{"id":34710,"date":"2021-05-06T13:00:45","date_gmt":"2021-05-06T13:00:45","guid":{"rendered":"https:\/\/toposuranos.com\/material\/?p=34710"},"modified":"2025-09-20T06:39:29","modified_gmt":"2025-09-20T06:39:29","slug":"microstatus-et-macrostatus-in-thermodynamica","status":"publish","type":"post","link":"http:\/\/toposuranos.com\/material\/la\/microstatus-et-macrostatus-in-thermodynamica\/","title":{"rendered":"Microstatus et macrostatus in Thermodynamica"},"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>Microstatus et macrostatus in Thermodynamica<\/h1>\n<p style=\"text-align:center;\"><em>In hac lectione disces distinguere microstatus et macrostatus in thermodynamica, explorans quomodo configurationes microscopicae systematis proprietates eius macroscopicas determinant. Per exempla concreta, ut calculus combinatoriarum in systematibus cum multiplicibus statibus possibilibus, intelleges notiones clavis quae microscopicum cum observabili conectunt. Cognosce quomodo hae ideae fundamentaliae sint ad interpretandum comportamentum systematum thermalium complexorum atque novam perspicientiam de principiis quae materiam regunt evolvas.<\/em><\/p>\n<p style=\"text-align:center;\"><strong>Proposita Discendi:<\/strong><br \/>\nAd finem huius lectionis discipulus poterit\n<\/p>\n<ol>\n<li><strong>Distinguere<\/strong> inter microstatum et macrostatum, definitiones earum et applicationes in thermodynamica intellegens.<\/li>\n<li><strong>Classificare<\/strong> microstatus in macrostatus secundum qualitates communes et numerum eorum per combinatoriam computare.<\/li>\n<li><strong>Explicare<\/strong> quomodo aequiprobabilitas microstatuum probabilitatem macrostatuum in systematibus thermodynamicis determinet.<\/li>\n<li><strong>Referre<\/strong> proprietates microscopicas systematis ad proprietates eius macroscopicas ut pressio, volumen et energia.<\/li>\n<li><strong>Analysare<\/strong> systemata thermica per exempla practica, eminens momentum microstatuum et macrostatuum.<\/li>\n<\/ol>\n<p style=\"text-align:center;\"><strong><u>INDEX CONTENTORUM<\/u>:<\/strong><br \/>\n<a href=\"#1\">Distinctio inter microstatum et macrostatum in thermodynamica<\/a><br \/>\n<a href=\"#2\">Qualitates macrostatuum in thermodynamica<\/a>\n<\/p>\n<p><center><iframe class=\"lazyload\" width=\"560\" height=\"315\" data-src=\"https:\/\/www.youtube.com\/embed\/O5RKp4Dt8Z0\" 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>Distinctio inter microstatum et macrostatum in thermodynamica<\/h2>\n<p><a href=\"https:\/\/www.youtube.com\/watch?v=O5RKp4Dt8Z0&amp;t=7s\" target=\"_blank\" rel=\"noopener\"><strong>Distinctio summae momenti in thermodynamica <\/strong><\/a>est illa quae implicat differentiam inter microstatum et macrostatum. Generaliter dicitur microstatus pertinere ad aspectus microscopicos materiae, dum macrostatus tractat de totalitate systematis ex multis micro-systematibus compositi. Quamvis talis distinctio adiuvet ad dirigendum cogitationem ad primam approximationem harum notionum, per se sola non comprehendit essentiam significationis microstati et macrostati.<\/p>\n<p>Ut notionum horum accuratiorem ideam habeamus, consideremus exemplum sequens<\/p>\n<h3>Microstatus et macrostatus cum nummis<\/h3>\n<p><strong><a href=\"https:\/\/www.youtube.com\/watch?v=O5RKp4Dt8Z0&amp;t=218s\" target=\"_blank\" rel=\"noopener\">Imagina te habere cistam cum 100 nummis,<\/a><\/strong> quae omni tempore clausa manet. Si vehementer hanc cistam concutias, nummi in eius interiori saltabunt et cadent in aliquam positionem: caput vel caudam. Totum systema consequenter habet multitudinem statuum possibilium in quos decidere potest: <span class=\"katex-eq\" data-katex-display=\"false\">2^{100}<\/span> in summa (conare aestimare ordinem magnitudinis illius numeri!), et per statum intelligimus varias configurationes capitum et caudarum quae evenire possent. Assumitur unamquamque harum configurationum aequaliter probabilem esse, unde unaquaeque harum probabilitatem <span class=\"katex-eq\" data-katex-display=\"false\">1\/2^{100}<\/span> habet eveniendi.<\/p>\n<h4>Quaevis configuratio particularis est microstatus<\/h4>\n<p>Dicemus quamlibet configurationem particularem microstatum huius systematis esse. Exempli gratia, primus nummus cadit caput, secundus caudam, tertius caput, et sic porro&#8230; Ad microstatum agnoscendum, necesse est unumquemque nummum singulariter agnoscere, quod in praxi aliquid grave est.<\/p>\n<h4>Macrostatus est familia omnium microstatuum qui qualitatem communem habent<\/h4>\n<p><a href=\"https:\/\/www.youtube.com\/watch?v=O5RKp4Dt8Z0&amp;t=372s\" target=\"_blank\" rel=\"noopener\"><strong>Hoc loco, pro singulos microstatus investigando<\/strong><\/a>, viam capere possumus ad microstatus possibiles in familiam cum qualitate communi ordinandos: qui unum caput habent, qui duo capita habent, qui tria capita habent, etc&#8230; Numeros combinatorios considerantes ad id perveniemus quod microstatus qui habent<\/p>\n<ul>\n<li style=\"list-style-type: none;\">\n<ul>\n<li>0 capita et 100 caudas sunt: <span class=\"katex-eq\" data-katex-display=\"false\">\\displaystyle{{100}\\choose{0}} = \\frac{100!}{(100 - 0)! 0!} = 1 <\/span> status in summa<\/li>\n<li>1 caput et 99 caudas sunt: <span class=\"katex-eq\" data-katex-display=\"false\">\\displaystyle {{100}\\choose{1}} = \\frac{100!}{(100 - 1)! 1!}= \\frac{100!}{99!} = 100 <\/span> status in summa<\/li>\n<li>2 capita et 98 caudas sunt: <span class=\"katex-eq\" data-katex-display=\"false\">\\displaystyle {{100}\\choose{2}} = \\frac{100!}{(100 - 2)! 2!}= \\frac{100!}{98!2!} = \\frac{99\\cdot 100}{2} = 99 \\cdot 50 = 4950 <\/span> status in summa<\/li>\n<\/ul>\n<\/li>\n<\/ul>\n<span class=\"katex-eq\" data-katex-display=\"false\">\\vdots<\/span>\n<ul>\n<li style=\"list-style-type: none;\">\n<ul>\n<li>49 capita et 51 caudas sunt: <span class=\"katex-eq\" data-katex-display=\"false\">\\displaystyle{{100}\\choose{49}} = \\frac{100!}{(100 - 49)! 49!}= \\frac{100!}{51!49!}\\approx 9.89\\cdot 10^{28}<\/span> status in summa<\/li>\n<li>50 capita et 50 caudas sunt: <span class=\"katex-eq\" data-katex-display=\"false\">\\displaystyle{{100}\\choose{50}} = \\frac{100!}{(100 - 50)! 50!}= \\frac{100!}{50!50!}\\approx 10^{29}<\/span> status in summa<\/li>\n<li>51 capita et 49 caudas sunt: <span class=\"katex-eq\" data-katex-display=\"false\">\\displaystyle{{100}\\choose{51}} = \\frac{100!}{(100 - 51)! 51!}= \\frac{100!}{49!51!}\\approx 9.89\\cdot 10^{28}<\/span> status in summa<\/li>\n<li>52 capita et 48 caudas sunt: <span class=\"katex-eq\" data-katex-display=\"false\">\\displaystyle{{100}\\choose{52}} = \\frac{100!}{(100 - 52)! 52!}= \\frac{100!}{48!52!}\\approx 9.32\\cdot 10^{28}<\/span> status in summa<\/li>\n<\/ul>\n<\/li>\n<\/ul>\n<span class=\"katex-eq\" data-katex-display=\"false\">\\vdots<\/span>\n<ul>\n<li style=\"list-style-type: none;\">\n<ul>\n<li>70 capita et 30 caudas sunt: <span class=\"katex-eq\" data-katex-display=\"false\">\\displaystyle{{100}\\choose{70}} = \\frac{100!}{(100 - 70)! 70!}= \\frac{100!}{30!70!}\\approx 2.93\\cdot 10^{25}<\/span> status in summa<\/li>\n<\/ul>\n<\/li>\n<\/ul>\n<span class=\"katex-eq\" data-katex-display=\"false\">\\vdots<\/span>\n<ul>\n<li>100 capita et 0 caudas sunt: <span class=\"katex-eq\" data-katex-display=\"false\">\\displaystyle{{100}\\choose{100}} = \\frac{100!}{(100 - 100)! 100!}= \\frac{100!}{0!100!} = 1<\/span> status in summa<\/li>\n<\/ul>\n<p>Itaque, macrostatus \u00ab0 capita\u00bb unum microstatum continet, macrostatus \u00ab1 caput\u00bb 100 microstatus continet, macrostatus \u00ab2 capita\u00bb 4950 microstatus habet et sic porro.<\/p>\n<p><a name=\"2\"><\/a><\/p>\n<h2>Qualitates macrostatuum in thermodynamica<\/h2>\n<p><a href=\"https:\/\/www.youtube.com\/watch?v=O5RKp4Dt8Z0&amp;t=607s\" target=\"_blank\" rel=\"noopener\"><strong>Generatim, macrostatus constat<\/strong><\/a> ex magno numero microstatuum aequaliter probabilium.<\/p>\n<p>Quamquam microstatus omnes aequiprobabiles sunt, macrostatus generaliter non sunt. Probabilitas macrostati proportionalis est numero microstatuum quos continet. Macrostatus probabilissimus est is qui maximum numerum microstatuum habet.<\/p>\n<p>Systemata thermica se gerunt modo valde simili exemplo quod modo recensuimus. Ad microstatum in systemate thermodynamico specificandum necesse est indicare magnitudines quae certam configurationem systematis ad gradum microscopicum definiunt: esse potest positio, velocitas vel energia atomorum qui systema componunt.<\/p>\n<p>In praxi impossibile est unumquemque microstatum systematis metiri. Contra, macrostatus tantum describi possunt in terminis proprietatum macroscopicorum systematis, ut pressio, energia totalis vel volumen. Configuratio macroscopica systematis <span class=\"katex-eq\" data-katex-display=\"false\">2[m^3]<\/span> voluminis sub pressione <span class=\"katex-eq\" data-katex-display=\"false\">35[kPa]<\/span> posita, multis configurationibus microscopicis coniungi potest.<\/p>\n","protected":false},"excerpt":{"rendered":"<p>Microstatus et macrostatus in Thermodynamica In hac lectione disces distinguere microstatus et macrostatus in thermodynamica, explorans quomodo configurationes microscopicae systematis proprietates eius macroscopicas determinant. Per exempla concreta, ut calculus combinatoriarum in systematibus cum multiplicibus statibus possibilibus, intelleges notiones clavis quae microscopicum cum observabili conectunt. Cognosce quomodo hae ideae fundamentaliae sint ad interpretandum comportamentum systematum thermalium [&hellip;]<\/p>\n","protected":false},"author":1,"featured_media":30705,"comment_status":"open","ping_status":"closed","sticky":false,"template":"","format":"standard","meta":{"iawp_total_views":18,"footnotes":""},"categories":[1250,1292],"tags":[],"class_list":["post-34710","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>Microstatus et macrostatus in Thermodynamica - toposuranos.com\/material<\/title>\n<meta name=\"description\" content=\"Disce distinguere microstatum et macrostatum in thermodynamica et quomodo microscopicum cum proprietatibus macroscopicis systematis conectantur.\" \/>\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\/microstatus-et-macrostatus-in-thermodynamica\/\" \/>\n<meta property=\"og:locale\" content=\"es_ES\" \/>\n<meta property=\"og:type\" content=\"article\" \/>\n<meta property=\"og:title\" content=\"Microstatus et macrostatus in Thermodynamica\" \/>\n<meta property=\"og:description\" content=\"Disce distinguere microstatum et macrostatum in thermodynamica et quomodo microscopicum cum proprietatibus macroscopicis systematis conectantur.\" \/>\n<meta property=\"og:url\" content=\"http:\/\/toposuranos.com\/material\/la\/microstatus-et-macrostatus-in-thermodynamica\/\" \/>\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=\"2021-05-06T13:00:45+00:00\" \/>\n<meta property=\"article:modified_time\" content=\"2025-09-20T06:39:29+00:00\" \/>\n<meta property=\"og:image\" content=\"http:\/\/toposuranos.com\/material\/wp-content\/uploads\/2025\/01\/micomacroestados-1024x585.jpg\" \/>\n<meta name=\"author\" content=\"giorgio.reveco\" \/>\n<meta name=\"twitter:card\" content=\"summary_large_image\" \/>\n<meta name=\"twitter:title\" content=\"Microstatus et macrostatus in Thermodynamica\" \/>\n<meta name=\"twitter:description\" content=\"Disce distinguere microstatum et macrostatum in thermodynamica et quomodo microscopicum cum proprietatibus macroscopicis systematis conectantur.\" \/>\n<meta name=\"twitter:image\" content=\"http:\/\/toposuranos.com\/material\/wp-content\/uploads\/2025\/01\/micomacroestados.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\/microstatus-et-macrostatus-in-thermodynamica\/#article\",\"isPartOf\":{\"@id\":\"http:\/\/toposuranos.com\/material\/la\/microstatus-et-macrostatus-in-thermodynamica\/\"},\"author\":{\"name\":\"giorgio.reveco\",\"@id\":\"http:\/\/toposuranos.com\/material\/#\/schema\/person\/e15164361c3f9a2a02cf6c234cf7fdc1\"},\"headline\":\"Microstatus et macrostatus in Thermodynamica\",\"datePublished\":\"2021-05-06T13:00:45+00:00\",\"dateModified\":\"2025-09-20T06:39:29+00:00\",\"mainEntityOfPage\":{\"@id\":\"http:\/\/toposuranos.com\/material\/la\/microstatus-et-macrostatus-in-thermodynamica\/\"},\"wordCount\":676,\"commentCount\":0,\"publisher\":{\"@id\":\"http:\/\/toposuranos.com\/material\/#organization\"},\"image\":{\"@id\":\"http:\/\/toposuranos.com\/material\/la\/microstatus-et-macrostatus-in-thermodynamica\/#primaryimage\"},\"thumbnailUrl\":\"http:\/\/toposuranos.com\/material\/wp-content\/uploads\/2025\/01\/micomacroestados.jpg\",\"articleSection\":[\"Physica\",\"Thermodynamica\"],\"inLanguage\":\"es\",\"potentialAction\":[{\"@type\":\"CommentAction\",\"name\":\"Comment\",\"target\":[\"http:\/\/toposuranos.com\/material\/la\/microstatus-et-macrostatus-in-thermodynamica\/#respond\"]}]},{\"@type\":\"WebPage\",\"@id\":\"http:\/\/toposuranos.com\/material\/la\/microstatus-et-macrostatus-in-thermodynamica\/\",\"url\":\"http:\/\/toposuranos.com\/material\/la\/microstatus-et-macrostatus-in-thermodynamica\/\",\"name\":\"Microstatus et macrostatus in Thermodynamica - 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