{"id":34686,"date":"2021-04-22T13:00:39","date_gmt":"2021-04-22T13:00:39","guid":{"rendered":"https:\/\/toposuranos.com\/material\/?p=34686"},"modified":"2025-09-20T04:54:18","modified_gmt":"2025-09-20T04:54:18","slug":"la-capacitas-calorica","status":"publish","type":"post","link":"https:\/\/toposuranos.com\/material\/la\/la-capacitas-calorica\/","title":{"rendered":"La Capacitas Calorica"},"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>Capacitas Calorica<\/h1>\n<p style=\"text-align:center;\"><em>Numquamne quaesivisti quid vere fiat cum obiectum calefacias? <strong>Capacitas calorica<\/strong> est clavis ad intellegendum hoc phaenomenon fundamentale quod energiam, temperaturam et status physicos materiae coniungit. Hoc conceptum mirabile non solum explicat cur aqua tardius calefiat quam metallum, sed etiam maximi momenti est in regionibus ut thermodynamica, ingenieria et scientiae materialium.<\/em><\/p>\n<p style=\"text-align:center;\"><strong>Proposita Discendi<\/strong><\/p>\n<ol>\n<li><strong>Intelligere<\/strong> notionem capacitatis caloricae tamquam mensuram quantitatis energiae necessariae ad temperaturam systematis mutandam.<\/li>\n<li><strong>Applicare<\/strong> definitiones capacitatis caloricae specificae et molaris in contextibus practicis.<\/li>\n<\/ol>\n<p style=\"text-align:center;\"><strong><u>INDEX CONTENTORUM<\/u>:<\/strong><br \/>\n<a href=\"#1\">Quaestio de Capacitate calorica<\/a><br \/>\n<a href=\"#2\">Genera capacitatum caloricarum<\/a><br \/>\n<a href=\"#3\">Exercitationes<\/a>\n<\/p>\n<p><center><iframe class=\"lazyload\" width=\"560\" height=\"315\" data-src=\"https:\/\/www.youtube.com\/embed\/JkDcmM8CMv0\" 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>Quaestio de Capacitate calorica<\/h2>\n<p>Loqui de capacitate calorica nos in condicionem singularem ponit. Non est possibile \u00abrecondere calorem\u00bb in corpore quasi aquam in situla cum capacitate definita, exempli gratia, 5 litrorum. Hoc non est significatio verborum calor neque capacitas calorica. Re vera, hic error ex hereditate historica physicae oritur, cum antiquitus putabatur calorem esse genus substantiae, opinionem quam nunc scimus falsam esse. Hodie intellegimus calorem esse energiam in transitu quae variationes temperatura efficit, analogum ad modum quo labor est energia ad statum systematis mutandum adhibita.<\/p>\n<p>Ab origine sua, terminus satis temporis habuit ut in usu cotidiano physicae confirmaretur. Quapropter, etsi vocabula ut \u00abcapacitantia\u00bb aptiora videri possent, eum nunc reponere significaret tantum miliones librorum renominare sine ullo fructu significativo.<\/p>\n<p>Tamen, et non obstante, notio caloris et capacitatis non est praesertim difficilis; ad intellegendam ideam quam tradit sufficit tantum hanc quaestionem proponere:<\/p>\n<p><strong>Quam relationem servat calor cum mutatione temperaturae <span class=\"katex-eq\" data-katex-display=\"false\">\\Delta T<\/span> obiecti?<\/strong><\/p>\n<p><a href=\"https:\/\/www.youtube.com\/watch?v=JkDcmM8CMv0&amp;t=184s\" target=\"_blank\" rel=\"noopener\"><strong>Responsio ad hanc quaestionem<\/strong><\/a> provenit ex relatione differentiali <span class=\"katex-eq\" data-katex-display=\"false\">dQ = CdT,<\/span> ubi <span class=\"katex-eq\" data-katex-display=\"false\">C<\/span> est capacitas calorica.<\/p>\n<p style=\"text-align:center;\"><span class=\"katex-eq\" data-katex-display=\"false\">C:= \\dfrac{dQ}{dT}.<\/span>\n<p>Hic, dum meminerimus hanc nos docere quantum caloris opus sit ad temperaturam cuiusdam obiecti elevandam (nullam habet relationem cum facultate obiecti ad res calefaciendas), erroris periculum non subibimus. Ut ex definitione capacitatis caloricae colligi potest, hae unitates habet <span class=\"katex-eq\" data-katex-display=\"false\">[J\/K].<\/span>\n<p><a name=\"2\"><\/a><\/p>\n<h2>Genera capacitatum caloricarum<\/h2>\n<h3>Capacitates caloricae specificae<\/h3>\n<p>\n    <a href=\"https:\/\/www.youtube.com\/watch?v=JkDcmM8CMv0&amp;t=250s\" target=\"_blank\" rel=\"noopener\"><br \/>\n        <strong>Cum de capacitate calorica loquimur,<\/strong><br \/>\n    <\/a><br \/>\n    duae formae diversa existunt: usitata, quam iam proposuimus, et specifica. Differentia inter has est quod capacitas specifica refertur ad capacitatem caloricam per unitatem massae, definita per:\n<\/p>\n<p style=\"text-align:center;\"><span class=\"katex-eq\" data-katex-display=\"false\">c := \\dfrac{C}{m}<\/span>\n<p>Ubi <span class=\"katex-eq\" data-katex-display=\"false\">m<\/span> significat massam corporis.<\/p>\n<p>Si multiplicemus capacitatem specificam per massam molarem, obtinemus capacitatem caloricam molarem specificam, definitam ut:<\/p>\n<p style=\"text-align:center;\"><span class=\"katex-eq\" data-katex-display=\"false\">c_{mol} := c \\cdot m_{mol}<\/span>\n<p>Meminisse interest quod, pro magnitudinibus specificis, semper litterae minusculae adhibentur.<\/p>\n<h4>Exemplum<\/h4>\n<p>\n    <a href=\"https:\/\/www.youtube.com\/watch?v=JkDcmM8CMv0&amp;t=301s\" target=\"_blank\" rel=\"noopener\"><br \/>\n        <strong>Capacitas calorica specifica<\/strong><br \/>\n    <\/a><br \/>\n    aquae ad temperaturam ambientem (<span class=\"katex-eq\" data-katex-display=\"false\">26^\\circ C<\/span>) est:\n<\/p>\n<p style=\"text-align:center;\"><span class=\"katex-eq\" data-katex-display=\"false\">c = 4.181 \\cdot 10^3 \\left[\\dfrac{J}{kg \\cdot K}\\right]<\/span>\n<p>Calcula:<\/p>\n<table>\n<tbody>\n<tr>\n<td>\n<p>a) Energiam necessariam ad temperaturam <span class=\"katex-eq\" data-katex-display=\"false\">2 \\, [kg]<\/span> aquae augendam in <span class=\"katex-eq\" data-katex-display=\"false\">14^\\circ C<\/span>.<\/p>\n<\/td>\n<\/tr>\n<tr>\n<td>\n<p>b) Capacitatem caloricam <span class=\"katex-eq\" data-katex-display=\"false\">3 \\, [L]<\/span> aquae.<\/p>\n<\/td>\n<\/tr>\n<tr>\n<td>\n<p>c) Capacitatem caloricam specificam molarem aquae.<\/p>\n<\/td>\n<\/tr>\n<\/tbody>\n<\/table>\n<h3>Capacitas calorica sub pressione constanti et sub volumine constante<\/h3>\n<p><a href=\"https:\/\/www.youtube.com\/watch?v=JkDcmM8CMv0&amp;t=706s\" target=\"_blank\" rel=\"noopener\"><strong>Cum de gasibus cogitamus<\/strong><\/a> occurrimus cum difficultate addita. Hoc in casu quaeremus quantum caloris super systema applicare debeamus ut hoc temperaturam suam augeat in <span class=\"katex-eq\" data-katex-display=\"false\">1[K].<\/span> Hoc autem facere possumus duobus modis diversis.<\/p>\n<table>\n<tbody>\n<tr>\n<td style=\"width: 50px;\">(1)<\/td>\n<td>\n<p>Ponendo gas in arca sigillata et addendo calorem. Dum temperatura crescit, prohibetur gas ne se extendat ita ut volumen suum constet, sed consequentia pressio augetur. Hic modus cognoscitur ut \u00absub volumine constante\u00bb.<\/p>\n<\/td>\n<\/tr>\n<tr>\n<td style=\"width: 50px;\">(2)<\/td>\n<td>\n<p>Collocando gas in camera cum pistone mobili. Dum temperatura crescit, sinitur gasi pistonem pellere servata pressione interna constante, sed consequentia volumen augetur. Hic modus cognoscitur ut \u00absub pressione constanti\u00bb.<\/p>\n<\/td>\n<\/tr>\n<\/tbody>\n<\/table>\n<p>In ambobus casibus <strong>limitationes<\/strong> systemati imponimus. His in condicionibus, necesse erit definitionem capacitatis caloricae pro unoquoque casu mutare, atque habemus igitur capacitates caloricas sub volumine et pressione constante: <span class=\"katex-eq\" data-katex-display=\"false\">C_V<\/span> et <span class=\"katex-eq\" data-katex-display=\"false\">C_P<\/span> respective. Hae magnitudines scribuntur in terminis derivatarum partialium hoc modo:<\/p>\n<p style=\"text-align:center;\"><span class=\"katex-eq\" data-katex-display=\"false\">C_V = \\left(\\dfrac{\\partial Q}{\\partial T}\\right)_V<\/span>\n<p style=\"text-align:center;\"><span class=\"katex-eq\" data-katex-display=\"false\">C_P = \\left(\\dfrac{\\partial Q}{\\partial T}\\right)_P<\/span>\n<h4>Exemplum<\/h4>\n<p><a href=\"https:\/\/www.youtube.com\/watch?v=JkDcmM8CMv0&amp;t=887s\" target=\"_blank\" rel=\"noopener\"><strong>Capacitas calorica helii<\/strong><\/a> mensa sub volumine constanti est <span class=\"katex-eq\" data-katex-display=\"false\">3,12\\left[\\dfrac{kJ}{kg \\cdot K}\\right],<\/span> et cum sub pressione constanti metitur dat <span class=\"katex-eq\" data-katex-display=\"false\">5.19\\left[\\dfrac{kJ}{kg \\cdot K}\\right].<\/span> Calcula capacitates caloricas molares sub pressione et volumine constantibus.<\/p>\n<p><a name=\"3\"><\/a><\/p>\n<h2>Exercitationes:<\/h2>\n<p><center><iframe class=\"lazyload\" width=\"560\" height=\"315\" data-src=\"https:\/\/www.youtube.com\/embed\/-LyA5Alrb8A\" title=\"YouTube video player\" frameborder=\"0\" allow=\"accelerometer; autoplay; clipboard-write; encrypted-media; gyroscope; picture-in-picture\" allowfullscreen><\/iframe><\/center><\/p>\n<ol>\n<li>Oceanus mundi circiter <span class=\"katex-eq\" data-katex-display=\"false\">10^{21}[kg]<\/span> aquae continet. Calcula capacitatem caloricam oceanorum mundi. <a href=\"https:\/\/www.youtube.com\/watch?v=-LyA5Alrb8A&amp;t=42s\" target=\"_blank\" rel=\"noopener\"><strong>[SOLUTIO]<\/strong><\/a><\/li>\n<li>Consumptio energiae mundialis prope <span class=\"katex-eq\" data-katex-display=\"false\">13[TW]<\/span> est (et crescit) (<span class=\"katex-eq\" data-katex-display=\"false\">1TW=10^{12}[W]<\/span>). Si una tonna petrolei crudi (quae circiter 7 dolia petrolei respondet) comburitur, circiter <span class=\"katex-eq\" data-katex-display=\"false\">42[GJ]<\/span> producuntur ( <span class=\"katex-eq\" data-katex-display=\"false\">1[GJ]=10^9[J]<\/span> ). Si consumptio mundialis solum in petroleo sustentatur, quot dolia per secundum comburenda sunt? <a href=\"https:\/\/www.youtube.com\/watch?v=-LyA5Alrb8A&amp;t=169s\" target=\"_blank\" rel=\"noopener\"><strong>[SOLUTIO]<\/strong><\/a><\/li>\n<li>Capacitas calorica molaris auri est <span class=\"katex-eq\" data-katex-display=\"false\">25,4\\left[\\dfrac{J}{mol \\cdot K}\\right].<\/span> Densitas eius est <span class=\"katex-eq\" data-katex-display=\"false\">19,3\\cdot 10^3 \\left[\\frac{kg}{m^3}\\right].<\/span> Calcula capacitatem caloricam specificam auri et eius valorem correspondentem per unitatem voluminis. <a href=\"https:\/\/www.youtube.com\/watch?v=-LyA5Alrb8A&amp;t=375s\" target=\"_blank\" rel=\"noopener\"><strong>[SOLUTIO]<\/strong><\/a><\/li>\n<li>Duo corpora, cum capacitatibus caloricis <span class=\"katex-eq\" data-katex-display=\"false\">C_1<\/span> et <span class=\"katex-eq\" data-katex-display=\"false\">C_2<\/span> (assumptis independentibus a temperatura) et temperaturis initialibus <span class=\"katex-eq\" data-katex-display=\"false\">T_1<\/span> et <span class=\"katex-eq\" data-katex-display=\"false\">T_2<\/span> respective, in contactum ponuntur. Ostende temperaturam finalem corporis <span class=\"katex-eq\" data-katex-display=\"false\">T_f<\/span> datam esse per\n<span class=\"katex-eq\" data-katex-display=\"false\">T_f = \\dfrac{C_1 T_1 + C_2 T_2}{C_1 + C_2}<\/span>\n<p>Et si <span class=\"katex-eq\" data-katex-display=\"false\">C_1<\/span> multo maior est quam <span class=\"katex-eq\" data-katex-display=\"false\">C_2,<\/span> tunc habebitur<\/p>\n<span class=\"katex-eq\" data-katex-display=\"false\">T_f \\approx T_1 + \\dfrac{C_2}{C_1}(T_2 - T_1)<\/span>\n<p><a href=\"https:\/\/www.youtube.com\/watch?v=-LyA5Alrb8A&amp;t=726s\" target=\"_blank\" rel=\"noopener\"><strong>[SOLUTIO]<\/strong><\/a><\/li>\n<\/ol>\n","protected":false},"excerpt":{"rendered":"<p>Capacitas Calorica Numquamne quaesivisti quid vere fiat cum obiectum calefacias? Capacitas calorica est clavis ad intellegendum hoc phaenomenon fundamentale quod energiam, temperaturam et status physicos materiae coniungit. Hoc conceptum mirabile non solum explicat cur aqua tardius calefiat quam metallum, sed etiam maximi momenti est in regionibus ut thermodynamica, ingenieria et scientiae materialium. Proposita Discendi Intelligere [&hellip;]<\/p>\n","protected":false},"author":1,"featured_media":30645,"comment_status":"open","ping_status":"closed","sticky":false,"template":"","format":"standard","meta":{"iawp_total_views":2,"footnotes":""},"categories":[1250,1292],"tags":[],"class_list":["post-34686","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 v28.0 - https:\/\/yoast.com\/product\/yoast-seo-wordpress\/ -->\n<title>La Capacitas Calorica - toposuranos.com\/material<\/title>\n<meta name=\"description\" content=\"Quid est capacitas calorica et quomodo calorem in obiecta afficit? 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