{"id":34722,"date":"2021-05-07T13:00:49","date_gmt":"2021-05-07T13:00:49","guid":{"rendered":"https:\/\/toposuranos.com\/material\/?p=34722"},"modified":"2025-09-20T06:47:12","modified_gmt":"2025-09-20T06:47:12","slug":"aequilibrium-thermicum-temperatura-eiusque-definitio-statistica","status":"publish","type":"post","link":"http:\/\/toposuranos.com\/material\/la\/aequilibrium-thermicum-temperatura-eiusque-definitio-statistica\/","title":{"rendered":"Aequilibrium thermicum, temperatura eiusque definitio statistica"},"content":{"rendered":"<style>\n\tp, ul, ol {\n\t\ttext-align: justify;\n\t}\n\th1, h2 {\n\ttext-align:center;\n\t}\n<\/style>\n<h1>Aequilibrium thermicum, temperatura eiusque definitio statistica<\/h1>\n<p style=\"text-align:center\"><em>Temperatura thermodynamica, intellecta ut nexus inter energiam et probabilitatem, oritur ex aequilibrio inter macrostatus et microstatus in systematibus thermicis. Hoc contentum explanat quomodo maximatio numeri microstatuum definit aequilibrium thermicum, utens deductionibus mathematicis et ratione mechanicae statisticae ad declarandam relationem eius cum constanti Boltzmann et scala Kelvin.<\/em><\/p>\n<p style=\"text-align:center;\"><strong>Proposita Discendi:<\/strong><br \/>\nPost hanc lectionem, discipulus poterit\n<\/p>\n<ol>\n<li><strong>Intellegere<\/strong> relationem inter macrostatus et microstatus in systematibus thermodynamicis atque notionem temperaturae.<\/li>\n<\/ol>\n<p style=\"text-align:center;\"><strong><u>INDEX CONTENTORUM<\/u>:<\/strong><br \/>\n<a href=\"#1\">Macrostatus et microstatus systematum in contactu thermico positum<\/a><br \/>\n<a href=\"#2\">Temperatura thermodynamica: Qualitas communis systematum in aequilibrio<\/a>\n<\/p>\n<p><center><iframe class=\"lazyload\" width=\"560\" height=\"315\" data-src=\"https:\/\/www.youtube.com\/embed\/7LPUN_vBoXE\" title=\"YouTube video player\" frameborder=\"0\" allow=\"accelerometer; autoplay; clipboard-write; encrypted-media; gyroscope; picture-in-picture\" allowfullscreen=\"allowfullscreen\"><\/iframe><\/center><br \/>\n<a name=\"1\"><\/a><\/p>\n<h2>Macrostatus et microstatus systematum in contactu thermico positum<\/h2>\n<p><a href=\"https:\/\/www.youtube.com\/watch?v=7LPUN_vBoXE&amp;t=218s\" target=\"_blank\" rel=\"noopener\"><strong>Ad tractandum conceptum temperaturae thermodynamicae <\/strong><\/a>videre debemus primum quomodo systemata thermodynamica inter se agant atque relationem eorum cum micro- et macrostatibus. Consideremus casum duorum systematum in contactu thermico inter se positorum, sed a reliquo universo isolatorum.<\/p>\n<p><img decoding=\"async\" src=\"data:image\/gif;base64,R0lGODlhAQABAIAAAAAAAP\/\/\/yH5BAEAAAAALAAAAAABAAEAAAIBRAA7\" data-src=\"https:\/\/1.bp.blogspot.com\/-kL0Rr2L4wys\/YJPlhBUTueI\/AAAAAAAAFEw\/OWpuyASOdGANXsSG5O-d09ed034DtMTuwCLcBGAsYHQ\/s0\/contacto%2Btermico.PNG\" alt=\"Contacto t\u00e9rmico\" class=\"aligncenter lazyload\" width=\"372\" height=\"158\" \/><noscript><img decoding=\"async\" src=\"https:\/\/1.bp.blogspot.com\/-kL0Rr2L4wys\/YJPlhBUTueI\/AAAAAAAAFEw\/OWpuyASOdGANXsSG5O-d09ed034DtMTuwCLcBGAsYHQ\/s0\/contacto%2Btermico.PNG\" alt=\"Contacto t\u00e9rmico\" class=\"aligncenter lazyload\" width=\"372\" height=\"158\" \/><\/noscript><\/p>\n<p>Ex una parte, cum systemata isolata maneant, energia totalis <span class=\"katex-eq\" data-katex-display=\"false\">E=E_1+E_2<\/span> constans erit, atque propter hoc macrostatus systematis definitur per quamlibet trium energiarium <span class=\"katex-eq\" data-katex-display=\"false\">E, E_1<\/span> et <span class=\"katex-eq\" data-katex-display=\"false\">E_2<\/span>. Ex altera parte, si de microstatibus loquimur, systema energiae <span class=\"katex-eq\" data-katex-display=\"false\">E_1<\/span> habet <span class=\"katex-eq\" data-katex-display=\"false\">\\Omega_1(E_1)<\/span> microstatus, et similiter illud energiae <span class=\"katex-eq\" data-katex-display=\"false\">E_2<\/span> alios <span class=\"katex-eq\" data-katex-display=\"false\">\\Omega_2(E_2)<\/span>, ita systema compositum constituitur ex toto <span class=\"katex-eq\" data-katex-display=\"false\">\\Omega_1(E_1)\\Omega_2(E_2)<\/span> microstatibus.<\/p>\n<h3>Praesumptiones de aequilibrio thermodynamico<\/h3>\n<p><a href=\"https:\/\/www.youtube.com\/watch?v=7LPUN_vBoXE&amp;t=392s\" target=\"_blank\" rel=\"noopener\"><strong>Si unumquodque systema potest energiam commutare<\/strong><\/a> donec attingatur <strong>aequilibrium thermicum,<\/strong> aliquando fiet ut <span class=\"katex-eq\" data-katex-display=\"false\">E_1<\/span> et <span class=\"katex-eq\" data-katex-display=\"false\">E_2,<\/span> ad valores constantes accedant. Idea in hoc momento tenenda est macrostatus maximae probabilitatis futurum esse eum qui numerum microstatuum maximat, unde sequuntur hae praesumptiones:<\/p>\n<ol>\n<li>Unusquisque microstatus eandem probabilitatem habet accidendi<\/li>\n<li>Dynamica interna systematis talis est ut microstatus continuo mutantur.<\/li>\n<li>Post aliquod tempus, systema omnes microstatus explorabit et aequalem temporis quantitatem in singulis eorum manebit<\/li>\n<\/ol>\n<p>Hae praesumptiones implicant systema maiorem temporis partem in macrostatibus degere quae maximum numerum microstatuum repraesentant, ideoque illa erunt probabilissima. Nunc, in systematibus quae plerumque in thermodynamica examinantur, expressio \u00abprobabilissima\u00bb revera significat \u00abquae esset practica et damnate impossibilis non eveniret\u00bb; quod videtur simplex enuntiatio statistica est re vera fere absoluta certitudinis declaratio.<\/p>\n<p><a name=\"2\"><\/a><\/p>\n<h2>Temperatura thermodynamica: Qualitas communis systematum in aequilibrio<\/h2>\n<p><a href=\"https:\/\/www.youtube.com\/watch?v=7LPUN_vBoXE&amp;t=617s\" target=\"_blank\" rel=\"noopener\"><strong>Ad nostrum problema duorum corporum positorum<\/strong><\/a> in contactu thermico, distributio probabilissima energiae est ea quae numerum <span class=\"katex-eq\" data-katex-display=\"false\">\\Omega_1(E_1)\\Omega_2(E_2)<\/span> microstatuum maximat. Cum systemata ingentia sint, uti possumus ut bona approximatione instrumentis calculi differentialis ad inferendum sensum harum affirmationum et proprietates earum deducendas.<\/p>\n<p>Si variationes infinitesimales de energia unius systematis facimus et casum quaerimus in quo numerus microstatuum maximatur, tunc obtinebimus hunc rationem:<\/p>\n<p style=\"text-align:center;\"><span class=\"katex-eq\" data-katex-display=\"false\">\\begin{array}{rl}\n\n(1) &amp; \\dfrac{d}{dE_1}\\left[  \\Omega_1(E_1) \\Omega_2(E_2) \\right] = 0 \\\\\n\n&amp; \\text{; Quia numerus microstatuum maximatus est} \\\\ \\\\\n\n\\equiv &amp; \\dfrac{d\\Omega_1(E_1)}{dE_1} \\Omega_2(E_2) + \\Omega_1(E_1) \\dfrac{d\\Omega_2(E_2)}{E_2}\\dfrac{dE_2}{dE_1} = 0 \\\\\n\n&amp; \\text{; Applicando derivatam producti et regulam catenae} \\\\ \\\\\n\n(2) &amp; E = E_1 + E_2 = \\text{Constans} \\\\\n\n&amp; \\text{; Energia totalis duorum systematum in contactu thermico} \\\\ \\\\\n\n\\equiv &amp; E_1 = E-E_1 \\\\ \\\\\n\n(3) &amp; \\dfrac{dE_2}{dE_1} = \\dfrac{d}{dE_1} (E - E_1) = -1\\;\\text{; Ex (2)} \\\\ \\\\\n\n(4) &amp; \\dfrac{d\\Omega_1}{dE_1}\\Omega_2 - \\Omega_2 \\dfrac{d\\Omega_2}{dE_2} = 0\\;\\text{; Ex (1) et (3)} \\\\ \\\\\n\n\\equiv &amp; \\dfrac{d\\Omega_1}{dE_1} \\Omega_2 = \\Omega_1 \\dfrac{d\\Omega_2}{dE_2} \\\\ \\\\\n\n\\equiv &amp; \\dfrac{1}{\\Omega_1} \\dfrac{d\\Omega_1}{dE_1} = \\dfrac{1}{\\Omega_2} \\dfrac{d\\Omega_2}{dE_2} \\\\ \\\\\n\n\\equiv &amp; \\dfrac{d\\ln(\\Omega_1)}{dE_1} = \\dfrac{d\\ln(\\Omega_2)}{dE_2}\n\n\\end{array}<\/span>\n<p>Hinc habemus quod, cum aequilibrium thermicum sit macrostatus probabilissimus duorum corporum in contactu thermico prolongato, hic est qui numerum microstatuum maximat. Si hoc fit, ex ratione modo exposita, habetur magnitudinem communem ambobus systematibus exsistere, quam <strong>temperaturam<\/strong> appellamus.<\/p>\n<h3>Definitio temperaturae thermodynamicae<\/h3>\n<p><a href=\"https:\/\/www.youtube.com\/watch?v=7LPUN_vBoXE&amp;t=972s\" target=\"_blank\" rel=\"noopener\"><strong>Cum hoc accidit, dicimus corpora<\/strong><\/a> \u00abesse ad eandem temperaturam\u00bb et conectimus <span class=\"katex-eq\" data-katex-display=\"false\">d\\ln\\Omega\/dE<\/span> cum temperatura <span class=\"katex-eq\" data-katex-display=\"false\">T<\/span> (ita ut <span class=\"katex-eq\" data-katex-display=\"false\">T_1 = T_2<\/span>). Sic temperatura thermodynamica definita est ut<\/p>\n<p style=\"text-align: center;\"><span class=\"katex-eq\" data-katex-display=\"false\">\\displaystyle \\frac{1}{k_B T} = \\frac{d\\ln\\Omega}{dE}<\/span>\n<p>ubi <span class=\"katex-eq\" data-katex-display=\"false\">k_B=1.3807\\cdot 10^{-23}[J\/K]<\/span> est <strong>constans Boltzmann.<\/strong><\/p>\n<p>Hac electione constantium efficitur ut temperatura <span class=\"katex-eq\" data-katex-display=\"false\">T<\/span> quam definivimus suam interpretationem usitatam adipiscatur in eo quod vocamus <strong>scala Kelvin.<\/strong><\/p>\n","protected":false},"excerpt":{"rendered":"<p>Aequilibrium thermicum, temperatura eiusque definitio statistica Temperatura thermodynamica, intellecta ut nexus inter energiam et probabilitatem, oritur ex aequilibrio inter macrostatus et microstatus in systematibus thermicis. Hoc contentum explanat quomodo maximatio numeri microstatuum definit aequilibrium thermicum, utens deductionibus mathematicis et ratione mechanicae statisticae ad declarandam relationem eius cum constanti Boltzmann et scala Kelvin. Proposita Discendi: Post [&hellip;]<\/p>\n","protected":false},"author":1,"featured_media":30760,"comment_status":"open","ping_status":"closed","sticky":false,"template":"","format":"standard","meta":{"iawp_total_views":1,"footnotes":""},"categories":[1250,1292],"tags":[],"class_list":["post-34722","post","type-post","status-publish","format-standard","has-post-thumbnail","hentry","category-physica","category-thermodynamica"],"yoast_head":"<!-- This site is optimized with the Yoast SEO plugin v26.7 - https:\/\/yoast.com\/wordpress\/plugins\/seo\/ -->\n<title>Aequilibrium thermicum, temperatura eiusque definitio statistica - toposuranos.com\/material<\/title>\n<meta name=\"description\" content=\"Intellige aequilibrium thermicum, eius relationem cum temperatura atque eius definitionem statisticam, mechanicam statisticam et scalam Kelvin coniunctam.\" \/>\n<meta name=\"robots\" content=\"index, follow, max-snippet:-1, max-image-preview:large, max-video-preview:-1\" \/>\n<link rel=\"canonical\" href=\"http:\/\/toposuranos.com\/material\/la\/aequilibrium-thermicum-temperatura-eiusque-definitio-statistica\/\" \/>\n<meta property=\"og:locale\" content=\"es_ES\" \/>\n<meta property=\"og:type\" content=\"article\" \/>\n<meta property=\"og:title\" content=\"Aequilibrium thermicum, temperatura eiusque definitio statistica\" \/>\n<meta property=\"og:description\" content=\"Intellige aequilibrium thermicum, eius relationem cum temperatura atque eius definitionem statisticam, mechanicam statisticam et scalam Kelvin coniunctam.\" \/>\n<meta property=\"og:url\" content=\"http:\/\/toposuranos.com\/material\/la\/aequilibrium-thermicum-temperatura-eiusque-definitio-statistica\/\" \/>\n<meta property=\"og:site_name\" content=\"toposuranos.com\/material\" \/>\n<meta property=\"article:publisher\" content=\"https:\/\/www.facebook.com\/groups\/toposuranos\" \/>\n<meta property=\"article:published_time\" content=\"2021-05-07T13:00:49+00:00\" \/>\n<meta property=\"article:modified_time\" content=\"2025-09-20T06:47:12+00:00\" \/>\n<meta property=\"og:image\" content=\"http:\/\/toposuranos.com\/material\/wp-content\/uploads\/2025\/01\/equilibriotermico-1024x585.jpg\" \/>\n<meta name=\"author\" content=\"giorgio.reveco\" \/>\n<meta name=\"twitter:card\" content=\"summary_large_image\" \/>\n<meta name=\"twitter:title\" content=\"Aequilibrium thermicum, temperatura eiusque definitio statistica\" \/>\n<meta name=\"twitter:description\" content=\"Intellige aequilibrium thermicum, eius relationem cum temperatura atque eius definitionem statisticam, mechanicam statisticam et scalam Kelvin coniunctam.\" \/>\n<meta name=\"twitter:image\" content=\"http:\/\/toposuranos.com\/material\/wp-content\/uploads\/2025\/01\/equilibriotermico.jpg\" \/>\n<meta name=\"twitter:creator\" content=\"@topuranos\" \/>\n<meta name=\"twitter:site\" content=\"@topuranos\" \/>\n<meta name=\"twitter:label1\" content=\"Escrito por\" \/>\n\t<meta name=\"twitter:data1\" content=\"giorgio.reveco\" \/>\n\t<meta name=\"twitter:label2\" content=\"Tiempo de lectura\" \/>\n\t<meta name=\"twitter:data2\" content=\"1 minuto\" \/>\n<script type=\"application\/ld+json\" class=\"yoast-schema-graph\">{\"@context\":\"https:\/\/schema.org\",\"@graph\":[{\"@type\":\"Article\",\"@id\":\"http:\/\/toposuranos.com\/material\/la\/aequilibrium-thermicum-temperatura-eiusque-definitio-statistica\/#article\",\"isPartOf\":{\"@id\":\"http:\/\/toposuranos.com\/material\/la\/aequilibrium-thermicum-temperatura-eiusque-definitio-statistica\/\"},\"author\":{\"name\":\"giorgio.reveco\",\"@id\":\"http:\/\/toposuranos.com\/material\/#\/schema\/person\/e15164361c3f9a2a02cf6c234cf7fdc1\"},\"headline\":\"Aequilibrium thermicum, temperatura eiusque definitio statistica\",\"datePublished\":\"2021-05-07T13:00:49+00:00\",\"dateModified\":\"2025-09-20T06:47:12+00:00\",\"mainEntityOfPage\":{\"@id\":\"http:\/\/toposuranos.com\/material\/la\/aequilibrium-thermicum-temperatura-eiusque-definitio-statistica\/\"},\"wordCount\":659,\"commentCount\":0,\"publisher\":{\"@id\":\"http:\/\/toposuranos.com\/material\/#organization\"},\"image\":{\"@id\":\"http:\/\/toposuranos.com\/material\/la\/aequilibrium-thermicum-temperatura-eiusque-definitio-statistica\/#primaryimage\"},\"thumbnailUrl\":\"http:\/\/toposuranos.com\/material\/wp-content\/uploads\/2025\/01\/equilibriotermico.jpg\",\"articleSection\":[\"Physica\",\"Thermodynamica\"],\"inLanguage\":\"es\",\"potentialAction\":[{\"@type\":\"CommentAction\",\"name\":\"Comment\",\"target\":[\"http:\/\/toposuranos.com\/material\/la\/aequilibrium-thermicum-temperatura-eiusque-definitio-statistica\/#respond\"]}]},{\"@type\":\"WebPage\",\"@id\":\"http:\/\/toposuranos.com\/material\/la\/aequilibrium-thermicum-temperatura-eiusque-definitio-statistica\/\",\"url\":\"http:\/\/toposuranos.com\/material\/la\/aequilibrium-thermicum-temperatura-eiusque-definitio-statistica\/\",\"name\":\"Aequilibrium thermicum, temperatura eiusque definitio statistica - 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