{"id":34746,"date":"2021-06-18T13:00:51","date_gmt":"2021-06-18T13:00:51","guid":{"rendered":"https:\/\/toposuranos.com\/material\/?p=34746"},"modified":"2025-09-20T08:04:35","modified_gmt":"2025-09-20T08:04:35","slug":"aequatio-et-functio-status","status":"publish","type":"post","link":"http:\/\/toposuranos.com\/material\/la\/aequatio-et-functio-status\/","title":{"rendered":"Aequatio et Functio Status"},"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>Aequatio et Functio Status<\/h1>\n<p style=\"text-align:center;\"><em>Thermodynamica nobis revelat quomodo describere et conectere statum systematis per notiones ut functiones et aequationes status. Quomodo inter se referuntur proprietates ut pressio, temperatura et aequatio gasorum idealium? Hoc contentum te ducet ad intellegendum regulas mathematicae et physicae quae regunt aequilibria universi, tuam intuitionem provocans et prospectum amplificans.<\/em><\/p>\n<p style=\"text-align:center;\"><strong>Proposita Discendi:<\/strong><br \/>\nAd finem huius lectionis discipulus poterit<\/p>\n<ol>\n<li><strong>Describere<\/strong> notionem functionis status eiusque relationem ad aequilibrium thermicum in systematibus thermodynamicis.<\/li>\n<li><strong>Distinguere<\/strong> inter functiones status et magnitudines quae non sunt functiones status, exempla concreta utriusque categoriae identificando.<\/li>\n<li><strong>Analyzare<\/strong> quomodo aequationes status, sicut ea gasorum idealium, conectant functiones status in systematibus in aequilibrio.<\/li>\n<\/ol>\n<p style=\"text-align:center;\"><strong><u>INDEX CONTENTORUM<\/u>:<\/strong><br \/>\n<a href=\"#1\">Functio status et systemata atque aequilibrium thermicum<\/a><br \/>\n<a href=\"#2\">Aequatio et variabiles status<\/a><br \/>\n<a href=\"#3\">Notio mathematica functionis status<\/a><br \/>\n<a href=\"#4\">Aequatio gasorum idealium est aequatio status<\/a>\n<\/p>\n<p><center><iframe class=\"lazyload\" width=\"560\" height=\"315\" data-src=\"https:\/\/www.youtube.com\/embed\/ZXX3KAS5WKs\" title=\"YouTube video player\" frameborder=\"0\" allow=\"accelerometer; autoplay; clipboard-write; encrypted-media; gyroscope; picture-in-picture\" allowfullscreen=\"allowfullscreen\"><\/iframe><\/center><\/p>\n<p>Unus ex notionibus clavibus thermodynamicae classicae est aequatio status et functiones status. Per haec, ut ita dicamus, poterimus describere statum systematum in aequilibrio thermodynamico. <\/p>\n<p><a name=\"1\"><\/a><\/p>\n<h2>Functio status et systemata atque aequilibrium thermicum<\/h2>\n<p><a href=\"https:\/\/www.youtube.com\/watch?v=ZXX3KAS5WKs&amp;t=115s\" target=\"_blank\" rel=\"noopener\"><strong>In thermodynamica systema definitur<\/strong><\/a> ut portio universi quae eligitur ad investigandum, et iuxta systema est ambitus. Meminerimus systema in aequilibrio thermico cum ambitu suo esse si observabilia eius macroscopica (exempli gratia: pressio, temperatura) invariabilia manent tempore. Ita, exempli gratia, si gasum in interiori continentis sumimus et eius temperatura stabilis tempore manet, dicimus gasum esse in aequilibrio thermodynamico, et ille coetus observabilium macroscopicorum est quod <strong>statum eius determinat.<\/strong> Contra, si repente magna copia caloris applicatur in aliqua parte continentis, tum saltem per aliquod tempus gasum erit in statu diverso ab aequilibrio thermico et eius status erit mutabilis tempore.<\/p>\n<p><a name=\"2\"><\/a><\/p>\n<h2>Aequatio et variabiles status<\/h2>\n<p><a href=\"https:\/\/www.youtube.com\/watch?v=ZXX3KAS5WKs&amp;t=115s\" target=\"_blank\" rel=\"noopener\"><strong>Cum systema in aequilibrio thermico est<\/strong><\/a> possumus agnoscere duo genera magnitudinum: quaedam pendent a modo quo systema illud aequilibrium attigit et aliae sunt independentes ab hoc processu. Quae huius posterioris generis sunt ea quae vocamus <strong>functiones status<\/strong> (aliquando dictae etiam <strong>variabiles status<\/strong>). Functio status est quaelibet quantitas physica quae habet valorem bene definitum pro quolibet statu aequilibrii systematis. Ita, in aequilibrio thermico, hae variabiles a tempore non pendent. Nonnulla exempla sunt:<\/p>\n<ul>\n<li>pressio<\/li>\n<li>temperatura<\/li>\n<li>volumen<\/li>\n<li>energia interna<\/li>\n<\/ul>\n<p>Exempla quantitatum quae non sunt functiones status includunt positionem particulae millesimae systematis, opus et calorem totalem systemati applicatum. Hoc ultimum intellegi potest intuitive observando manus tuas attingere eandem temperaturam (et ergo eundem statum) per duos processus diversos: unum applicando quandam quantitatem operis, eas inter se fricando, aut calorem applicando, manus in aqua tepida ponendo.<\/p>\n<p><a name=\"3\"><\/a><\/p>\n<h2>Notio mathematica functionis status<\/h2>\n<p>His notionibus intuitivis habitis, ad plenioris intellectus consecutionem tantum deest expositio magis mathematica de significatione post functionem status. Consideremus systema ut descriptum per vectorem parameterum <span class=\"katex-eq\" data-katex-display=\"false\">\\vec{x}=(x_1, x_2, x_3, \\cdots)<\/span> et sit <span class=\"katex-eq\" data-katex-display=\"false\">f(\\vec{x})<\/span> aliqua functio status. Tum si systema parameterum mutatur ex valore initiali <span class=\"katex-eq\" data-katex-display=\"false\">\\vec{x}_i<\/span> ad alium finalem <span class=\"katex-eq\" data-katex-display=\"false\">\\vec{x}_f,<\/span> tum variatio functionis <span class=\"katex-eq\" data-katex-display=\"false\">f<\/span> erit<\/p>\n<p style=\"text-align: center;\"><span class=\"katex-eq\" data-katex-display=\"false\">\\Delta f = \\displaystyle \\int_{\\vec{x}_i}^{\\vec{x}_f}df = f(\\vec{x}_f) - f(\\vec{x}_i)<\/span>\n<p>Si res ita se habent, tum variatio functionis status solum pendet a valoribus initialibus et finalibus <span class=\"katex-eq\" data-katex-display=\"false\">\\vec{x}.<\/span> Hoc fit cum quantitas <span class=\"katex-eq\" data-katex-display=\"false\">df<\/span> est <strong>differentiale exactum.<\/strong> Omnes functiones status habent differentiales exactos; contra, quantitas cuius differentiale non est exactum functio status esse non potest.<\/p>\n<p><a name=\"4\"><\/a><\/p>\n<h2>Aequatio gasorum idealium est aequatio status<\/h2>\n<p>In universum, semper fieri potest, saltem adproximative, invenire aequationem status quae conectat functiones status. Exemplum est <a href=\"https:\/\/toposuranos.com\/la-ecuacion-de-los-gases-ideales\/\" rel=\"noopener\" target=\"_blank\">aequatio status gasorum idealium<\/a> <span class=\"katex-eq\" data-katex-display=\"false\">f(P,V,T)=0<\/span> quae formam capit<\/p>\n<p style=\"text-align: center;\"><span class=\"katex-eq\" data-katex-display=\"false\">f(P,V,T) = PV - nRT = 0<\/span>\n","protected":false},"excerpt":{"rendered":"<p>Aequatio et Functio Status Thermodynamica nobis revelat quomodo describere et conectere statum systematis per notiones ut functiones et aequationes status. Quomodo inter se referuntur proprietates ut pressio, temperatura et aequatio gasorum idealium? Hoc contentum te ducet ad intellegendum regulas mathematicae et physicae quae regunt aequilibria universi, tuam intuitionem provocans et prospectum amplificans. Proposita Discendi: Ad [&hellip;]<\/p>\n","protected":false},"author":1,"featured_media":30827,"comment_status":"open","ping_status":"closed","sticky":false,"template":"","format":"standard","meta":{"iawp_total_views":13,"footnotes":""},"categories":[1250,1292],"tags":[],"class_list":["post-34746","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>Aequatio et Functio Status - toposuranos.com\/material<\/title>\n<meta name=\"description\" content=\"Quid est Aequatio Status? 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