org\/wiki\/Degr%C3%A9_Fahrenheit\" target=\"_blank\" rel=\"noreferrer noopener\">https:\/\/fr.wikipedia.org\/wiki\/Degr%C3%A9_Fahrenheit<\/a><\/cite><\/blockquote>\n\n\n\n<p class=\"wp-block-paragraph\">On a alors la relation suivante : $$\\text{F} = \\frac{9}{5} \\text{C}+32,$$o\u00f9 \\(F\\) et \\(C\\) repr\u00e9sentent respectivement les temp\u00e9ratures en degr\u00e9 Fahrenheit et Celsius.<\/p>\n\n\n\n<h2 class=\"wp-block-heading\"><span class=\"ez-toc-section\" id=\"Taux_devolution_dune_temperature_un_calcul_simple\"><\/span>Taux d&rsquo;\u00e9volution d&rsquo;une temp\u00e9rature: un calcul simple<span class=\"ez-toc-section-end\"><\/span><\/h2>\n\n\n\n<p class=\"wp-block-paragraph\">Maintenant que nous avons bien compris que les degr\u00e9 Celsius et Fahrenheit n&rsquo;\u00e9taient pas des unit\u00e9s, mais des <em>\u00e9chelles<\/em>, faisons un petit calcul.<\/p>\n\n\n\n<p class=\"wp-block-paragraph\">On fait chauffer de l&rsquo;eau, initialement \u00e0 15\u00b0C, afin qu&rsquo;elle ait une temp\u00e9rature finale de 30\u00b0C. On pourrait alors penser que la temp\u00e9rature a doubl\u00e9&#8230;<\/p>\n\n\n\n<p class=\"wp-block-paragraph\">Mais si on exprime les deux temp\u00e9ratures en degr\u00e9 Fahrenheit, l&rsquo;eau passe de 59\u00b0F \u00e0 86\u00b0F&#8230; Elle n&rsquo;a donc pas doubl\u00e9!<\/p>\n\n\n\n<p class=\"wp-block-paragraph\">En fait, parler de \u00ab\u00a0doublement\u00a0\u00bb pour une temp\u00e9rature n&rsquo;a aucun sens car la temp\u00e9rature n&rsquo;est pas une <em>grandeur mesurable<\/em>.<\/p>\n\n\n\n<blockquote class=\"wp-block-quote is-layout-flow wp-block-quote-is-layout-flow\"><p>Une grandeur est dite <em>mesurable <\/em>si on peut lui affecter une valeur num\u00e9rique \u00e0 partir d&rsquo;observations. En outre, la somme et\/ou le produit de grandeurs mesurables a une signification. Parmi les grandeurs mesurables, on peut citer la longueur, la temp\u00e9rature absolue, la r\u00e9sistance,\u2026<\/p><cite><a href=\"https:\/\/ics.utc.fr\/PS90\/chapitre1\/co\/definition-grandeur\" target=\"_blank\" rel=\"noreferrer noopener\">https:\/\/ics.utc.fr\/PS90\/chapitre1\/co\/definition-grandeur<\/a><\/cite><\/blockquote>\n\n\n\n<p class=\"wp-block-paragraph\">Si on ajoute de l&rsquo;eau \u00e0 15\u00b0C et de l&rsquo;eau \u00e0 20\u00b0C, m\u00eame \u00e0 volume \u00e9gal, cela ne donnera pas une eau \u00e0 35\u00b0C !<\/p>\n\n\n\n<p class=\"wp-block-paragraph\">C&rsquo;est la raison pour laquelle on ne peut en aucun cas parler d&rsquo;\u00e9volution en pourcentage de temp\u00e9ratures exprim\u00e9e en \u00b0C et en \u00b0F.<\/p>\n\n\n\n<p class=\"wp-block-paragraph\">En revanche, on peut le faire si la temp\u00e9rature est exprim\u00e9e en Kelvin.<\/p>\n","protected":false},"excerpt":{"rendered":"<p>Au DNB 2021, en m\u00e9tropole, il \u00e9tait question de taux d&rsquo;\u00e9volution d&rsquo;une temp\u00e9rature exprim\u00e9e en degr\u00e9 Celsius. Il s&rsquo;agit en l&rsquo;occurrence de la question 5. Bien que cela ne soit pas r\u00e9ellement probl\u00e9matique au niveau coll\u00e8ge, nous sommes en droit de nous demander s&rsquo;il \u00e9tait p\u00e9dagogiquement correct de proposer une [&hellip;]<\/p>\n","protected":false},"author":1,"featured_media":6340,"comment_status":"open","ping_status":"open","sticky":false,"template":"","format":"standard","meta":{"footnotes":""},"categories":[21,6],"tags":[297,298,299,296],"class_list":["post-6337","post","type-post","status-publish","format-standard","has-post-thumbnail","hentry","category-enseignement","category-mathematiques","tag-celsius","tag-fahrenheit","tag-kelvin","tag-temperature"],"yoast_head":"<!-- This site is optimized with the Yoast SEO plugin v27.9 - https:\/\/yoast.com\/product\/yoast-seo-wordpress\/ -->\n<title>Taux d&#039;\u00e9volution d&#039;une temp\u00e9rature: esbroufe ou l\u00e9gitime ? - Mathweb.fr<\/title>\n<meta name=\"description\" content=\"Au DNB 2021, en m\u00e9tropole, il \u00e9tait question de taux d&#039;\u00e9volution d&#039;une temp\u00e9rature exprim\u00e9e en degr\u00e9 Celsius. 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