{"id":3529,"date":"2015-04-27T09:09:31","date_gmt":"2015-04-27T12:09:31","guid":{"rendered":"https:\/\/www.antonioguilherme.web.br.com\/blog\/?page_id=3529"},"modified":"2025-09-30T10:54:46","modified_gmt":"2025-09-30T13:54:46","slug":"radiacao-termica","status":"publish","type":"page","link":"https:\/\/www.antonioguilherme.web.br.com\/blog\/materiais-eletricos-e-magneticos\/propriedades-termicas\/radiacao-termica\/","title":{"rendered":"Radia\u00e7\u00e3o T\u00e9rmica"},"content":{"rendered":"<p style=\"text-align: right;\"><span style=\"font-family: verdana, geneva, sans-serif; font-size: 14pt;\">&#8220;<em><strong>Uma vez que podemos produzir todos os tipos de luz por meio de corpos quentes, podemos atribuir, \u00e0 radia\u00e7\u00e3o em equil\u00edbrio t\u00e9rmico com corpos quentes, a temperatura desses corpos e, portanto, toda radia\u00e7\u00e3o, mesmo aquela proveniente de um corpo fosforescente, tem uma certa temperatura para cada cor.&#8221;<\/strong><\/em><\/span><\/p>\n<p style=\"text-align: right;\"><span style=\"font-family: verdana, geneva, sans-serif; font-size: 14pt;\">Wilhelm Wien<\/span><\/p>\n<hr \/>\n<p><span style=\"font-family: verdana, geneva, sans-serif;\">A radia\u00e7\u00e3o t\u00e9rmica consiste na radia\u00e7\u00e3o eletromagn\u00e9tica gerada pelo movimento t\u00e9rmico das part\u00edculas eletricamente carregadas que formam a mat\u00e9ria. <\/span><span style=\"font-family: verdana, geneva, sans-serif;\">Portanto, toda mat\u00e9ria, com temperatura superior ao zero absoluto, emite radia\u00e7\u00e3o eletromagn\u00e9tica e a transfer\u00eancia de energia ocorre mesmo atrav\u00e9s do v\u00e1cuo. <\/span><\/p>\n<p><span style=\"font-family: verdana, geneva, sans-serif;\">Exemplos importantes desta forma de transfer\u00eancia de calor s\u00e3o:<\/span><\/p>\n<ul>\n<li style=\"list-style-type: none;\">\n<ul>\n<li><span style=\"font-family: verdana, geneva, sans-serif;\">\u00a0o aquecimento da terra pelo sol;<\/span><\/li>\n<li><span style=\"font-family: verdana, geneva, sans-serif;\">\u00a0a l\u00e2mpada incandescente.<\/span><\/li>\n<\/ul>\n<\/li>\n<\/ul>\n<p><span style=\"font-family: verdana, geneva, sans-serif;\">Por se tratar de um fen\u00f4meno relacionado a part\u00edculas da mat\u00e9ria, seu comportamento somente foi explicado pela f\u00edsica qu\u00e2ntica.<\/span><\/p>\n<p><span style=\"font-family: verdana, geneva, sans-serif;\">A Figura 1 apresenta o espectro eletromagn\u00e9tico e a Figura 2 o espectro da luz vis\u00edvel. <\/span><\/p>\n<p><span style=\"font-family: verdana, geneva, sans-serif;\">Observa-se que o espectro da luz vis\u00edvel ocupa uma min\u00fascula parcela do espectro eletromagn\u00e9tico dentro da faixa da radia\u00e7\u00e3o t\u00e9rmica. <\/span><\/p>\n<p><span style=\"font-family: verdana, geneva, sans-serif;\">Portanto, surge a quest\u00e3o: por que nossa vis\u00e3o capta apenas esta parcela do espectro eletromagn\u00e9tico?<\/span><\/p>\n<figure id=\"attachment_22524\" aria-describedby=\"caption-attachment-22524\" style=\"width: 800px\" class=\"wp-caption aligncenter\"><a href=\"https:\/\/www.antonioguilherme.web.br.com\/blog\/wp-content\/uploads\/2020\/10\/espectro_elemag.png\"><img decoding=\"async\" class=\"wp-image-22524 size-full\" src=\"https:\/\/www.antonioguilherme.web.br.com\/blog\/wp-content\/uploads\/2020\/10\/espectro_elemag.png\" alt=\"\" width=\"800\" height=\"600\" srcset=\"https:\/\/www.antonioguilherme.web.br.com\/blog\/wp-content\/uploads\/2020\/10\/espectro_elemag.png 800w, https:\/\/www.antonioguilherme.web.br.com\/blog\/wp-content\/uploads\/2020\/10\/espectro_elemag-300x225.png 300w, https:\/\/www.antonioguilherme.web.br.com\/blog\/wp-content\/uploads\/2020\/10\/espectro_elemag-768x576.png 768w\" sizes=\"(max-width: 800px) 100vw, 800px\" \/><\/a><figcaption id=\"caption-attachment-22524\" class=\"wp-caption-text\">Figura 1. Espectro Eletromagn\u00e9tico<\/figcaption><\/figure>\n<figure id=\"attachment_22525\" aria-describedby=\"caption-attachment-22525\" style=\"width: 2000px\" class=\"wp-caption aligncenter\"><a href=\"https:\/\/www.antonioguilherme.web.br.com\/blog\/wp-content\/uploads\/2020\/10\/espectro_visivel.png\"><img decoding=\"async\" class=\"size-full wp-image-22525\" src=\"https:\/\/www.antonioguilherme.web.br.com\/blog\/wp-content\/uploads\/2020\/10\/espectro_visivel.png\" alt=\"\" width=\"2000\" height=\"612\" data-wp-editing=\"1\" srcset=\"https:\/\/www.antonioguilherme.web.br.com\/blog\/wp-content\/uploads\/2020\/10\/espectro_visivel.png 2000w, https:\/\/www.antonioguilherme.web.br.com\/blog\/wp-content\/uploads\/2020\/10\/espectro_visivel-300x92.png 300w, https:\/\/www.antonioguilherme.web.br.com\/blog\/wp-content\/uploads\/2020\/10\/espectro_visivel-1024x313.png 1024w, https:\/\/www.antonioguilherme.web.br.com\/blog\/wp-content\/uploads\/2020\/10\/espectro_visivel-768x235.png 768w, https:\/\/www.antonioguilherme.web.br.com\/blog\/wp-content\/uploads\/2020\/10\/espectro_visivel-1536x470.png 1536w, https:\/\/www.antonioguilherme.web.br.com\/blog\/wp-content\/uploads\/2020\/10\/espectro_visivel-1200x367.png 1200w, https:\/\/www.antonioguilherme.web.br.com\/blog\/wp-content\/uploads\/2020\/10\/espectro_visivel-1980x606.png 1980w\" sizes=\"(max-width: 2000px) 100vw, 2000px\" \/><\/a><figcaption id=\"caption-attachment-22525\" class=\"wp-caption-text\">Figura 2. Espectro da Luz vis\u00edvel. Fonte:Original Horst Frank, with some modifications by Jailbird. Traduci\u00f3n da versi\u00f3n de Alebergen. \/ CC BY-SA (https:\/\/creativecommons.org\/licenses\/by-sa\/3.0)<\/figcaption><\/figure>\n<p><span style=\"font-family: verdana, geneva, sans-serif;\">Durante muito tempo o mecanismo de trasfer\u00eancia de calor entre o sol e a terra permaneceu misterioso porque considerava-se imposs\u00edvel a propaga\u00e7\u00e3o de luz e calor atrav\u00e9s do v\u00e1cuo.<\/span><\/p>\n<hr \/>\n<h3 id='atividade-proposta'  id=\"boomdevs_1\"><span style=\"font-family: verdana, geneva, sans-serif;\">Atividade Proposta<\/span><\/h3>\n<p><span style=\"font-family: verdana, geneva, sans-serif;\">Assista o <a href=\"https:\/\/youtu.be\/rCfPQLVzus4?si=84rU3TPVSzoxizHL\" target=\"_blank\" rel=\"noopener\">v\u00eddeo<\/a> nesse link e relacione suas d\u00favidas, conceitos que desconhecia, e suas discord\u00e2ncias.<\/span><\/p>\n<hr \/>\n<p><span style=\"font-family: verdana, geneva, sans-serif;\">Somente em 1900, <a href=\"http:\/\/pt.wikipedia.org\/wiki\/Max_Planck\" target=\"_blank\" rel=\"noopener noreferrer\">Planck<\/a> prop\u00f4s que a distribui\u00e7\u00e3o espectral da pot\u00eancia radiada por um <strong>Corpo Negro<\/strong> seria dada por: <span id='easy-footnote-1-3529' class='easy-footnote-margin-adjust'><\/span><span class='easy-footnote'><a href=\"https:\/\/www.antonioguilherme.web.br.com\/blog\/materiais-eletricos-e-magneticos\/propriedades-termicas\/radiacao-termica\/#easy-footnote-bottom-1-3529\" title=\" [8,Yunus] Deve-se ter cuidado ao utilizar esta express\u00e3o porque existem outras formas da equa\u00e7\u00e3o. \"><sup>1<\/sup><\/a><\/span><\/span><\/p>\n<figure id=\"attachment_43960\" aria-describedby=\"caption-attachment-43960\" style=\"width: 500px\" class=\"wp-caption aligncenter\"><img decoding=\"async\" class=\"wp-image-43960\" src=\"https:\/\/www.antonioguilherme.web.br.com\/blog\/wp-content\/uploads\/2023\/04\/radiancia_espectral_1.png\" alt=\"\" width=\"500\" height=\"121\" srcset=\"https:\/\/www.antonioguilherme.web.br.com\/blog\/wp-content\/uploads\/2023\/04\/radiancia_espectral_1.png 515w, https:\/\/www.antonioguilherme.web.br.com\/blog\/wp-content\/uploads\/2023\/04\/radiancia_espectral_1-300x73.png 300w\" sizes=\"(max-width: 500px) 100vw, 500px\" \/><figcaption id=\"caption-attachment-43960\" class=\"wp-caption-text\">Equa\u00e7\u00e3o 1. Irradi\u00e2ncia espectral<\/figcaption><\/figure>\n<p><span style=\"font-family: verdana, geneva, sans-serif;\">A Equa\u00e7\u00e3o 2 fornece os coeficientes C<sub>1<\/sub> e C<sub>2<\/sub>.<\/span><\/p>\n<figure id=\"attachment_22530\" aria-describedby=\"caption-attachment-22530\" style=\"width: 294px\" class=\"wp-caption aligncenter\"><a href=\"https:\/\/www.antonioguilherme.web.br.com\/blog\/wp-content\/uploads\/2020\/10\/const_irradiancia_espec.png\"><img decoding=\"async\" class=\"wp-image-22530 size-full\" src=\"https:\/\/www.antonioguilherme.web.br.com\/blog\/wp-content\/uploads\/2020\/10\/const_irradiancia_espec.png\" alt=\"\" width=\"294\" height=\"139\" \/><\/a><figcaption id=\"caption-attachment-22530\" class=\"wp-caption-text\">Equa\u00e7\u00e3o 2. Coeficientes da irradi\u00e2ncia espectral<\/figcaption><\/figure>\n<p><span style=\"font-family: verdana, geneva, sans-serif;\">Onde:<\/span><\/p>\n<ul>\n<li style=\"list-style-type: none;\">\n<ul>\n<li class=\"paragraph_style_3\"><span style=\"font-family: verdana, geneva, sans-serif;\">E<sub>b\u03bb<\/sub> \u00e9 a irradi\u00e2ncia espectral [W \/ (m2.\u03bcm)];<\/span><\/li>\n<li class=\"paragraph_style_3\"><span style=\"font-family: verdana, geneva, sans-serif;\">h \u00e9 a <a title=\"http:\/\/en.wikipedia.org\/wiki\/Planck_constant\" href=\"http:\/\/en.wikipedia.org\/wiki\/Planck_constant\" target=\"_blank\" rel=\"noopener\">constante de Planck<\/a> [6,626 069 57 e<sup><span class=\"style\">-34<\/span><\/sup>\u00a0 J.s];<\/span><\/li>\n<li class=\"paragraph_style_3\"><span style=\"font-family: verdana, geneva, sans-serif;\">c \u00e9 a <a title=\"http:\/\/en.wikipedia.org\/wiki\/Speed_of_light\" href=\"http:\/\/en.wikipedia.org\/wiki\/Speed_of_light\" target=\"_blank\" rel=\"noopener\">velocidade da luz<\/a> no meio em quest\u00e3o [ 299 792 458 m\/s no v\u00e1cuo];<\/span><\/li>\n<li class=\"paragraph_style_3\"><span style=\"font-family: verdana, geneva, sans-serif;\">\u03bb \u00e9 o comprimento de onda da radia\u00e7\u00e3o [m];<\/span><\/li>\n<li class=\"paragraph_style_3\"><span style=\"font-family: verdana, geneva, sans-serif;\">T \u00e9 a temperatura do corpo negro [K];<\/span><\/li>\n<li class=\"paragraph_style_3\"><span style=\"font-family: verdana, geneva, sans-serif;\">k \u00e9 a <a title=\"http:\/\/en.wikipedia.org\/wiki\/Boltzmann_constant#Value_in_different_units\" href=\"http:\/\/en.wikipedia.org\/wiki\/Boltzmann_constant#Value_in_different_units\" target=\"_blank\" rel=\"noopener\">constante de Boltzmann <\/a>[ 1,380 648 8 e<sup><span class=\"style\">-23 <\/span><\/sup>J\/K];<\/span><\/li>\n<li class=\"paragraph_style_3\"><span style=\"font-family: verdana, geneva, sans-serif;\">C<sub>1 <\/sub>e C<sub>2<\/sub> s\u00e3o constantes; <span id='easy-footnote-2-3529' class='easy-footnote-margin-adjust'><\/span><span class='easy-footnote'><a href=\"https:\/\/www.antonioguilherme.web.br.com\/blog\/materiais-eletricos-e-magneticos\/propriedades-termicas\/radiacao-termica\/#easy-footnote-bottom-2-3529\" title=\" As constantes C&lt;sub&gt;1&lt;\/sub&gt; e C&lt;sub&gt;2&lt;\/sub&gt; devem ser ajustadas cuidadosamente ao utilizarmos outras unidades. \"><sup>2<\/sup><\/a><\/span><\/span><\/li>\n<li><span style=\"font-family: verdana, geneva, sans-serif;\">C<sub>1<\/sub>= 3,742 e<sup>8<\/sup> [W.\u03bcm<sup>4<\/sup>\/m<sup>2\u00a0<\/sup>];<\/span><\/li>\n<li><span style=\"font-family: verdana, geneva, sans-serif;\">C<sub>2<\/sub> =1,439 e<sup>4<\/sup> [\u03bcm.K]<\/span><\/li>\n<\/ul>\n<\/li>\n<\/ul>\n<p><span style=\"font-family: verdana, geneva, sans-serif;\">A F\u00edsica define <strong>Corpo Negro<\/strong> como sendo o material que absorve e\/ou emite totalmente a radia\u00e7\u00e3o eletromagn\u00e9tica incidente\/emitida de\/para todas as dire\u00e7\u00f5es e comprimentos de onda. <\/span><\/p>\n<p><span style=\"font-family: verdana, geneva, sans-serif;\">De acordo com esta defini\u00e7\u00e3o, um Corpo Negro jamais poderia ser visto porque n\u00e3o reflete nenhuma luz, a menos que estivesse quente. Este conceito originou a denomina\u00e7\u00e3o de Buracos Negros.<\/span><\/p>\n<p><span style=\"font-family: verdana, geneva, sans-serif;\">Por analogia, o <strong>Corpo Branco<\/strong> se comporta ao contr\u00e1rio. <span id='easy-footnote-3-3529' class='easy-footnote-margin-adjust'><\/span><span class='easy-footnote'><a href=\"https:\/\/www.antonioguilherme.web.br.com\/blog\/materiais-eletricos-e-magneticos\/propriedades-termicas\/radiacao-termica\/#easy-footnote-bottom-3-3529\" title=\" Pode-se sentir isso na pr\u00e1tica ao caminhar descal\u00e7o no cal\u00e7ad\u00e3o de Copacabana num dia de ver\u00e3o. As pedras pretas se encontram sempre mais quentes que as brancas. \"><sup>3<\/sup><\/a><\/span><\/span><\/p>\n<p><span style=\"font-family: verdana, geneva, sans-serif;\">A Figura 3 apresenta as curvas da irradi\u00e2ncia espectral do corpo negro para diversas temperaturas. <\/span><\/p>\n<p><span style=\"font-family: verdana, geneva, sans-serif;\">A partir da dessa figura, observa-se que:<\/span><\/p>\n<ul>\n<li style=\"list-style-type: none;\">\n<ul>\n<li><span style=\"font-family: verdana, geneva, sans-serif;\">O espectro da radia\u00e7\u00e3o \u00e9 cont\u00ednuo com rela\u00e7\u00e3o \u00e0 frequ\u00eancia (comprimento de onda);<\/span><\/li>\n<li><span style=\"font-family: verdana, geneva, sans-serif;\">O espectro da radia\u00e7\u00e3o apresenta um valor m\u00e1ximo que aumenta com o aumento da temperatura;<\/span><\/li>\n<li><span style=\"font-family: verdana, geneva, sans-serif;\">A energia emitida aumenta com a temperatura para todas as frequ\u00eancias e, consequentemente, a energia total emitida aumenta com a temperatura;<\/span><\/li>\n<li><span style=\"font-family: verdana, geneva, sans-serif;\">O aumento da temperatura do corpo negro desloca a curva para mais altas frequ\u00eancias (menores comprimentos de onda).<\/span><\/li>\n<\/ul>\n<\/li>\n<\/ul>\n<p><span style=\"font-family: verdana, geneva, sans-serif;\">A maior temperatura apresentada na figura &#8211; 5 800K &#8211; corresponde aproximadamente \u00e0 temperatura na superf\u00edcie do sol e seu m\u00e1ximo se encontra dentro do espectro da luz vis\u00edvel. <\/span><\/p>\n<p><span style=\"font-family: verdana, geneva, sans-serif;\">Isto significa que nossos olhos evolu\u00edram para enxergar a luz do nosso sol.<\/span><\/p>\n<p style=\"text-align: center;\">\n<div class=\"wdt-wrapper-chart-loader\" data-id=\"130\"\n     style=\"height: 600px;\">\n    <div class=\"wdt-main-item\">\n                <div class=\"wdt-chart-animated-background\" style=\"height: 150px\">\n            <div 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           engine: \"google\",\n            type: \"google_line_chart\",\n            title: \"Irradi\u00e2ncia espectral do corpo negro\",\n            container: \"wpDataChart_130\",\n            follow_filtering: 0,\n            wpdatatable_id: 83,\n            group_chart: 0        }\n    <\/script>\n\n    <div id=\"wpDataChart_130\" class=\"google_line_chart\" style=\"width: 100%\"><\/div>\n<\/p>\n<p style=\"text-align: center;\"><span style=\"font-family: verdana, geneva, sans-serif; font-size: 12pt;\">Figura 3. Irradi\u00e2ncia Espectral do Corpo Negro<\/span><\/p>\n<p class=\"paragraph_style_3\"><span style=\"font-family: verdana, geneva, sans-serif;\">A integral da Equa\u00e7\u00e3o 1 com rela\u00e7\u00e3o ao comprimento de onda fornece a pot\u00eancia radiada por \u00e1rea ou fluxo de energia radiada. <\/span><\/p>\n<p class=\"paragraph_style_3\"><span style=\"font-family: verdana, geneva, sans-serif;\">A Equa\u00e7\u00e3o 3, deduzida por <a href=\"https:\/\/en.wikipedia.org\/wiki\/Stefan%E2%80%93Boltzmann_law\" target=\"_blank\" rel=\"noopener\">Stefan<\/a> em 1879, fornece o valor dessa integral apesar de Planck somente ter revelado a Equa\u00e7\u00e3o 1 posteriormente em 1900.<\/span><\/p>\n<p class=\"paragraph_style_3\"><span style=\"font-family: verdana, geneva, sans-serif;\"> Isto representa mais um exemplo da beleza da evolu\u00e7\u00e3o da ci\u00eancia, onde resultados experimentais antecipam descobertas te\u00f3ricas. <\/span><\/p>\n<p class=\"paragraph_style_3\"><span style=\"font-family: verdana, geneva, sans-serif;\">A Equa\u00e7\u00e3o 4 apenas real\u00e7a esta beleza, a constante de Stefan-Boltzman se revelou exata e definida a partir de outras constantes fundamentais da f\u00edsica descobertas ap\u00f3s a morte Stefan em 1894.<\/span><\/p>\n<figure id=\"attachment_3638\" aria-describedby=\"caption-attachment-3638\" style=\"width: 264px\" class=\"wp-caption aligncenter\"><a href=\"https:\/\/www.antonioguilherme.web.br.com\/blog\/wp-content\/uploads\/2015\/04\/P_irradiada-e1431274631762.png\"><img decoding=\"async\" class=\"wp-image-3638 size-full\" src=\"https:\/\/www.antonioguilherme.web.br.com\/blog\/wp-content\/uploads\/2015\/04\/P_irradiada-e1431274631762.png\" alt=\"\" width=\"264\" height=\"50\" \/><\/a><figcaption id=\"caption-attachment-3638\" class=\"wp-caption-text\"><span style=\"font-family: verdana, geneva, sans-serif;\">Equa\u00e7\u00e3o 3. Lei de Stefan-Boltzmann<\/span><\/figcaption><\/figure>\n<figure id=\"attachment_22536\" aria-describedby=\"caption-attachment-22536\" style=\"width: 260px\" class=\"wp-caption aligncenter\"><a href=\"https:\/\/www.antonioguilherme.web.br.com\/blog\/wp-content\/uploads\/2020\/10\/stefan_boltzman.png\"><img decoding=\"async\" class=\"wp-image-22536 size-full\" src=\"https:\/\/www.antonioguilherme.web.br.com\/blog\/wp-content\/uploads\/2020\/10\/stefan_boltzman.png\" alt=\"\" width=\"260\" height=\"101\" \/><\/a><figcaption id=\"caption-attachment-22536\" class=\"wp-caption-text\">Equa\u00e7\u00e3o 4. Constante de Stefan-Boltzmann<\/figcaption><\/figure>\n<p class=\"paragraph_style_3\"><span style=\"font-family: verdana, geneva, sans-serif;\">Onde:<\/span><\/p>\n<ul>\n<li style=\"list-style-type: none;\">\n<ul>\n<li><span style=\"font-family: verdana, geneva, sans-serif;\">E<sub>b<\/sub> \u00e9 a pot\u00eancia radiada por um corpo negro [W];<\/span><\/li>\n<li><span style=\"font-family: verdana, geneva, sans-serif;\">\u03c3 \u00e9 a constante de <a href=\"http:\/\/en.wikipedia.org\/wiki\/Stefan%E2%80%93Boltzmann_constant\" target=\"_blank\" rel=\"noopener noreferrer\">Stefan-Boltzmann<\/a> [5,670 374 419 e<sup>-8<\/sup> W\/(m<sup>2 <\/sup>K<sup>4<\/sup>)];<\/span><\/li>\n<li><span style=\"font-family: verdana, geneva, sans-serif;\">A \u00e9 a \u00e1rea [m<sup>2<\/sup>];<\/span><\/li>\n<li><span style=\"font-family: verdana, geneva, sans-serif;\">T \u00e9 a temperatura [K];<\/span><\/li>\n<li><span style=\"font-family: verdana, geneva, sans-serif;\"><span style=\"font-family: verdana, geneva, sans-serif;\">k \u00e9 a constante de Boltzmann [1,380 649 000 00 e<sup>-23<\/sup> (J\/Hz)];<\/span><\/span><\/li>\n<li><span style=\"font-family: verdana, geneva, sans-serif;\"><span style=\"font-family: verdana, geneva, sans-serif;\">c \u00e9 a velocidade da luz [2,997 924 58 e<sup>8<\/sup> (m\/s)];<\/span><\/span><\/li>\n<li><span style=\"font-family: verdana, geneva, sans-serif;\">h \u00e9 a constante de Planck [6.62607015000 e<sup>-34<\/sup> (J\/Hz)].<\/span><\/li>\n<\/ul>\n<\/li>\n<\/ul>\n<p><span style=\"font-family: verdana, geneva, sans-serif;\">A Equa\u00e7\u00e3o 5 apresenta a Irradi\u00e2ncia Espectral Normalizada com rela\u00e7\u00e3o \u00e0 temperatura, tamb\u00e9m chamada de fun\u00e7\u00e3o<strong>\u00a0corpo negro<\/strong>, que consiste na equa\u00e7\u00e3o 1 dividida pela temperatura elevada a quinta pot\u00eancia.<\/span><\/p>\n<figure id=\"attachment_5552\" aria-describedby=\"caption-attachment-5552\" style=\"width: 500px\" class=\"wp-caption aligncenter\"><a href=\"https:\/\/www.antonioguilherme.web.br.com\/blog\/wp-content\/uploads\/2015\/04\/planck5.png\"><img decoding=\"async\" class=\"wp-image-5552\" src=\"https:\/\/www.antonioguilherme.web.br.com\/blog\/wp-content\/uploads\/2015\/04\/planck5.png\" alt=\"planck5\" width=\"500\" height=\"88\" srcset=\"https:\/\/www.antonioguilherme.web.br.com\/blog\/wp-content\/uploads\/2015\/04\/planck5.png 815w, https:\/\/www.antonioguilherme.web.br.com\/blog\/wp-content\/uploads\/2015\/04\/planck5-300x53.png 300w, https:\/\/www.antonioguilherme.web.br.com\/blog\/wp-content\/uploads\/2015\/04\/planck5-768x135.png 768w\" sizes=\"(max-width: 500px) 100vw, 500px\" \/><\/a><figcaption id=\"caption-attachment-5552\" class=\"wp-caption-text\"><span style=\"font-family: verdana, geneva, sans-serif;\">Equa\u00e7\u00e3o 5. Irradi\u00e2ncia Espectral Normalizada<\/span><\/figcaption><\/figure>\n<p class=\"Free_Form\"><span style=\"font-family: verdana, geneva, sans-serif;\">A Figura 4 apresenta o gr\u00e1fico desta express\u00e3o.<\/span><\/p>\n<p class=\"Free_Form\"><span style=\"font-family: verdana, geneva, sans-serif;\"> Observa-se que a Irradi\u00e2ncia Espectral Normalizada independe da temperatura e pode ser utilizada para resolver diversos problemas pr\u00e1ticos.<\/span><\/p>\n<p style=\"text-align: center;\">\n<div class=\"wdt-wrapper-chart-loader\" data-id=\"131\"\n     style=\"height: 600px;\">\n    <div class=\"wdt-main-item\">\n                <div class=\"wdt-chart-animated-background\" style=\"height: 150px\">\n            <div class=\"wdt-background-masker wdt-btn-divide-left wdt-chart-one\"><\/div>\n            <div class=\"wdt-background-masker wdt-btn-divide-left-2\"><\/div>\n            <div class=\"wdt-background-masker wdt-btn-divide-left-3\"><\/div>\n            <div 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class=\"wdt-chart-animated-background\" style=\"height: 150px\">\n            <div class=\"wdt-background-masker wdt-btn-divide-left\"><\/div>\n            <div class=\"wdt-background-masker wdt-btn-divide-left-2\"><\/div>\n            <div class=\"wdt-background-masker wdt-btn-divide-left-3\"><\/div>\n            <div class=\"wdt-background-masker wdt-btn-divide-left-4\"><\/div>\n            <div class=\"wdt-background-masker wdt-btn-divide-left-5\"><\/div>\n            <div class=\"wdt-background-masker wdt-btn-divide-left-6\"><\/div>\n            <div class=\"wdt-background-masker wdt-btn-divide-left-7\"><\/div>\n            <div class=\"wdt-background-masker wdt-btn-divide-left-8\"><\/div>\n        <\/div>\n        <div class=\"wdt-static-background\">\n            <div class=\"wdt-background-masker\"><\/div>\n        <\/div>\n    <\/div>\n<\/div>\n<style>\n    \n<\/style>    <script type=\"text\/javascript\">\n        if (typeof (wpDataCharts) == 'undefined') wpDataCharts = {};\n  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[MW\\\/(m2.um.T5]\",\"color\":\"#3366CC\",\"orig_header\":\"irradiancianormalizadawm2umt5\"}],\"group_chart\":false,\"loader\":true,\"chartLoaderColorSettings\":\"\",\"chartLoaderAnimationColorSettings\":\"\",\"show_grid\":true,\"type\":\"google_line_chart\"},\n            engine: \"google\",\n            type: \"google_line_chart\",\n            title: \"Irradi\u00e2ncia Normalizada\",\n            container: \"wpDataChart_131\",\n            follow_filtering: 0,\n            wpdatatable_id: 135,\n            group_chart: 0        }\n    <\/script>\n\n    <div id=\"wpDataChart_131\" class=\"google_line_chart\" style=\"width: 100%\"><\/div>\n<\/p>\n<p style=\"text-align: center;\"><span style=\"font-family: verdana, geneva, sans-serif; font-size: 12pt;\">Figura 4. Irradi\u00e2ncia Espectral Normalizada<\/span><\/p>\n<p class=\"Free_Form\"><span style=\"font-family: verdana, geneva, sans-serif;\">Por exemplo, a Irradi\u00e2ncia Espectral Normalizada m\u00e1xima ocorre sempre com o produto \u03bbT igual a 2897,8 \u03bcm.K e isto ficou conhecido como a <a href=\"http:\/\/en.wikipedia.org\/wiki\/Wien%27s_displacement_law\" target=\"_blank\" rel=\"noopener noreferrer\"><strong>Lei de Wien<\/strong><\/a>. <\/span><\/p>\n<p class=\"Free_Form\"><span style=\"font-family: verdana, geneva, sans-serif;\">Mais uma vez, esta descoberta experimental se tornou p\u00fablica antes de Planck revelar a sua equa\u00e7\u00e3o.<\/span><\/p>\n<div id=\"id5\" class=\"style_SkipStroke_1 shape-with-text\">\n<div class=\"text-content graphic_textbox_layout_style_default_External_660_92\">\n<div class=\"graphic_textbox_layout_style_default\">\n<p class=\"Free_Form\"><span style=\"font-family: verdana, geneva, sans-serif;\">Em decorr\u00eancia desta lei, corpos s\u00f3lidos aquecidos come\u00e7am a emitir luz vis\u00edvel<span id='easy-footnote-4-3529' class='easy-footnote-margin-adjust'><\/span><span class='easy-footnote'><a href=\"https:\/\/www.antonioguilherme.web.br.com\/blog\/materiais-eletricos-e-magneticos\/propriedades-termicas\/radiacao-termica\/#easy-footnote-bottom-4-3529\" title=\" ver a refer\u00eancia 3 \"><sup>4<\/sup><\/a><\/span> quando atingem a temperatura de <strong>798 K (524,85 \u00baC)<\/strong>, chamada de <a href=\"http:\/\/en.wikipedia.org\/wiki\/Draper_point\" target=\"_blank\" rel=\"noopener noreferrer\"><strong>Ponto de Draper<\/strong><\/a>. <\/span><\/p>\n<p class=\"Free_Form\"><span style=\"font-family: verdana, geneva, sans-serif;\">Esta emiss\u00e3o come\u00e7a com um tom vermelho escuro e com o aumento da temperatura passa para um tom mais azulado at\u00e9 atingir o \u201cbranco quente\u201d. <\/span><\/p>\n<p class=\"Free_Form\"><span style=\"font-family: verdana, geneva, sans-serif;\">Esta lei se tornou extremamente \u00fatil para realizarmos medi\u00e7\u00f5es de temperatura razoavelmente precisas utilizando apenas a vis\u00e3o ou equipamentos \u00f3ticos.<\/span><\/p>\n<p class=\"Free_Form\"><span style=\"font-family: verdana, geneva, sans-serif;\">Al\u00e9m disso, um corpo negro no Ponto de Draper emite aproximadamente 23 kW\/m<sup>2<\/sup> praticamente toda no infravermelho.<\/span><\/p>\n<p class=\"Free_Form\"><span style=\"font-family: verdana, geneva, sans-serif;\">A equa\u00e7\u00e3o 6 relaciona a frequ\u00eancia com a temperatura no Ponto de Draper.<\/span><\/p>\n<figure id=\"attachment_21937\" aria-describedby=\"caption-attachment-21937\" style=\"width: 337px\" class=\"wp-caption aligncenter\"><a href=\"https:\/\/www.antonioguilherme.web.br.com\/blog\/wp-content\/uploads\/2020\/09\/draper.png\"><img decoding=\"async\" class=\"wp-image-21937 size-full\" src=\"https:\/\/www.antonioguilherme.web.br.com\/blog\/wp-content\/uploads\/2020\/09\/draper.png\" alt=\"\" width=\"337\" height=\"87\" srcset=\"https:\/\/www.antonioguilherme.web.br.com\/blog\/wp-content\/uploads\/2020\/09\/draper.png 337w, https:\/\/www.antonioguilherme.web.br.com\/blog\/wp-content\/uploads\/2020\/09\/draper-300x77.png 300w\" sizes=\"(max-width: 337px) 100vw, 337px\" \/><\/a><figcaption id=\"caption-attachment-21937\" class=\"wp-caption-text\">Equa\u00e7\u00e3o 6. Ponto de Draper<\/figcaption><\/figure>\n<p><span style=\"font-family: verdana, geneva, sans-serif;\">Onde<\/span>:<\/p>\n<ul>\n<li style=\"list-style-type: none;\">\n<ul>\n<li><span style=\"font-family: verdana, geneva, sans-serif;\"><em>v<\/em> \u00e9 a frequ\u00eancia [Hz]<\/span><\/li>\n<li><span style=\"font-family: verdana, geneva, sans-serif;\">k \u00e9 a <a title=\"http:\/\/en.wikipedia.org\/wiki\/Boltzmann_constant#Value_in_different_units\" href=\"http:\/\/en.wikipedia.org\/wiki\/Boltzmann_constant#Value_in_different_units\" target=\"_blank\" rel=\"noopener\">constante de Boltzmann <\/a>[1,380 648 8 e<sup><span class=\"style\">-23 <\/span><\/sup>J\/K];<\/span><\/li>\n<li><span style=\"font-family: verdana, geneva, sans-serif;\">h \u00e9 a <a title=\"http:\/\/en.wikipedia.org\/wiki\/Planck_constant\" href=\"http:\/\/en.wikipedia.org\/wiki\/Planck_constant\" target=\"_blank\" rel=\"noopener\">constante de Planck<\/a> [6,626 069 57 e<sup><span class=\"style\">-34<\/span><\/sup>\u00a0 J.s];<\/span><\/li>\n<li><span style=\"font-family: verdana, geneva, sans-serif;\">T \u00e9 a temperatura [K].<\/span><\/li>\n<\/ul>\n<\/li>\n<\/ul>\n<\/div>\n<hr \/>\n<h6 id='problema-proposto'  id=\"boomdevs_2\"><span style=\"font-family: verdana, geneva, sans-serif;\">Problema Proposto<\/span><\/h6>\n<p><span style=\"font-family: verdana, geneva, sans-serif; letter-spacing: normal; font-size: 21px;\">Determine a frequ\u00eancia do ponto de Drapper emitida por seres humanos a 36,5 \u00baC e a situe no espectro eletromagn\u00e9tico.<\/span><\/p>\n<hr \/>\n<p><span style=\"font-family: verdana, geneva, sans-serif;\">Finalmente, precisamos considerar a quest\u00e3o da <\/span><strong style=\"font-family: verdana, geneva, sans-serif;\">Emissividade.\u00a0<\/strong><\/p>\n<\/div>\n<\/div>\n<p><span style=\"font-family: verdana, geneva, sans-serif;\">Corpos Negro e Branco representam casos limites da realidade. <\/span><\/p>\n<p><span style=\"font-family: verdana, geneva, sans-serif;\">Na pr\u00e1tica, os objetos e materiais emitem e absorvem menos radia\u00e7\u00e3o t\u00e9rmica do que o Corpo Negro.<\/span><\/p>\n<p><span style=\"font-family: verdana, geneva, sans-serif;\">Por isso, a Equa\u00e7\u00e3o 4 acrescenta um fator multiplicativo, denominado de <strong>Emissividade<\/strong> &#8211; \u03b5, \u00e0 Equa\u00e7\u00e3o 3. <\/span><\/p>\n<p><span style=\"font-family: verdana, geneva, sans-serif;\">Este fator adimensional se encontra entre 0 e 1 e ser\u00e1 abordado posteriormente.<\/span><\/p>\n<figure id=\"attachment_22550\" aria-describedby=\"caption-attachment-22550\" style=\"width: 296px\" class=\"wp-caption aligncenter\"><a href=\"https:\/\/www.antonioguilherme.web.br.com\/blog\/wp-content\/uploads\/2020\/10\/P_irradiada2.png\"><img decoding=\"async\" class=\"wp-image-22550 size-full\" src=\"https:\/\/www.antonioguilherme.web.br.com\/blog\/wp-content\/uploads\/2020\/10\/P_irradiada2.png\" alt=\"\" width=\"296\" height=\"49\" \/><\/a><figcaption id=\"caption-attachment-22550\" class=\"wp-caption-text\">Equa\u00e7\u00e3o 4. Equa\u00e7\u00e3o Stefan-Boltzmann com emissividade<\/figcaption><\/figure>\n<hr \/>\n<p><a href=\"https:\/\/youtu.be\/7hxYGaegxAM?si=s_YxVGX9_srlqXgX\" target=\"_blank\" rel=\"noopener\"><span style=\"font-family: verdana, geneva, sans-serif;\">Video<\/span><\/a><\/p>\n<hr \/>\n<h2 id='refer\u00eancias'  id=\"boomdevs_3\"><span style=\"font-family: verdana, geneva, sans-serif;\">Refer\u00eancias<a id=\"ref\"><\/a><\/span><\/h2>\n<ol>\n<li><span style=\"font-family: verdana, geneva, sans-serif;\">CAO, E., <strong>Heat Transfer in Process Engineering<\/strong>, McGraw-Hill, 2010<\/span><\/li>\n<li><span style=\"font-family: verdana, geneva, sans-serif;\">MAHAN, J.R.,<strong> Radiation Heat Transfer<\/strong>, John Wiley &amp; Sons, New York, 2002.<\/span><\/li>\n<li><span style=\"font-family: verdana, geneva, sans-serif;\">OSTLIE, A. D., CARROL, B., W., <strong>Introduction to Modern Stellar Astrophysics<\/strong>, Addison-Wesley, USA, 1996.<\/span><\/li>\n<li><span style=\"font-family: verdana, geneva, sans-serif;\">YUNUS, A. C., <strong>Heat Transfer &#8211; A Practical Approach<\/strong>, 2 edi\u00e7\u00e3o, McGraw-Hill, 2003.<\/span><\/li>\n<li><span style=\"font-family: verdana, geneva, sans-serif;\">INMETRO, <strong>Sistema Internacional de Unidades SI<\/strong>, 1<sup>\u00aa<\/sup> edi\u00e7\u00e3o Brasileira do The International System of Units, Rio de Janeiro, 2012, dispon\u00edvel em &lt;<a href=\"http:\/\/www.inmetro.gov.br\" target=\"_blank\" rel=\"noopener\">http:\/\/www.inmetro.gov.br<\/a>&gt;<\/span><\/li>\n<li><span style=\"font-family: verdana, geneva, sans-serif;\"><a title=\"Constantes F\u00edsicas\" href=\"https:\/\/www.antonioguilherme.web.br.com\/blog\/materiais\/constantes-fisicas\/\" target=\"_blank\" rel=\"noopener noreferrer\">Constantes F\u00edsicas<\/a><\/span><\/li>\n<li><span style=\"font-family: verdana, geneva, sans-serif;\"><a title=\"Espectro Eletromagn\u00e9tico\" href=\"https:\/\/www.antonioguilherme.web.br.com\/blog\/materiais\/particulas-materiais\/espectro-eletromagnetico\/\">Espectro Eletromagn\u00e9tico<\/a><\/span><\/li>\n<li><span style=\"font-family: verdana, geneva, sans-serif;\"><span style=\"font-family: verdana, geneva, sans-serif;\"><a href=\"https:\/\/en.wikipedia.org\/wiki\/Planck&#039;s_law#References\" target=\"_blank\" rel=\"noopener\">https:\/\/en.wikipedia.org\/wiki\/Planck&#8217;s_law#References<\/a><\/span><\/span><\/li>\n<\/ol>\n","protected":false},"excerpt":{"rendered":"<p>&#8220;Uma vez que podemos produzir todos os tipos de luz por meio de corpos quentes, podemos atribuir, \u00e0 radia\u00e7\u00e3o em equil\u00edbrio t\u00e9rmico com corpos quentes, a temperatura desses corpos e, portanto, toda radia\u00e7\u00e3o, mesmo aquela proveniente de um corpo fosforescente, tem uma certa temperatura para cada cor.&#8221; Wilhelm Wien A radia\u00e7\u00e3o t\u00e9rmica consiste na radia\u00e7\u00e3o [&hellip;]<\/p>\n","protected":false},"author":1,"featured_media":43955,"parent":2380,"menu_order":2,"comment_status":"closed","ping_status":"closed","template":"templates\/template-full-width.php","meta":{"_uag_custom_page_level_css":"","footnotes":""},"class_list":["post-3529","page","type-page","status-publish","has-post-thumbnail","hentry"],"uagb_featured_image_src":{"full":["https:\/\/www.antonioguilherme.web.br.com\/blog\/wp-content\/uploads\/2023\/04\/radiacao_termica.jpg",1200,280,false],"thumbnail":["https:\/\/www.antonioguilherme.web.br.com\/blog\/wp-content\/uploads\/2023\/04\/radiacao_termica-150x150.jpg",150,150,true],"medium":["https:\/\/www.antonioguilherme.web.br.com\/blog\/wp-content\/uploads\/2023\/04\/radiacao_termica-300x70.jpg",300,70,true],"medium_large":["https:\/\/www.antonioguilherme.web.br.com\/blog\/wp-content\/uploads\/2023\/04\/radiacao_termica-768x179.jpg",580,135,true],"large":["https:\/\/www.antonioguilherme.web.br.com\/blog\/wp-content\/uploads\/2023\/04\/radiacao_termica-1024x239.jpg",580,135,true],"1536x1536":["https:\/\/www.antonioguilherme.web.br.com\/blog\/wp-content\/uploads\/2023\/04\/radiacao_termica.jpg",1200,280,false],"2048x2048":["https:\/\/www.antonioguilherme.web.br.com\/blog\/wp-content\/uploads\/2023\/04\/radiacao_termica.jpg",1200,280,false],"post-thumbnail":["https:\/\/www.antonioguilherme.web.br.com\/blog\/wp-content\/uploads\/2023\/04\/radiacao_termica.jpg",1200,280,false],"twentytwenty-fullscreen":["https:\/\/www.antonioguilherme.web.br.com\/blog\/wp-content\/uploads\/2023\/04\/radiacao_termica.jpg",1200,280,false]},"uagb_author_info":{"display_name":"admin","author_link":"https:\/\/www.antonioguilherme.web.br.com\/blog\/author\/admin\/"},"uagb_comment_info":0,"uagb_excerpt":"&#8220;Uma vez que podemos produzir todos os tipos de luz por meio de corpos quentes, podemos atribuir, \u00e0 radia\u00e7\u00e3o em equil\u00edbrio t\u00e9rmico com corpos quentes, a temperatura desses corpos e, portanto, toda radia\u00e7\u00e3o, mesmo aquela proveniente de um corpo fosforescente, tem uma certa temperatura para cada cor.&#8221; Wilhelm Wien A radia\u00e7\u00e3o t\u00e9rmica consiste na radia\u00e7\u00e3o&hellip;","_links":{"self":[{"href":"https:\/\/www.antonioguilherme.web.br.com\/blog\/wp-json\/wp\/v2\/pages\/3529","targetHints":{"allow":["GET"]}}],"collection":[{"href":"https:\/\/www.antonioguilherme.web.br.com\/blog\/wp-json\/wp\/v2\/pages"}],"about":[{"href":"https:\/\/www.antonioguilherme.web.br.com\/blog\/wp-json\/wp\/v2\/types\/page"}],"author":[{"embeddable":true,"href":"https:\/\/www.antonioguilherme.web.br.com\/blog\/wp-json\/wp\/v2\/users\/1"}],"replies":[{"embeddable":true,"href":"https:\/\/www.antonioguilherme.web.br.com\/blog\/wp-json\/wp\/v2\/comments?post=3529"}],"version-history":[{"count":154,"href":"https:\/\/www.antonioguilherme.web.br.com\/blog\/wp-json\/wp\/v2\/pages\/3529\/revisions"}],"predecessor-version":[{"id":45277,"href":"https:\/\/www.antonioguilherme.web.br.com\/blog\/wp-json\/wp\/v2\/pages\/3529\/revisions\/45277"}],"up":[{"embeddable":true,"href":"https:\/\/www.antonioguilherme.web.br.com\/blog\/wp-json\/wp\/v2\/pages\/2380"}],"wp:featuredmedia":[{"embeddable":true,"href":"https:\/\/www.antonioguilherme.web.br.com\/blog\/wp-json\/wp\/v2\/media\/43955"}],"wp:attachment":[{"href":"https:\/\/www.antonioguilherme.web.br.com\/blog\/wp-json\/wp\/v2\/media?parent=3529"}],"curies":[{"name":"wp","href":"https:\/\/api.w.org\/{rel}","templated":true}]}}