{"id":1324,"date":"2026-03-05T10:43:49","date_gmt":"2026-03-05T14:43:49","guid":{"rendered":"https:\/\/fiziko.net\/?page_id=1324"},"modified":"2026-03-22T10:52:57","modified_gmt":"2026-03-22T14:52:57","slug":"termometria-e-calorimetria","status":"publish","type":"page","link":"https:\/\/fiziko.net\/?page_id=1324","title":{"rendered":"Termometria e Calorimetria"},"content":{"rendered":"\n<p>Os termos \u201c<strong>temperatura<\/strong>\u201d e \u201c<strong>calor<\/strong>\u201d costumam ser usados como sin\u00f4nimos na linguagem cotidiana. Em F\u00edsica, contudo, esses dois termos t\u00eam significados muito diferentes.<\/p>\n\n\n\n<p>O conceito de calor, utilizado no cotidiano \u00e9 confundido com a <strong>sensa\u00e7\u00e3o t\u00e9rmica<\/strong>. Podemos definir calor como:<\/p>\n\n\n\n<p><strong>Calor<\/strong> \u00e9 a <strong>energia em tr\u00e2nsito transferida entre sistemas devido exclusivamente a uma diferen\u00e7a de temperatura.<\/strong><\/p>\n\n\n\n<p>Pontos fundamentais:<\/p>\n\n\n\n<ul class=\"wp-block-list\">\n<li>Calor <strong>n\u00e3o \u00e9 uma sensa\u00e7\u00e3o<\/strong>.<\/li>\n\n\n\n<li>Calor <strong>n\u00e3o \u00e9 algo que um corpo \u201ctem\u201d<\/strong>, mas algo que <strong>\u00e9 transferido<\/strong>.<\/li>\n\n\n\n<li>O fluxo de calor ocorre <strong>do corpo de maior temperatura para o de menor temperatura<\/strong>.<\/li>\n<\/ul>\n\n\n\n<p>\ud83d\udc49 Exemplo f\u00edsico:<br>Uma panela quente transfere calor para sua m\u00e3o quando voc\u00ea a toca, porque existe uma diferen\u00e7a de temperatura entre os dois corpos.<\/p>\n\n\n\n<p>A <strong>sensa\u00e7\u00e3o t\u00e9rmica<\/strong> <strong>n\u00e3o \u00e9 uma grandeza f\u00edsica<\/strong>, e sim uma <strong>percep\u00e7\u00e3o humana<\/strong> de conforto ou desconforto t\u00e9rmico.<\/p>\n\n\n\n<p>Ela depende de <strong>como o corpo humano troca calor com o ambiente<\/strong>, e n\u00e3o apenas da temperatura do ar.<\/p>\n\n\n\n<p>Ou seja:<\/p>\n\n\n\n<ul class=\"wp-block-list\">\n<li>Sensa\u00e7\u00e3o t\u00e9rmica <strong>n\u00e3o mede calor<\/strong>.<\/li>\n\n\n\n<li>Sensa\u00e7\u00e3o t\u00e9rmica <strong>n\u00e3o mede temperatura real<\/strong>.<\/li>\n\n\n\n<li>Ela expressa <strong>como o ambiente \u201c\u00e9 sentido\u201d pelo corpo humano<\/strong>.<\/li>\n<\/ul>\n\n\n\n<p>Mesmo com a <strong>mesma temperatura<\/strong>, a sensa\u00e7\u00e3o pode mudar por causa de fatores que <strong>afetam a troca de calor entre o corpo e o ambiente<\/strong>, como:<\/p>\n\n\n\n<ul class=\"wp-block-list\">\n<li><strong>Velocidade do vento<\/strong><\/li>\n\n\n\n<li><strong>Umidade do ar<\/strong><\/li>\n\n\n\n<li><strong>Radia\u00e7\u00e3o solar<\/strong><\/li>\n\n\n\n<li><strong>Roupas e atividade f\u00edsica<\/strong><\/li>\n\n\n\n<li><strong>Estado fisiol\u00f3gico do corpo<\/strong><\/li>\n<\/ul>\n\n\n\n<p>Esses fatores alteram <strong>a taxa de perda ou ganho de calor do corpo<\/strong>, e n\u00e3o a temperatura do ar em si.<\/p>\n\n\n\n<figure class=\"wp-block-table\"><table class=\"has-fixed-layout\"><tbody><tr><th>Conceito<\/th><th>Calor<\/th><th>Sensa\u00e7\u00e3o t\u00e9rmica<\/th><\/tr><tr><td>Natureza<\/td><td>F\u00edsica<\/td><td>Fisiol\u00f3gica<\/td><\/tr><tr><td>\u00c9 energia?<\/td><td>Sim<\/td><td>N\u00e3o<\/td><\/tr><tr><td>\u00c9 mensur\u00e1vel fisicamente?<\/td><td>Sim (joule)<\/td><td>N\u00e3o diretamente<\/td><\/tr><tr><td>Depende do corpo humano?<\/td><td>N\u00e3o<\/td><td>Sim<\/td><\/tr><tr><td>Usada em leis da f\u00edsica?<\/td><td>Sim<\/td><td>N\u00e3o<\/td><\/tr><tr><td>Usada em meteorologia<\/td><td>Direta\/Indiretamente<\/td><td>Sim<\/td><\/tr><\/tbody><\/table><\/figure>\n\n\n\n<p>Na F\u00edsica, <strong>temperatura<\/strong> \u00e9 uma <strong>grandeza que caracteriza o estado t\u00e9rmico de um sistema<\/strong>, estando relacionada \u00e0 <strong>energia cin\u00e9tica m\u00e9dia das part\u00edculas microsc\u00f3picas (\u00e1tomos e mol\u00e9culas)<\/strong> que o comp\u00f5em.<\/p>\n\n\n\n<p>Em termos microsc\u00f3picos:<\/p>\n\n\n\n<ul class=\"wp-block-list\">\n<li>Quanto <strong>maior a temperatura<\/strong>, maior \u00e9 a <strong>agita\u00e7\u00e3o m\u00e9dia<\/strong> das part\u00edculas.<\/li>\n\n\n\n<li>Quanto <strong>menor a temperatura<\/strong>, menor \u00e9 essa agita\u00e7\u00e3o.<\/li>\n<\/ul>\n\n\n\n<p>Essa interpreta\u00e7\u00e3o \u00e9 central na <strong>teoria cin\u00e9tica dos gases<\/strong> e na <strong>termodin\u00e2mica estat\u00edstica<\/strong>.<\/p>\n\n\n\n<h3 class=\"wp-block-heading\">Propriedades importantes<\/h3>\n\n\n\n<ul class=\"wp-block-list\">\n<li>A temperatura <strong>n\u00e3o depende da quantidade de mat\u00e9ria<\/strong> (n\u00e3o \u00e9 extensiva).<\/li>\n\n\n\n<li>Dois corpos com massas muito diferentes podem ter <strong>a mesma temperatura<\/strong>, mesmo contendo quantidades muito diferentes de energia interna.<\/li>\n\n\n\n<li>A temperatura determina <strong>o sentido do fluxo de calor<\/strong>, conforme a <strong>Lei Zero da Termodin\u00e2mica<\/strong>.<\/li>\n<\/ul>\n\n\n\n<p>A temperatura \u00e9 definida <strong>operacionalmente<\/strong> como aquilo que um <strong>term\u00f4metro<\/strong> mede, sendo as escalas mais comuns:<\/p>\n\n\n\n<ul class=\"wp-block-list\">\n<li><strong>Kelvin (K)<\/strong> \u2013 escala absoluta usada em ci\u00eancia.<\/li>\n\n\n\n<li><strong>Celsius (\u00b0C)<\/strong> \u2013 uso cotidiano.<\/li>\n\n\n\n<li><strong>Fahrenheit (\u00b0F)<\/strong> \u2013 uso regional.<\/li>\n<\/ul>\n\n\n\n<p>O zero absoluto (0 K) corresponde ao estado de m\u00ednima agita\u00e7\u00e3o t\u00e9rmica poss\u00edvel.<\/p>\n\n\n\n<figure class=\"wp-block-table\"><table class=\"has-fixed-layout\"><tbody><tr><th>Aspecto<\/th><th>Temperatura<\/th><th>Calor<\/th><\/tr><tr><td>Natureza<\/td><td>Grandeza f\u00edsica<\/td><td>Processo de transfer\u00eancia<\/td><\/tr><tr><td>Depende da massa?<\/td><td>N\u00e3o<\/td><td>Sim<\/td><\/tr><tr><td>\u00c9 propriedade do sistema?<\/td><td>Sim<\/td><td>N\u00e3o<\/td><\/tr><tr><td>Unidade SI<\/td><td>Kelvin (K)<\/td><td>Joule (J)<\/td><\/tr><tr><td>Interpreta\u00e7\u00e3o microsc\u00f3pica<\/td><td>Energia cin\u00e9tica m\u00e9dia<\/td><td>Energia transferida<\/td><\/tr><\/tbody><\/table><\/figure>\n\n\n\n<h2 class=\"wp-block-heading\">Lei Zero da Termodin\u00e2mica<\/h2>\n\n\n\n<p>A Lei Zero da Termodin\u00e2mica pode ser enunciada da seguinte forma:<\/p>\n\n\n\n<blockquote class=\"wp-block-quote is-layout-flow wp-block-quote-is-layout-flow\">\n<p><strong>Se dois sistemas A e B est\u00e3o separadamente em equil\u00edbrio t\u00e9rmico com um terceiro sistema C, ent\u00e3o A e B est\u00e3o em equil\u00edbrio t\u00e9rmico entre si.<\/strong><\/p>\n<\/blockquote>\n\n\n\n<p>Esse enunciado parece simples, mas tem consequ\u00eancias profundas para toda a Termodin\u00e2mica.<\/p>\n\n\n\n<p>Do ponto de vista f\u00edsico podemos definir o <strong>Equil\u00edbrio T\u00e9rmico<\/strong> como:<\/p>\n\n\n\n<ul class=\"wp-block-list\">\n<li>Dois sistemas est\u00e3o em <strong>equil\u00edbrio t\u00e9rmico<\/strong> quando, ao serem colocados em contato t\u00e9rmico, <strong>n\u00e3o ocorre troca de calor entre eles<\/strong>.<\/li>\n\n\n\n<li>A aus\u00eancia de troca de calor indica que <strong>as temperaturas s\u00e3o iguais<\/strong>.<\/li>\n<\/ul>\n\n\n\n<p>A Lei Zero formaliza exatamente essa ideia: a <strong>igualdade de temperatura<\/strong> \u00e9 uma rela\u00e7\u00e3o <strong>transitiva<\/strong>.<\/p>\n\n\n\n<p>A denomina\u00e7\u00e3o \u201cLei Zero\u201d surgiu <strong>ap\u00f3s<\/strong> a formula\u00e7\u00e3o da Primeira e da Segunda Leis da Termodin\u00e2mica.<\/p>\n\n\n\n<ul class=\"wp-block-list\">\n<li>A ideia de equil\u00edbrio t\u00e9rmico j\u00e1 era usada implicitamente desde o desenvolvimento dos primeiros term\u00f4metros.<\/li>\n\n\n\n<li>No entanto, <strong>somente no s\u00e9culo XX<\/strong> essa rela\u00e7\u00e3o foi explicitamente reconhecida como um princ\u00edpio fundamental.<\/li>\n\n\n\n<li>O f\u00edsico brit\u00e2nico <strong>Ralph H. Fowler (1889\u20131944)<\/strong> prop\u00f4s que esse princ\u00edpio deveria vir <strong>antes<\/strong> das demais leis, pois define o pr\u00f3prio conceito de temperatura.<\/li>\n<\/ul>\n\n\n\n<p>Como a Primeira e a Segunda Leis j\u00e1 estavam nomeadas, a solu\u00e7\u00e3o foi cham\u00e1\u2011la de <strong>Lei Zero<\/strong> \u2014 indicando sua preced\u00eancia l\u00f3gica, n\u00e3o cronol\u00f3gica.<\/p>\n\n\n\n<p>A Lei Zero permite definir <strong>temperatura como uma grandeza f\u00edsica bem\u2011definida<\/strong>, independente da subst\u00e2ncia utilizada para medi\u2011la.<\/p>\n\n\n\n<p>Sem essa lei:<\/p>\n\n\n\n<ul class=\"wp-block-list\">\n<li>N\u00e3o haveria garantia de que diferentes term\u00f4metros concordariam entre si.<\/li>\n\n\n\n<li>A no\u00e7\u00e3o de \u201cmesma temperatura\u201d seria subjetiva.<\/li>\n<\/ul>\n\n\n\n<p>Por isso, diz\u2011se que a Lei Zero <strong>fundamenta o conceito de temperatura<\/strong>.<\/p>\n\n\n\n<p>Um <strong>term\u00f4metro<\/strong> funciona como o <strong>terceiro sistema (C)<\/strong> da Lei Zero:<\/p>\n\n\n\n<ul class=\"wp-block-list\">\n<li>Se o term\u00f4metro entra em equil\u00edbrio t\u00e9rmico com o corpo A, ele indica a temperatura de A.<\/li>\n\n\n\n<li>Se o mesmo term\u00f4metro entra em equil\u00edbrio com o corpo B e indica o mesmo valor, ent\u00e3o A e B t\u00eam a mesma temperatura.<\/li>\n<\/ul>\n\n\n\n<p>Esse racioc\u00ednio \u00e9 diretamente sustentado pela Lei Zero.<\/p>\n\n\n\n<p>A Lei Zero \u00e9 logicamente anterior \u00e0s demais:<\/p>\n\n\n\n<ul class=\"wp-block-list\">\n<li><strong>Lei Zero<\/strong> \u2192 define temperatura e equil\u00edbrio t\u00e9rmico<\/li>\n\n\n\n<li><strong>Primeira Lei<\/strong> \u2192 relaciona calor, trabalho e energia interna, estabelecendo a Lei da Conserva\u00e7\u00e3o de Energia<\/li>\n\n\n\n<li><strong>Segunda Lei<\/strong> \u2192 estabelece o sentido natural das transforma\u00e7\u00f5es t\u00e9rmicas e estuda a disponibilidade da energia \u00fatil<\/li>\n\n\n\n<li><strong>Terceira Lei<\/strong> \u2192 trata do comportamento da entropia em temperaturas extremas, como no zero absoluto (0K)<\/li>\n<\/ul>\n\n\n\n<p>Sem a Lei Zero, as outras leis <strong>n\u00e3o teriam uma base operacional clara<\/strong>, pois a temperatura n\u00e3o estaria bem definida.<\/p>\n\n\n\n<h2 class=\"wp-block-heading\">Escalas de Temperatura<\/h2>\n\n\n\n<p>Uma <strong>escala de temperatura<\/strong> \u00e9 um <strong>sistema de atribui\u00e7\u00e3o de valores num\u00e9ricos<\/strong> \u00e0 grandeza f\u00edsica <strong>temperatura<\/strong>, permitindo comparar estados t\u00e9rmicos de diferentes sistemas.<br>Do ponto de vista cient\u00edfico, a constru\u00e7\u00e3o de escalas de temperatura \u00e9 fundamentada na <strong>Lei Zero da Termodin\u00e2mica<\/strong>, que garante a exist\u00eancia de uma grandeza comum associada ao equil\u00edbrio t\u00e9rmico. <\/p>\n\n\n\n<p>As escalas podem ser classificadas em:<\/p>\n\n\n\n<ul class=\"wp-block-list\">\n<li><strong>Escalas emp\u00edricas<\/strong>: baseadas em propriedades f\u00edsicas mensur\u00e1veis (como dilata\u00e7\u00e3o de l\u00edquidos).<\/li>\n\n\n\n<li><strong>Escalas absolutas (termodin\u00e2micas)<\/strong>: fundamentadas em princ\u00edpios da termodin\u00e2mica e no conceito de zero absoluto.<\/li>\n<\/ul>\n\n\n\n<p>A <strong>escala Celsius<\/strong> foi proposta em 1742 pelo astr\u00f4nomo sueco <strong>Anders Celsius<\/strong>. Originalmente, a escala era invertida (0 \u00b0C para ebuli\u00e7\u00e3o e 100 \u00b0C para fus\u00e3o da \u00e1gua), sendo posteriormente ajustada para a forma atual.<\/p>\n\n\n\n<ul class=\"wp-block-list\">\n<li><strong>0 \u00b0C<\/strong> \u2192 ponto de fus\u00e3o da \u00e1gua (a 1 atm)<\/li>\n\n\n\n<li><strong>100 \u00b0C<\/strong> \u2192 ponto de ebuli\u00e7\u00e3o da \u00e1gua (a 1 atm)<\/li>\n\n\n\n<li>Intervalo dividido em <strong>100 partes iguais<\/strong><\/li>\n<\/ul>\n\n\n\n<p>A escala Celsius \u00e9 <strong>emp\u00edrica<\/strong>, mas possui <strong>incrementos id\u00eanticos aos da escala Kelvin<\/strong> (1 \u00b0C = 1 K). <\/p>\n\n\n\n<ul class=\"wp-block-list\">\n<li>Escala mais utilizada no mundo para fins cotidianos<\/li>\n\n\n\n<li>Amplamente empregada em ensino, meteorologia e aplica\u00e7\u00f5es t\u00e9cnicas.<\/li>\n<\/ul>\n\n\n\n<p>A <strong>escala Fahrenheit<\/strong> foi criada em 1724 pelo f\u00edsico e instrumentista <strong>Daniel Gabriel Fahrenheit<\/strong>, juntamente com o desenvolvimento do term\u00f4metro de merc\u00fario. <\/p>\n\n\n\n<ul class=\"wp-block-list\">\n<li><strong>32 \u00b0F<\/strong> \u2192 congelamento da \u00e1gua<\/li>\n\n\n\n<li><strong>212 \u00b0F<\/strong> \u2192 ebuli\u00e7\u00e3o da \u00e1gua<\/li>\n\n\n\n<li>Intervalo de <strong>180 divis\u00f5es<\/strong><\/li>\n<\/ul>\n\n\n\n<p>Ainda podemos destacar<\/p>\n\n\n\n<ul class=\"wp-block-list\">\n<li>Escala emp\u00edrica<\/li>\n\n\n\n<li>Incremento diferente do Celsius e Kelvin<\/li>\n\n\n\n<li>Valores n\u00e3o diretamente relacionados ao zero absoluto.<\/li>\n\n\n\n<li>Utilizada principalmente nos <strong>Estados Unidos<\/strong> e em alguns territ\u00f3rios associados<\/li>\n\n\n\n<li>Presente em aplica\u00e7\u00f5es meteorol\u00f3gicas e dom\u00e9sticas nesses pa\u00edses.<\/li>\n<\/ul>\n\n\n\n<p>A <strong>escala Kelvin<\/strong> \u00e9 a <strong>escala absoluta de temperatura<\/strong> e a <strong>unidade base do Sistema Internacional de Unidades (SI)<\/strong> para temperatura termodin\u00e2mica.<\/p>\n\n\n\n<p>Ela foi proposta em 1848 por <strong>William Thomson<\/strong>, conhecido como <strong>Lorde Kelvin<\/strong>, com base em princ\u00edpios da termodin\u00e2mica.<\/p>\n\n\n\n<ul class=\"wp-block-list\">\n<li><strong>0 K<\/strong> \u2192 zero absoluto (estado de m\u00ednima energia t\u00e9rmica)<\/li>\n\n\n\n<li>O incremento \u00e9 definido de modo que:\n<ul class=\"wp-block-list\">\n<li><strong>1 K = 1 \u00b0C<\/strong> em varia\u00e7\u00e3o de temperatura<\/li>\n<\/ul>\n<\/li>\n\n\n\n<li>N\u00e3o utiliza o termo \u201cgrau\u201d (escreve\u2011se apenas K)<\/li>\n<\/ul>\n\n\n\n<p>A defini\u00e7\u00e3o moderna est\u00e1 relacionada ao <strong>ponto triplo da \u00e1gua (273,16 K)<\/strong>, conforme padroniza\u00e7\u00e3o metrol\u00f3gica internacional.<\/p>\n\n\n\n<p>A escala Kelvin \u00e9 essencial porque:<\/p>\n\n\n\n<ul class=\"wp-block-list\">\n<li>Evita valores negativos<\/li>\n\n\n\n<li>\u00c9 indispens\u00e1vel em equa\u00e7\u00f5es da termodin\u00e2mica, como a <strong>lei dos gases ideais<\/strong><\/li>\n\n\n\n<li>Representa diretamente o conte\u00fado energ\u00e9tico microsc\u00f3pico do sistema. <\/li>\n<\/ul>\n\n\n\n<p>A <strong>escala Rankine<\/strong> \u00e9 uma <strong>escala absoluta<\/strong>, an\u00e1loga \u00e0 Kelvin, mas constru\u00edda a partir da escala Fahrenheit.<\/p>\n\n\n\n<ul class=\"wp-block-list\">\n<li><strong>0 \u00b0R<\/strong> \u2192 zero absoluto<\/li>\n\n\n\n<li>Incremento igual ao Fahrenheit<\/li>\n\n\n\n<li>Pouco utilizada atualmente<\/li>\n\n\n\n<li>Aparece em contextos espec\u00edficos da <strong>engenharia t\u00e9rmica<\/strong> em pa\u00edses que usam Fahrenheit.<\/li>\n<\/ul>\n\n\n\n<figure class=\"wp-block-table\"><table class=\"has-fixed-layout\"><tbody><tr><th>Escala<\/th><th>Tipo<\/th><th>Zero absoluto<\/th><th>Incremento<\/th><th>Uso principal<\/th><\/tr><tr><td>Celsius (\u00b0C)<\/td><td>Emp\u00edrica<\/td><td>\u2212273,15 \u00b0C<\/td><td>Igual ao K<\/td><td>Cotidiano e ensino<\/td><\/tr><tr><td>Fahrenheit (\u00b0F)<\/td><td>Emp\u00edrica<\/td><td>\u2212459,67 \u00b0F<\/td><td>Pr\u00f3prio<\/td><td>Uso regional<\/td><\/tr><tr><td>Kelvin (K)<\/td><td>Absoluta<\/td><td>0 K<\/td><td>Igual ao \u00b0C<\/td><td>Ci\u00eancia e SI<\/td><\/tr><tr><td>Rankine (\u00b0R)<\/td><td>Absoluta<\/td><td>0 \u00b0R<\/td><td>Igual ao \u00b0F<\/td><td>Engenharia<\/td><\/tr><\/tbody><\/table><\/figure>\n\n\n\n<p>Considerando <strong>\u00e1gua pura sob press\u00e3o atmosf\u00e9rica padr\u00e3o (1 atm)<\/strong> \u2014 que \u00e9 a condi\u00e7\u00e3o usada na defini\u00e7\u00e3o cl\u00e1ssica das escalas \u2014 os <strong>pontos de gelo (fus\u00e3o\/congelamento)<\/strong> e de <strong>vapor (ebuli\u00e7\u00e3o)<\/strong> s\u00e3o os seguintes:<\/p>\n\n\n\n<figure class=\"wp-block-table\"><table class=\"has-fixed-layout\"><tbody><tr><th>Escala<\/th><th>Ponto de gelo (fus\u00e3o)<\/th><th>Ponto de vapor (ebuli\u00e7\u00e3o)<\/th><\/tr><tr><th><strong>Celsius (\u00b0C)<\/strong><\/th><td>0 \u00b0C<\/td><td>100 \u00b0C<\/td><\/tr><tr><th><strong>Fahrenheit (\u00b0F)<\/strong><\/th><td>32 \u00b0F<\/td><td>212 \u00b0F<\/td><\/tr><tr><th><strong>Kelvin (K)<\/strong><\/th><td>273,15 K<\/td><td>373,15 K<\/td><\/tr><tr><th><strong>Rankine (\u00b0R)<\/strong><\/th><td>491,67 \u00b0R<\/td><td>671,67 \u00b0R<\/td><\/tr><\/tbody><\/table><\/figure>\n\n\n\n<h3 class=\"wp-block-heading\">Rela\u00e7\u00e3o entre as escalas<\/h3>\n\n\n\n<p>Calculamos as rela\u00e7\u00f5es pela raz\u00e3o entre os intervalos equivalentes em cada escala, asim<\/p>\n\n\n\n<div class=\"wp-block-katex-display-block katex-eq\" data-katex-display=\"true\"><pre>\\frac{a}{b}=\\frac{T_{C}-0}{100-0}=\\frac{T_{F}-32}{212-32}=\\frac{T_{K}-273}{373-273}=\\frac{T_{R}-491}{671-491}<\/pre><\/div>\n\n\n\n<p>portanto,<\/p>\n\n\n\n<div class=\"wp-block-katex-display-block katex-eq\" data-katex-display=\"true\"><pre>\\frac{T_{C}}{100}=\\frac{T_{F}-32}{180}=\\frac{T_{K}-273}{100}=\\frac{T_{R}-491}{180}<\/pre><\/div>\n\n\n\n<p>logo,<\/p>\n\n\n\n<div class=\"wp-block-katex-display-block katex-eq\" data-katex-display=\"true\"><pre>\\frac{T_{C}}{5}=\\frac{T_{F}-32}{9}=\\frac{T_{K}-273}{5}=\\frac{T_{R}-491}{9}<\/pre><\/div>\n\n\n\n<h2 class=\"wp-block-heading\">Dilata\u00e7\u00e3o T\u00e9rmica<\/h2>\n\n\n\n<p><strong>Dilata\u00e7\u00e3o t\u00e9rmica<\/strong> \u00e9 o fen\u00f4meno em que um material muda de tamanho quando sua temperatura varia. O ponto central \u00e9: ao esquentar, as part\u00edculas vibram mais e tendem a se afastar; ao esfriar, vibram menos e se aproximam. Isso vale para s\u00f3lidos, l\u00edquidos e gases, mas cada um se comporta de um jeito.<\/p>\n\n\n\n<p>\ud83d\udd25 <strong>O que realmente acontece na dilata\u00e7\u00e3o<\/strong><br>A ideia essencial \u00e9 que a <strong>temperatura altera a energia interna do material<\/strong>. Com mais energia, as liga\u00e7\u00f5es entre \u00e1tomos \u201ccedem\u201d um pouco, permitindo que o corpo aumente de comprimento, \u00e1rea ou volume.<\/p>\n\n\n\n<ul class=\"wp-block-list\">\n<li>S\u00f3lidos \u2014 dilatam pouco, mas de forma bem previs\u00edvel.<\/li>\n\n\n\n<li>L\u00edquidos \u2014 dilatam mais que s\u00f3lidos, por\u00e9m sem forma fixa.<\/li>\n\n\n\n<li>Gases \u2014 s\u00e3o os que mais dilatam, e sua dilata\u00e7\u00e3o depende muito da press\u00e3o.<\/li>\n<\/ul>\n\n\n\n<p>\ud83d\udccf Tipos de dilata\u00e7\u00e3o em s\u00f3lidos<\/p>\n\n\n\n<ul class=\"wp-block-list\">\n<li>Dilata\u00e7\u00e3o linear \u2014 mudan\u00e7a no comprimento.\n<ul class=\"wp-block-list\">\n<li><math data-latex=\"\\Delta L=L_0\\cdot \\alpha \\cdot \\Delta T\"><semantics><mrow><mrow><mi mathvariant=\"normal\">\u0394<\/mi><\/mrow><mi>L<\/mi><mo>=<\/mo><msub><mi>L<\/mi><mn>0<\/mn><\/msub><mo>\u22c5<\/mo><mi>\u03b1<\/mi><mo>\u22c5<\/mo><mrow><mi mathvariant=\"normal\">\u0394<\/mi><\/mrow><mi>T<\/mi><\/mrow><annotation encoding=\"application\/x-tex\">\\Delta L=L_0\\cdot \\alpha \\cdot \\Delta T<\/annotation><\/semantics><\/math> &#8211; Onde \u03b1 \u00e9 o coeficiente de dilata\u00e7\u00e3o linear.<\/li>\n<\/ul>\n<\/li>\n\n\n\n<li>Dilata\u00e7\u00e3o superficial \u2014 mudan\u00e7a na \u00e1rea.\n<ul class=\"wp-block-list\">\n<li><math data-latex=\"\\Delta A=A_0\\cdot \\beta \\cdot \\Delta T\"><semantics><mrow><mrow><mi mathvariant=\"normal\">\u0394<\/mi><\/mrow><mi>A<\/mi><mo>=<\/mo><msub><mi>A<\/mi><mn>0<\/mn><\/msub><mo>\u22c5<\/mo><mi>\u03b2<\/mi><mo>\u22c5<\/mo><mrow><mi mathvariant=\"normal\">\u0394<\/mi><\/mrow><mi>T<\/mi><\/mrow><annotation encoding=\"application\/x-tex\">\\Delta A=A_0\\cdot \\beta \\cdot \\Delta T<\/annotation><\/semantics><\/math> &#8211; Com \u03b2 = 2\u03b1.<\/li>\n<\/ul>\n<\/li>\n\n\n\n<li>Dilata\u00e7\u00e3o volum\u00e9trica \u2014 mudan\u00e7a no volume.\n<ul class=\"wp-block-list\">\n<li><math data-latex=\"\\Delta V=V_0\\cdot \\gamma \\cdot \\Delta T\"><semantics><mrow><mrow><mi mathvariant=\"normal\">\u0394<\/mi><\/mrow><mi>V<\/mi><mo>=<\/mo><msub><mi>V<\/mi><mn>0<\/mn><\/msub><mo>\u22c5<\/mo><mi>\u03b3<\/mi><mo>\u22c5<\/mo><mrow><mi mathvariant=\"normal\">\u0394<\/mi><\/mrow><mi>T<\/mi><\/mrow><annotation encoding=\"application\/x-tex\">\\Delta V=V_0\\cdot \\gamma \\cdot \\Delta T<\/annotation><\/semantics><\/math> &#8211; Com \u03b3 =3\u03b1.<\/li>\n<\/ul>\n<\/li>\n\n\n\n<li>Essas rela\u00e7\u00f5es mostram que a dilata\u00e7\u00e3o \u00e9 proporcional ao tamanho inicial e \u00e0 varia\u00e7\u00e3o de temperatura.<\/li>\n<\/ul>\n\n\n\n<p>\ud83e\uddea Dilata\u00e7\u00e3o em l\u00edquidos e gases<\/p>\n\n\n\n<ul class=\"wp-block-list\">\n<li>L\u00edquidos usam o coeficiente de dilata\u00e7\u00e3o volum\u00e9trica (\u03b3).<\/li>\n\n\n\n<li>Gases seguem as leis dos gases (como a de Charles e a de Gay-Lussac), que relacionam volume, temperatura e press\u00e3o.<br>Um detalhe curioso: a \u00e1gua entre 0\u00b0C e 4\u00b0C se comporta ao contr\u00e1rio, contraindo ao aquecer \u2014 isso explica por que lagos congelam de cima para baixo.<\/li>\n<\/ul>\n\n\n\n<p>\ud83c\udfd7\ufe0f Aplica\u00e7\u00f5es pr\u00e1ticas no dia a dia<\/p>\n\n\n\n<ul class=\"wp-block-list\">\n<li>Juntas de dilata\u00e7\u00e3o em pontes e viadutos para evitar rachaduras.<\/li>\n\n\n\n<li>Frestas em trilhos de trem para impedir empenamento.<\/li>\n\n\n\n<li>Term\u00f4metros que usam a dilata\u00e7\u00e3o de l\u00edquidos como o \u00e1lcool.<\/li>\n\n\n\n<li>Tampas de metal que abrem mais f\u00e1cil quando aquecidas.<\/li>\n\n\n\n<li>Cabos el\u00e9tricos ficam mais frouxos no calor e mais esticados no frio.<\/li>\n<\/ul>\n\n\n\n<p>\u26a0\ufe0f Um detalhe importante<br>A dilata\u00e7\u00e3o n\u00e3o depende s\u00f3 da temperatura, mas tamb\u00e9m do material. Metais como alum\u00ednio e cobre dilatam bastante; vidro e cer\u00e2mica, pouco; concreto, moderadamente.<\/p>\n\n\n\n<p>\ud83d\udcd8 Exemplos resolvidos de dilata\u00e7\u00e3o t\u00e9rmica<\/p>\n\n\n\n<p>1) Dilata\u00e7\u00e3o linear (s\u00f3lidos)<\/p>\n\n\n\n<p>Um fio met\u00e1lico de <strong>2,0 m<\/strong> tem coeficiente de dilata\u00e7\u00e3o linear<\/p>\n\n\n\n<p><math data-latex=\"\\alpha =2,0\\times 10^{-5}\\, {}^{\\circ }\\mathrm{C^{\\mathnormal{-1}}}\"><semantics><mrow><mi>\u03b1<\/mi><mo>=<\/mo><mn>2,0<\/mn><mo>\u00d7<\/mo><msup><mn>10<\/mn><mrow><mo lspace=\"0em\" rspace=\"0em\">\u2212<\/mo><mn>5<\/mn><\/mrow><\/msup><mspace width=\"0.1667em\"><\/mspace><msup><mrow><\/mrow><mo lspace=\"0em\" rspace=\"0em\">\u2218<\/mo><\/msup><msup><mrow><mi mathvariant=\"normal\">C<\/mi><\/mrow><mrow><mo lspace=\"0em\" rspace=\"0em\">\u2212<\/mo><mn>1<\/mn><\/mrow><\/msup><\/mrow><annotation encoding=\"application\/x-tex\">\\alpha =2,0\\times 10^{-5}\\, {}^{\\circ }\\mathrm{C^{\\mathnormal{-1}}}<\/annotation><\/semantics><\/math><br><br>Ele \u00e9 aquecido de <strong>20\u00b0C para 70\u00b0C<\/strong>.<\/p>\n\n\n\n<p> <math data-latex=\"\\Delta L=L_0\\cdot \\alpha \\cdot \\Delta T\"><semantics><mrow><mrow><mi mathvariant=\"normal\">\u0394<\/mi><\/mrow><mi>L<\/mi><mo>=<\/mo><msub><mi>L<\/mi><mn>0<\/mn><\/msub><mo>\u22c5<\/mo><mi>\u03b1<\/mi><mo>\u22c5<\/mo><mrow><mi mathvariant=\"normal\">\u0394<\/mi><\/mrow><mi>T<\/mi><\/mrow><annotation encoding=\"application\/x-tex\">\\Delta L=L_0\\cdot \\alpha \\cdot \\Delta T<\/annotation><\/semantics><\/math><\/p>\n\n\n\n<p><math data-latex=\"\\Delta L=2,0\\cdot (2,0\\times 10^{-5})\\cdot 50\"><semantics><mrow><mrow><mi mathvariant=\"normal\">\u0394<\/mi><\/mrow><mi>L<\/mi><mo>=<\/mo><mn>2,0<\/mn><mo>\u22c5<\/mo><mo form=\"prefix\" stretchy=\"false\">(<\/mo><mn>2,0<\/mn><mo>\u00d7<\/mo><msup><mn>10<\/mn><mrow><mo lspace=\"0em\" rspace=\"0em\">\u2212<\/mo><mn>5<\/mn><\/mrow><\/msup><mo form=\"postfix\" stretchy=\"false\">)<\/mo><mo>\u22c5<\/mo><mn>50<\/mn><\/mrow><annotation encoding=\"application\/x-tex\">\\Delta L=2,0\\cdot (2,0\\times 10^{-5})\\cdot 50<\/annotation><\/semantics><\/math><\/p>\n\n\n\n<p><math data-latex=\"\\Delta L=0,002\\, \\mathrm{m}=2\\, \\mathrm{mm}\"><semantics><mrow><mrow><mi mathvariant=\"normal\">\u0394<\/mi><\/mrow><mi>L<\/mi><mo>=<\/mo><mn>0,002<\/mn><mspace width=\"0.1667em\"><\/mspace><mrow><mi mathvariant=\"normal\">m<\/mi><\/mrow><mo>=<\/mo><mn>2<\/mn><mspace width=\"0.1667em\"><\/mspace><mrow><mtext><\/mtext><mi>mm<\/mi><\/mrow><\/mrow><annotation encoding=\"application\/x-tex\">\\Delta L=0,002\\, \\mathrm{m}=2\\, \\mathrm{mm}<\/annotation><\/semantics><\/math><\/p>\n\n\n\n<p><strong>O fio aumenta 2 mm.<\/strong><\/p>\n\n\n\n<p>2) Dilata\u00e7\u00e3o superficial<\/p>\n\n\n\n<p>Uma chapa quadrada de alum\u00ednio tem \u00e1rea inicial de <strong>0,50 m\u00b2<\/strong>.<br>O coeficiente superficial \u00e9 <math data-latex=\"\\beta =2\\alpha\"><semantics><mrow><mi>\u03b2<\/mi><mo>=<\/mo><mn>2<\/mn><mi>\u03b1<\/mi><\/mrow><annotation encoding=\"application\/x-tex\">\\beta =2\\alpha<\/annotation><\/semantics><\/math> .<br>Se <math data-latex=\"\\alpha =2,4\\times 10^{-5}\"><semantics><mrow><mi>\u03b1<\/mi><mo>=<\/mo><mn>2,4<\/mn><mo>\u00d7<\/mo><msup><mn>10<\/mn><mrow><mo lspace=\"0em\" rspace=\"0em\">\u2212<\/mo><mn>5<\/mn><\/mrow><\/msup><\/mrow><annotation encoding=\"application\/x-tex\">\\alpha =2,4\\times 10^{-5}<\/annotation><\/semantics><\/math>, ent\u00e3o <math data-latex=\"\\beta =4,8\\times 10^{-5}\"><semantics><mrow><mi>\u03b2<\/mi><mo>=<\/mo><mn>4,8<\/mn><mo>\u00d7<\/mo><msup><mn>10<\/mn><mrow><mo lspace=\"0em\" rspace=\"0em\">\u2212<\/mo><mn>5<\/mn><\/mrow><\/msup><\/mrow><annotation encoding=\"application\/x-tex\">\\beta =4,8\\times 10^{-5}<\/annotation><\/semantics><\/math>.<\/p>\n\n\n\n<p>Aquecimento: <strong>\u0394T = 40\u00b0C<\/strong>.<\/p>\n\n\n\n<p><math data-latex=\"\\Delta A=A_0\\cdot \\beta \\cdot \\Delta T\"><semantics><mrow><mrow><mi mathvariant=\"normal\">\u0394<\/mi><\/mrow><mi>A<\/mi><mo>=<\/mo><msub><mi>A<\/mi><mn>0<\/mn><\/msub><mo>\u22c5<\/mo><mi>\u03b2<\/mi><mo>\u22c5<\/mo><mrow><mi mathvariant=\"normal\">\u0394<\/mi><\/mrow><mi>T<\/mi><\/mrow><annotation encoding=\"application\/x-tex\">\\Delta A=A_0\\cdot \\beta \\cdot \\Delta T<\/annotation><\/semantics><\/math><\/p>\n\n\n\n<p><math data-latex=\"\\Delta A=0,50\\cdot (4,8\\times 10^{-5})\\cdot 40\"><semantics><mrow><mrow><mi mathvariant=\"normal\">\u0394<\/mi><\/mrow><mi>A<\/mi><mo>=<\/mo><mn>0,50<\/mn><mo>\u22c5<\/mo><mo form=\"prefix\" stretchy=\"false\">(<\/mo><mn>4,8<\/mn><mo>\u00d7<\/mo><msup><mn>10<\/mn><mrow><mo lspace=\"0em\" rspace=\"0em\">\u2212<\/mo><mn>5<\/mn><\/mrow><\/msup><mo form=\"postfix\" stretchy=\"false\">)<\/mo><mo>\u22c5<\/mo><mn>40<\/mn><\/mrow><annotation encoding=\"application\/x-tex\">\\Delta A=0,50\\cdot (4,8\\times 10^{-5})\\cdot 40<\/annotation><\/semantics><\/math><\/p>\n\n\n\n<p><math data-latex=\"\\Delta A=0,00096\\, \\mathrm{m^{\\mathnormal{2}}}\"><semantics><mrow><mrow><mi mathvariant=\"normal\">\u0394<\/mi><\/mrow><mi>A<\/mi><mo>=<\/mo><mn>0,00096<\/mn><mspace width=\"0.1667em\"><\/mspace><msup><mrow><mi mathvariant=\"normal\">m<\/mi><\/mrow><mn>2<\/mn><\/msup><\/mrow><annotation encoding=\"application\/x-tex\">\\Delta A=0,00096\\, \\mathrm{m^{\\mathnormal{2}}}<\/annotation><\/semantics><\/math><\/p>\n\n\n\n<p><strong>A \u00e1rea aumenta 0,00096 m\u00b2.<\/strong><\/p>\n\n\n\n<p>3) Dilata\u00e7\u00e3o volum\u00e9trica (l\u00edquidos)<\/p>\n\n\n\n<p>Um frasco cont\u00e9m <strong>1,0 L<\/strong> de \u00e1lcool.<br>Coeficiente volum\u00e9trico: <math data-latex=\"\\gamma =1,1\\times 10^{-3}\\, {}^{\\circ }\\mathrm{C^{\\mathnormal{-1}}}.\"><semantics><mrow><mi>\u03b3<\/mi><mo>=<\/mo><mn>1,1<\/mn><mo>\u00d7<\/mo><msup><mn>10<\/mn><mrow><mo lspace=\"0em\" rspace=\"0em\">\u2212<\/mo><mn>3<\/mn><\/mrow><\/msup><mspace width=\"0.1667em\"><\/mspace><msup><mrow><\/mrow><mo lspace=\"0em\" rspace=\"0em\">\u2218<\/mo><\/msup><msup><mrow><mi mathvariant=\"normal\">C<\/mi><\/mrow><mrow><mo lspace=\"0em\" rspace=\"0em\">\u2212<\/mo><mn>1<\/mn><\/mrow><\/msup><mi>.<\/mi><\/mrow><annotation encoding=\"application\/x-tex\">\\gamma =1,1\\times 10^{-3}\\, {}^{\\circ }\\mathrm{C^{\\mathnormal{-1}}}.<\/annotation><\/semantics><\/math><br>Aquecimento: <strong>\u0394T = 30\u00b0C<\/strong>.<\/p>\n\n\n\n<p><math data-latex=\"\\Delta V=V_0\\cdot \\gamma \\cdot \\Delta T\"><semantics><mrow><mrow><mi mathvariant=\"normal\">\u0394<\/mi><\/mrow><mi>V<\/mi><mo>=<\/mo><msub><mi>V<\/mi><mn>0<\/mn><\/msub><mo>\u22c5<\/mo><mi>\u03b3<\/mi><mo>\u22c5<\/mo><mrow><mi mathvariant=\"normal\">\u0394<\/mi><\/mrow><mi>T<\/mi><\/mrow><annotation encoding=\"application\/x-tex\">\\Delta V=V_0\\cdot \\gamma \\cdot \\Delta T<\/annotation><\/semantics><\/math><\/p>\n\n\n\n<p><math data-latex=\"\\Delta V=1,0\\cdot (1,1\\times 10^{-3})\\cdot 30\"><semantics><mrow><mrow><mi mathvariant=\"normal\">\u0394<\/mi><\/mrow><mi>V<\/mi><mo>=<\/mo><mn>1,0<\/mn><mo>\u22c5<\/mo><mo form=\"prefix\" stretchy=\"false\">(<\/mo><mn>1,1<\/mn><mo>\u00d7<\/mo><msup><mn>10<\/mn><mrow><mo lspace=\"0em\" rspace=\"0em\">\u2212<\/mo><mn>3<\/mn><\/mrow><\/msup><mo form=\"postfix\" stretchy=\"false\">)<\/mo><mo>\u22c5<\/mo><mn>30<\/mn><\/mrow><annotation encoding=\"application\/x-tex\">\\Delta V=1,0\\cdot (1,1\\times 10^{-3})\\cdot 30<\/annotation><\/semantics><\/math><\/p>\n\n\n\n<p><math data-latex=\"\\Delta V=0,033\\, \\mathrm{L}\"><semantics><mrow><mrow><mi mathvariant=\"normal\">\u0394<\/mi><\/mrow><mi>V<\/mi><mo>=<\/mo><mn>0,033<\/mn><mspace width=\"0.1667em\"><\/mspace><mrow><mi mathvariant=\"normal\">L<\/mi><\/mrow><\/mrow><annotation encoding=\"application\/x-tex\">\\Delta V=0,033\\, \\mathrm{L}<\/annotation><\/semantics><\/math><\/p>\n\n\n\n<p><strong>O volume aumenta 33 mL.<\/strong><\/p>\n\n\n\n<p>Desprezamos a dilata\u00e7\u00e3o do reservat\u00f3rio.<\/p>\n\n\n\n<p>4) Dilata\u00e7\u00e3o de gases (Lei de Charles)<\/p>\n\n\n\n<p>Um g\u00e1s ocupa <strong>2,0 L<\/strong> a <strong>300 K<\/strong>.<br>Aquecido para <strong>450 K<\/strong>, com press\u00e3o constante:<\/p>\n\n\n\n<p><math data-latex=\"\\displaystyle\\frac{V_1}{T_1}=\\frac{V_2}{T_2}\"><semantics><mstyle scriptlevel=\"0\" displaystyle=\"true\"><mfrac><msub><mi>V<\/mi><mn>1<\/mn><\/msub><msub><mi>T<\/mi><mn>1<\/mn><\/msub><\/mfrac><mo>=<\/mo><mfrac><msub><mi>V<\/mi><mn>2<\/mn><\/msub><msub><mi>T<\/mi><mn>2<\/mn><\/msub><\/mfrac><\/mstyle><annotation encoding=\"application\/x-tex\">\\displaystyle\\frac{V_1}{T_1}=\\frac{V_2}{T_2}<\/annotation><\/semantics><\/math><\/p>\n\n\n\n<p><math data-latex=\"\\displaystyle V_2=V_1\\cdot \\frac{T_2}{T_1}\"><semantics><mstyle scriptlevel=\"0\" displaystyle=\"true\"><msub><mi>V<\/mi><mn>2<\/mn><\/msub><mo>=<\/mo><msub><mi>V<\/mi><mn>1<\/mn><\/msub><mo>\u22c5<\/mo><mfrac><msub><mi>T<\/mi><mn>2<\/mn><\/msub><msub><mi>T<\/mi><mn>1<\/mn><\/msub><\/mfrac><\/mstyle><annotation encoding=\"application\/x-tex\">\\displaystyle V_2=V_1\\cdot \\frac{T_2}{T_1}<\/annotation><\/semantics><\/math><\/p>\n\n\n\n<p><math data-latex=\"\\displaystyle V_2=2,0\\cdot \\frac{450}{300}=3,0\\, \\mathrm{L}\"><semantics><mstyle scriptlevel=\"0\" displaystyle=\"true\"><msub><mi>V<\/mi><mn>2<\/mn><\/msub><mo>=<\/mo><mn>2,0<\/mn><mo>\u22c5<\/mo><mfrac><mn>450<\/mn><mn>300<\/mn><\/mfrac><mo>=<\/mo><mn>3,0<\/mn><mspace width=\"0.1667em\"><\/mspace><mrow><mi mathvariant=\"normal\">L<\/mi><\/mrow><\/mstyle><annotation encoding=\"application\/x-tex\">\\displaystyle V_2=2,0\\cdot \\frac{450}{300}=3,0\\, \\mathrm{L}<\/annotation><\/semantics><\/math><\/p>\n\n\n\n<p><strong>O g\u00e1s passa a ocupar 3,0 L.<\/strong><\/p>\n\n\n\n<p>O que \u00e9 dilata\u00e7\u00e3o t\u00e9rmica: \u00c9 o fen\u00f4meno em que <strong>corpos aumentam ou diminuem de tamanho quando a temperatura varia<\/strong>, devido ao afastamento ou aproxima\u00e7\u00e3o das part\u00edculas.<\/p>\n\n\n\n<p>Dilata\u00e7\u00e3o em l\u00edquidos<\/p>\n\n\n\n<ul class=\"wp-block-list\">\n<li>S\u00f3 consideramos <strong>volum\u00e9trica<\/strong>.<\/li>\n\n\n\n<li>Cada l\u00edquido tem seu pr\u00f3prio coeficiente.<\/li>\n\n\n\n<li>A \u00e1gua \u00e9 exce\u00e7\u00e3o entre <strong>0\u00b0C e 4\u00b0C<\/strong>, pois <strong>contrai ao aquecer<\/strong>.<\/li>\n<\/ul>\n\n\n\n<p>Dilata\u00e7\u00e3o em gases<\/p>\n\n\n\n<ul class=\"wp-block-list\">\n<li>Governada pelas leis dos gases.<\/li>\n\n\n\n<li>Aumentam muito o volume quando aquecidos.<\/li>\n\n\n\n<li>A rela\u00e7\u00e3o mais usada \u00e9:<\/li>\n<\/ul>\n\n\n\n<p><math data-latex=\"\\frac{V}{T}=\\mathrm{constante\\ (press\u00e3o\\ constante)}\"><semantics><mrow><mfrac><mi>V<\/mi><mi>T<\/mi><\/mfrac><mo>=<\/mo><mrow><mrow><mi mathvariant=\"normal\">c<\/mi><\/mrow><mrow><mi mathvariant=\"normal\">o<\/mi><\/mrow><mrow><mi mathvariant=\"normal\">n<\/mi><\/mrow><mrow><mi mathvariant=\"normal\">s<\/mi><\/mrow><mrow><mi mathvariant=\"normal\">t<\/mi><\/mrow><mrow><mi mathvariant=\"normal\">a<\/mi><\/mrow><mrow><mi mathvariant=\"normal\">n<\/mi><\/mrow><mrow><mi mathvariant=\"normal\">t<\/mi><\/mrow><mrow><mi mathvariant=\"normal\">e<\/mi><\/mrow><mtext>&nbsp;<\/mtext><mo form=\"prefix\" stretchy=\"false\">(<\/mo><mrow><mi mathvariant=\"normal\">p<\/mi><\/mrow><mrow><mi mathvariant=\"normal\">r<\/mi><\/mrow><mrow><mi mathvariant=\"normal\">e<\/mi><\/mrow><mrow><mi mathvariant=\"normal\">s<\/mi><\/mrow><mrow><mi mathvariant=\"normal\">s<\/mi><\/mrow><mover><mrow><mi mathvariant=\"normal\">a<\/mi><\/mrow><mo stretchy=\"false\" style=\"math-style:normal;math-depth:0;\">~<\/mo><\/mover><mrow><mi mathvariant=\"normal\">o<\/mi><\/mrow><mtext>&nbsp;<\/mtext><mrow><mi mathvariant=\"normal\">c<\/mi><\/mrow><mrow><mi mathvariant=\"normal\">o<\/mi><\/mrow><mrow><mi mathvariant=\"normal\">n<\/mi><\/mrow><mrow><mi mathvariant=\"normal\">s<\/mi><\/mrow><mrow><mi mathvariant=\"normal\">t<\/mi><\/mrow><mrow><mi mathvariant=\"normal\">a<\/mi><\/mrow><mrow><mi mathvariant=\"normal\">n<\/mi><\/mrow><mrow><mi mathvariant=\"normal\">t<\/mi><\/mrow><mrow><mi mathvariant=\"normal\">e<\/mi><\/mrow><mo form=\"postfix\" stretchy=\"false\" lspace=\"0em\" rspace=\"0em\">)<\/mo><\/mrow><\/mrow><annotation encoding=\"application\/x-tex\">\\frac{V}{T}=\\mathrm{constante\\ (press\u00e3o\\ constante)}<\/annotation><\/semantics><\/math><\/p>\n\n\n\n<p>Aplica\u00e7\u00f5es importantes<\/p>\n\n\n\n<ul class=\"wp-block-list\">\n<li>Juntas de dilata\u00e7\u00e3o em pontes e viadutos.<\/li>\n\n\n\n<li>Trilhos de trem com folgas.<\/li>\n\n\n\n<li>Term\u00f4metros de l\u00edquido.<\/li>\n\n\n\n<li>Cabos el\u00e9tricos mais frouxos no calor.<\/li>\n\n\n\n<li>Tampas met\u00e1licas que abrem mais f\u00e1cil quando aquecidas.<\/li>\n<\/ul>\n\n\n\n<p>A <strong>tens\u00e3o de dilata\u00e7\u00e3o<\/strong> aparece quando um corpo <strong>tenta se dilatar ou se contrair<\/strong>, mas <strong>n\u00e3o consegue<\/strong>, porque algo o impede. Isso gera uma for\u00e7a interna que pode ser grande o suficiente para deformar, trincar ou at\u00e9 romper materiais \u2014 especialmente em estruturas r\u00edgidas.<\/p>\n\n\n\n<p>\ud83c\udf21\ufe0f Tens\u00e3o de dilata\u00e7\u00e3o: o que \u00e9 e por que acontece<\/p>\n\n\n\n<p>Quando um material aquece, ele quer aumentar de tamanho. Se estiver <strong>preso<\/strong>, <strong>engastado<\/strong>, <strong>aparafusado<\/strong> ou <strong>travado<\/strong>, essa dilata\u00e7\u00e3o n\u00e3o ocorre livremente. O resultado \u00e9 uma <strong>tens\u00e3o interna<\/strong>.<\/p>\n\n\n\n<p>Como calcular (ideia geral)<\/p>\n\n\n\n<p>Se o corpo est\u00e1 impedido de se dilatar, a tens\u00e3o gerada \u00e9:<\/p>\n\n\n\n<p><math data-latex=\"\\sigma =E\\cdot \\alpha \\cdot \\Delta T\"><semantics><mrow><mi>\u03c3<\/mi><mo>=<\/mo><mi>E<\/mi><mo>\u22c5<\/mo><mi>\u03b1<\/mi><mo>\u22c5<\/mo><mrow><mi mathvariant=\"normal\">\u0394<\/mi><\/mrow><mi>T<\/mi><\/mrow><annotation encoding=\"application\/x-tex\">\\sigma =E\\cdot \\alpha \\cdot \\Delta T<\/annotation><\/semantics><\/math><\/p>\n\n\n\n<ul class=\"wp-block-list\">\n<li><strong>\u03c3<\/strong> \u2014 tens\u00e3o de dilata\u00e7\u00e3o<\/li>\n\n\n\n<li><strong>E<\/strong> \u2014 m\u00f3dulo de elasticidade (rigidez do material)<\/li>\n\n\n\n<li><strong>\u03b1<\/strong> \u2014 coeficiente de dilata\u00e7\u00e3o t\u00e9rmica<\/li>\n\n\n\n<li><strong>\u0394T<\/strong> \u2014 varia\u00e7\u00e3o de temperatura<\/li>\n<\/ul>\n\n\n\n<p>Quanto mais r\u00edgido o material (E alto), maior a tens\u00e3o gerada.<\/p>\n\n\n\n<p>Exemplo r\u00e1pido<\/p>\n\n\n\n<p>Uma barra de a\u00e7o (E = 200 GPa, \u03b1 = 1,2\u00d710\u207b\u2075) sofre \u0394T = 40\u00b0C, mas est\u00e1 totalmente presa.<\/p>\n\n\n\n<div class=\"wp-block-math\"><math display=\"block\"><semantics><mrow><mi>\u03c3<\/mi><mo>=<\/mo><mn>200<\/mn><mo>\u00d7<\/mo><msup><mn>10<\/mn><mn>9<\/mn><\/msup><mo>\u22c5<\/mo><mn>1,2<\/mn><mo>\u00d7<\/mo><msup><mn>10<\/mn><mrow><mo lspace=\"0em\" rspace=\"0em\">\u2212<\/mo><mn>5<\/mn><\/mrow><\/msup><mo>\u22c5<\/mo><mn>40<\/mn><\/mrow><annotation encoding=\"application\/x-tex\">\\sigma =200\\times 10^9\\cdot 1,2\\times 10^{-5}\\cdot 40<\/annotation><\/semantics><\/math><\/div>\n\n\n\n<div class=\"wp-block-math\"><math display=\"block\"><semantics><mrow><mi>\u03c3<\/mi><mo>\u2248<\/mo><mn>96<\/mn><mrow><mtext>&nbsp;<\/mtext><mrow><mi mathvariant=\"normal\">M<\/mi><\/mrow><mrow><mi mathvariant=\"normal\">P<\/mi><\/mrow><mrow><mi mathvariant=\"normal\">a<\/mi><\/mrow><\/mrow><\/mrow><annotation encoding=\"application\/x-tex\">\\sigma \\approx 96\\mathrm{\\ MPa}<\/annotation><\/semantics><\/math><\/div>\n\n\n\n<p><strong>96 MPa \u00e9 enorme<\/strong> \u2014 suficiente para causar trincas em concreto ou deforma\u00e7\u00f5es permanentes em estruturas met\u00e1licas se n\u00e3o houver juntas de dilata\u00e7\u00e3o.<\/p>\n\n\n\n<p>\ud83e\uddf1 Onde a tens\u00e3o de dilata\u00e7\u00e3o aparece na pr\u00e1tica<\/p>\n\n\n\n<ul class=\"wp-block-list\">\n<li>Trilhos de trem que empenam no calor.<\/li>\n\n\n\n<li>Vidros que quebram quando aquecidos de forma desigual.<\/li>\n\n\n\n<li>Pontes e viadutos que precisam de juntas de dilata\u00e7\u00e3o.<\/li>\n\n\n\n<li>Tubula\u00e7\u00f5es met\u00e1licas que estalam ou se deformam com varia\u00e7\u00f5es t\u00e9rmicas.<\/li>\n\n\n\n<li>Concreto que racha quando exposto ao sol intenso.<\/li>\n<\/ul>\n\n\n\n<p>\ud83d\udd27 Diferen\u00e7a entre <strong>tens\u00e3o<\/strong>, <strong>tra\u00e7\u00e3o<\/strong> e <strong>tor\u00e7\u00e3o<\/strong><\/p>\n\n\n\n<p>Esses tr\u00eas termos s\u00e3o relacionados, mas n\u00e3o s\u00e3o a mesma coisa.<\/p>\n\n\n\n<p>1) <strong>Tens\u00e3o<\/strong> (conceito geral)<\/p>\n\n\n\n<p>\u00c9 a <strong>for\u00e7a interna por unidade de \u00e1rea<\/strong> dentro de um material.<\/p>\n\n\n\n<p><math data-latex=\"\\displaystyle \\sigma =\\frac{F}{A}\"><semantics><mstyle scriptlevel=\"0\" displaystyle=\"true\"><mi>\u03c3<\/mi><mo>=<\/mo><mfrac><mi>F<\/mi><mi>A<\/mi><\/mfrac><\/mstyle><annotation encoding=\"application\/x-tex\">\\displaystyle \\sigma =\\frac{F}{A}<\/annotation><\/semantics><\/math><\/p>\n\n\n\n<p>Pode aparecer em v\u00e1rias formas: tra\u00e7\u00e3o, compress\u00e3o, cisalhamento, tor\u00e7\u00e3o, flex\u00e3o e tamb\u00e9m <strong>dilata\u00e7\u00e3o t\u00e9rmica<\/strong>.<\/p>\n\n\n\n<p><strong>Tens\u00e3o \u00e9 o conceito amplo.<\/strong><\/p>\n\n\n\n<p>2) <strong>Tra\u00e7\u00e3o<\/strong> (tipo de esfor\u00e7o)<\/p>\n\n\n\n<p>\u00c9 quando o material \u00e9 <strong>puxado<\/strong>, esticado.<\/p>\n\n\n\n<ul class=\"wp-block-list\">\n<li>Aumenta o comprimento.<\/li>\n\n\n\n<li>Tende a romper o material \u201cabrindo\u201d suas fibras.<\/li>\n\n\n\n<li>Exemplo: um cabo de a\u00e7o sustentando um elevador.<\/li>\n<\/ul>\n\n\n\n<p>A tra\u00e7\u00e3o gera <strong>tens\u00e3o de tra\u00e7\u00e3o<\/strong>, que \u00e9 um tipo espec\u00edfico de tens\u00e3o.<\/p>\n\n\n\n<p>3) <strong>Tor\u00e7\u00e3o<\/strong> (tipo de esfor\u00e7o)<\/p>\n\n\n\n<p>\u00c9 quando o material \u00e9 <strong>torcido<\/strong> ao redor de seu eixo.<\/p>\n\n\n\n<ul class=\"wp-block-list\">\n<li>Gera tens\u00f5es de cisalhamento internas.<\/li>\n\n\n\n<li>Exemplo: eixo de carro transmitindo torque do motor.<\/li>\n\n\n\n<li>Exemplo: chave de fenda girando um parafuso.<\/li>\n<\/ul>\n\n\n\n<p>A tor\u00e7\u00e3o n\u00e3o alonga nem comprime diretamente \u2014 ela <strong>cisalha<\/strong>.<\/p>\n\n\n\n<p>\ud83e\udde9 Compara\u00e7\u00e3o r\u00e1pida<\/p>\n\n\n\n<figure class=\"wp-block-table\"><table class=\"has-fixed-layout\"><tbody><tr><td><strong>Conceito<\/strong><\/td><td><strong>O que \u00e9<\/strong><\/td><td><strong>Como age<\/strong><\/td><td><strong>Exemplo<\/strong><\/td><\/tr><tr><td><strong>Tens\u00e3o<\/strong><\/td><td>For\u00e7a interna por \u00e1rea<\/td><td>Pode ser tra\u00e7\u00e3o, compress\u00e3o, cisalhamento, t\u00e9rmica<\/td><td>Qualquer pe\u00e7a sob carga<\/td><\/tr><tr><td><strong>Tra\u00e7\u00e3o<\/strong><\/td><td>Esfor\u00e7o que puxa\/estica<\/td><td>Aumenta o comprimento<\/td><td>Cabo sendo puxado<\/td><\/tr><tr><td><strong>Tor\u00e7\u00e3o<\/strong><\/td><td>Esfor\u00e7o que gira\/torce<\/td><td>Gera cisalhamento<\/td><td>Eixo de motor<\/td><\/tr><\/tbody><\/table><\/figure>\n\n\n\n<p>\ud83d\udd0d Conex\u00e3o entre os conceitos<\/p>\n\n\n\n<ul class=\"wp-block-list\">\n<li>A <strong>dilata\u00e7\u00e3o t\u00e9rmica<\/strong> pode gerar <strong>tens\u00e3o<\/strong> se for impedida.<\/li>\n\n\n\n<li>Essa tens\u00e3o pode ser de <strong>compress\u00e3o<\/strong> (ao aquecer) ou <strong>tra\u00e7\u00e3o<\/strong> (ao esfriar).<\/li>\n\n\n\n<li>A <strong>tor\u00e7\u00e3o<\/strong> \u00e9 outro tipo de esfor\u00e7o, independente da temperatura, mas tamb\u00e9m gera tens\u00f5es internas.<\/li>\n<\/ul>\n\n\n\n<p>Essas defini\u00e7\u00f5es v\u00eam diretamente de <strong>conceitos formais da F\u00edsica e da Engenharia Mec\u00e2nica<\/strong>, consolidados em livros\u2011texto, normas t\u00e9cnicas e literatura cient\u00edfica. <\/p>\n\n\n\n<h2 class=\"wp-block-heading\">\ud83d\udcda Base cient\u00edfica da tens\u00e3o de dilata\u00e7\u00e3o<\/h2>\n\n\n\n<p>A tens\u00e3o de dilata\u00e7\u00e3o \u00e9 tratada em <strong>Mec\u00e2nica dos S\u00f3lidos<\/strong> e <strong>Resist\u00eancia dos Materiais<\/strong>. Ela deriva da combina\u00e7\u00e3o de dois princ\u00edpios:<\/p>\n\n\n\n<ul class=\"wp-block-list\">\n<li><strong>Lei de Hooke generalizada<\/strong>:<br><math data-latex=\" \\sigma = E \\cdot \\varepsilon  \\text{ onde } ( \\sigma ) \\text{ \u00e9 a tens\u00e3o, ( E ) \u00e9 o m\u00f3dulo de elasticidade e } ( \\varepsilon ) \\text{ \u00e9 a deforma\u00e7\u00e3o.}\"><semantics><mrow><mi>\u03c3<\/mi><mo>=<\/mo><mi>E<\/mi><mo>\u22c5<\/mo><mi>\u03b5<\/mi><mtext>&nbsp;onde&nbsp;<\/mtext><mo form=\"prefix\" stretchy=\"false\">(<\/mo><mi>\u03c3<\/mi><mo form=\"postfix\" stretchy=\"false\">)<\/mo><mtext>&nbsp;\u00e9&nbsp;a&nbsp;tens\u00e3o,&nbsp;(&nbsp;E&nbsp;)&nbsp;\u00e9&nbsp;o&nbsp;m\u00f3dulo&nbsp;de&nbsp;elasticidade&nbsp;e&nbsp;<\/mtext><mo form=\"prefix\" stretchy=\"false\">(<\/mo><mi>\u03b5<\/mi><mo form=\"postfix\" stretchy=\"false\">)<\/mo><mtext>&nbsp;\u00e9&nbsp;a&nbsp;deforma\u00e7\u00e3o.<\/mtext><\/mrow><annotation encoding=\"application\/x-tex\"> \\sigma = E \\cdot \\varepsilon  \\text{ onde } ( \\sigma ) \\text{ \u00e9 a tens\u00e3o, ( E ) \u00e9 o m\u00f3dulo de elasticidade e } ( \\varepsilon ) \\text{ \u00e9 a deforma\u00e7\u00e3o.}<\/annotation><\/semantics><\/math><\/li>\n\n\n\n<li><strong>Deforma\u00e7\u00e3o t\u00e9rmica livre<\/strong>:<br><math data-latex=\" \\varepsilon_{\\text{t\u00e9rmica}} = \\alpha \\cdot \\Delta T \"><semantics><mrow><msub><mi>\u03b5<\/mi><mtext>t\u00e9rmica<\/mtext><\/msub><mo>=<\/mo><mi>\u03b1<\/mi><mo>\u22c5<\/mo><mrow><mi mathvariant=\"normal\">\u0394<\/mi><\/mrow><mi>T<\/mi><\/mrow><annotation encoding=\"application\/x-tex\"> \\varepsilon_{\\text{t\u00e9rmica}} = \\alpha \\cdot \\Delta T <\/annotation><\/semantics><\/math><\/li>\n<\/ul>\n\n\n\n<p>Quando o corpo <strong>n\u00e3o pode se dilatar<\/strong>, essa deforma\u00e7\u00e3o t\u00e9rmica vira <strong>deforma\u00e7\u00e3o imposta<\/strong>, e a lei de Hooke transforma isso em tens\u00e3o:<\/p>\n\n\n\n<p><math data-latex=\" \\sigma = E \\cdot \\alpha \\cdot \\Delta T \"><semantics><mrow><mi>\u03c3<\/mi><mo>=<\/mo><mi>E<\/mi><mo>\u22c5<\/mo><mi>\u03b1<\/mi><mo>\u22c5<\/mo><mrow><mi mathvariant=\"normal\">\u0394<\/mi><\/mrow><mi>T<\/mi><\/mrow><annotation encoding=\"application\/x-tex\"> \\sigma = E \\cdot \\alpha \\cdot \\Delta T <\/annotation><\/semantics><\/math><\/p>\n\n\n\n<p>Esse modelo aparece em refer\u00eancias como:<\/p>\n\n\n\n<ul class=\"wp-block-list\">\n<li><em>Beer &amp; Johnston \u2013 Mec\u00e2nica dos Materiais<\/em><\/li>\n\n\n\n<li><em>Hibbeler \u2013 Resist\u00eancia dos Materiais<\/em><\/li>\n\n\n\n<li><em>Callister \u2013 Ci\u00eancia e Engenharia de Materiais<\/em><\/li>\n\n\n\n<li>Normas t\u00e9cnicas como ASME e Eurocode (para estruturas met\u00e1licas e tubula\u00e7\u00f5es)<\/li>\n<\/ul>\n\n\n\n<h2 class=\"wp-block-heading\">\ud83e\udde9 Base cient\u00edfica das diferen\u00e7as entre tens\u00e3o, tra\u00e7\u00e3o e tor\u00e7\u00e3o<\/h2>\n\n\n\n<h3 class=\"wp-block-heading\">\ud83d\udd39 Tens\u00e3o (stress)<\/h3>\n\n\n\n<p>\u00c9 um conceito geral da mec\u00e2nica cont\u00ednua: <strong>for\u00e7a interna por unidade de \u00e1rea<\/strong>.<br>\u00c9 definido formalmente na teoria da elasticidade e aparece em qualquer livro de mec\u00e2nica dos s\u00f3lidos.<\/p>\n\n\n\n<p><math data-latex=\"\\displaystyle \\sigma = \\frac{F}{A} \"><semantics><mstyle scriptlevel=\"0\" displaystyle=\"true\"><mi>\u03c3<\/mi><mo>=<\/mo><mfrac><mi>F<\/mi><mi>A<\/mi><\/mfrac><\/mstyle><annotation encoding=\"application\/x-tex\">\\displaystyle \\sigma = \\frac{F}{A} <\/annotation><\/semantics><\/math><\/p>\n\n\n\n<p>A tens\u00e3o pode ser:<\/p>\n\n\n\n<ul class=\"wp-block-list\">\n<li>de tra\u00e7\u00e3o<\/li>\n\n\n\n<li>de compress\u00e3o<\/li>\n\n\n\n<li>de cisalhamento<\/li>\n\n\n\n<li>t\u00e9rmica<\/li>\n\n\n\n<li>de flex\u00e3o<\/li>\n\n\n\n<li>de tor\u00e7\u00e3o<\/li>\n<\/ul>\n\n\n\n<p>Ou seja, <strong>tens\u00e3o \u00e9 o conceito guarda\u2011chuva<\/strong>.<\/p>\n\n\n\n<h3 class=\"wp-block-heading\">\ud83d\udd39 Tra\u00e7\u00e3o (tensile loading)<\/h3>\n\n\n\n<p>\u00c9 um <strong>tipo espec\u00edfico de carregamento<\/strong> que puxa o material, gerando alongamento.<br>A tens\u00e3o associada \u00e9 a <strong>tens\u00e3o de tra\u00e7\u00e3o<\/strong>.<\/p>\n\n\n\n<p>Esse conceito \u00e9 padronizado em:<\/p>\n\n\n\n<ul class=\"wp-block-list\">\n<li>Ensaios de tra\u00e7\u00e3o (ASTM E8, ISO 6892)<\/li>\n\n\n\n<li>Teoria da elasticidade linear<\/li>\n<\/ul>\n\n\n\n<h3 class=\"wp-block-heading\">\ud83d\udd39 Tor\u00e7\u00e3o (torsional loading)<\/h3>\n\n\n\n<p>\u00c9 um carregamento que <strong>gira<\/strong> o corpo ao redor de seu eixo, gerando <strong>tens\u00f5es de cisalhamento<\/strong>.<\/p>\n\n\n\n<p>A teoria de tor\u00e7\u00e3o aparece em:<\/p>\n\n\n\n<ul class=\"wp-block-list\">\n<li>F\u00f3rmula de tens\u00e3o de cisalhamento em eixos circulares:<br><math data-latex=\"\\displaystyle \\tau = \\frac{T \\cdot r}{J} \"><semantics><mstyle scriptlevel=\"0\" displaystyle=\"true\"><mi>\u03c4<\/mi><mo>=<\/mo><mfrac><mrow><mi>T<\/mi><mo>\u22c5<\/mo><mi>r<\/mi><\/mrow><mi>J<\/mi><\/mfrac><\/mstyle><annotation encoding=\"application\/x-tex\">\\displaystyle \\tau = \\frac{T \\cdot r}{J} <\/annotation><\/semantics><\/math><\/li>\n\n\n\n<li>Normas de projeto de eixos (como DIN e ISO)<\/li>\n<\/ul>\n\n\n\n<hr class=\"wp-block-separator has-alpha-channel-opacity\"\/>\n\n\n\n<h2 class=\"wp-block-heading\">\ud83e\udde0 S\u00edntese conceitual (com rigor cient\u00edfico)<\/h2>\n\n\n\n<figure class=\"wp-block-table\"><table class=\"has-fixed-layout\"><thead><tr><th>Conceito<\/th><th>Natureza<\/th><th>Base cient\u00edfica<\/th><th>Tipo de tens\u00e3o gerada<\/th><\/tr><\/thead><tbody><tr><td><strong>Tens\u00e3o<\/strong><\/td><td>Quantidade f\u00edsica geral<\/td><td>Mec\u00e2nica dos s\u00f3lidos<\/td><td>Pode ser tra\u00e7\u00e3o, compress\u00e3o, cisalhamento, t\u00e9rmica<\/td><\/tr><tr><td><strong>Tra\u00e7\u00e3o<\/strong><\/td><td>Tipo de carregamento<\/td><td>Ensaios mec\u00e2nicos e elasticidade<\/td><td>Tens\u00e3o normal (positiva)<\/td><\/tr><tr><td><strong>Tor\u00e7\u00e3o<\/strong><\/td><td>Tipo de carregamento<\/td><td>Teoria de tor\u00e7\u00e3o e cisalhamento<\/td><td>Tens\u00e3o de cisalhamento<\/td><\/tr><tr><td><strong>Tens\u00e3o de dilata\u00e7\u00e3o<\/strong><\/td><td>Tens\u00e3o causada por dilata\u00e7\u00e3o impedida<\/td><td>Dilata\u00e7\u00e3o t\u00e9rmica + Lei de Hooke<\/td><td>Compress\u00e3o (aquecimento) ou tra\u00e7\u00e3o (resfriamento)<\/td><\/tr><\/tbody><\/table><\/figure>\n\n\n\n<h2 class=\"wp-block-heading\">\ud83d\udd0d Por que isso \u00e9 cientificamente confi\u00e1vel?<\/h2>\n\n\n\n<p>Porque todos esses conceitos:<\/p>\n\n\n\n<ul class=\"wp-block-list\">\n<li>s\u00e3o <strong>matematicamente definidos<\/strong> na teoria da elasticidade;<\/li>\n\n\n\n<li>s\u00e3o <strong>experimentados e medidos<\/strong> em laborat\u00f3rio;<\/li>\n\n\n\n<li>s\u00e3o <strong>usados em normas t\u00e9cnicas internacionais<\/strong>;<\/li>\n\n\n\n<li>aparecem em <strong>livros cl\u00e1ssicos de engenharia e f\u00edsica<\/strong> h\u00e1 d\u00e9cadas.<\/li>\n<\/ul>\n\n\n\n<h2 class=\"wp-block-heading\">Calor e Troca de Calor<\/h2>\n\n\n\n<p>A teoria do <strong>cal\u00f3rico<\/strong> foi uma das etapas centrais na evolu\u00e7\u00e3o do conceito de calor e, portanto, na forma\u00e7\u00e3o da termodin\u00e2mica. Ela n\u00e3o apenas moldou a forma como cientistas dos s\u00e9culos XVII e XVIII entendiam os fen\u00f4menos t\u00e9rmicos, mas tamb\u00e9m forneceu a base conceitual que mais tarde seria superada, abrindo caminho para as leis modernas da termodin\u00e2mica.<\/p>\n\n\n\n<h2 class=\"wp-block-heading\">\ud83c\udf21\ufe0f O que era o cal\u00f3rico<\/h2>\n\n\n\n<p>A teoria do cal\u00f3rico afirmava que o <strong>calor era um fluido imponder\u00e1vel<\/strong>, invis\u00edvel, que podia entrar e sair dos corpos. Esse fluido \u2014 o <em>cal\u00f3rico<\/em> \u2014 explicaria:<\/p>\n\n\n\n<ul class=\"wp-block-list\">\n<li>O aquecimento (entrada de cal\u00f3rico)<\/li>\n\n\n\n<li>O resfriamento (sa\u00edda de cal\u00f3rico)<\/li>\n\n\n\n<li>Mudan\u00e7as de estado (calor latente)<\/li>\n\n\n\n<li>A dilata\u00e7\u00e3o t\u00e9rmica<\/li>\n<\/ul>\n\n\n\n<p>Essa vis\u00e3o foi defendida por nomes como <strong>Lavoisier<\/strong>, <strong>Laplace<\/strong>, <strong>Joseph Black<\/strong> e outros.<\/p>\n\n\n\n<h2 class=\"wp-block-heading\">\ud83d\udd70\ufe0f Linha hist\u00f3rica essencial<\/h2>\n\n\n\n<h3 class=\"wp-block-heading\">1. <strong>Origens filos\u00f3ficas<\/strong><\/h3>\n\n\n\n<p>Desde os gregos, o calor era associado ao elemento fogo. Essa vis\u00e3o perdurou por s\u00e9culos e influenciou alquimistas e naturalistas.<\/p>\n\n\n\n<h3 class=\"wp-block-heading\">2. <strong>S\u00e9culo XVIII: consolida\u00e7\u00e3o da teoria do cal\u00f3rico<\/strong><\/h3>\n\n\n\n<ul class=\"wp-block-list\">\n<li><strong>Lavoisier<\/strong> introduz formalmente o termo <em>cal\u00f3rico<\/em> e o trata como um elemento fundamental.<\/li>\n\n\n\n<li><strong>Joseph Black<\/strong> desenvolve os conceitos de <strong>calor sens\u00edvel<\/strong>, <strong>calor latente<\/strong>, <strong>capacidade t\u00e9rmica<\/strong> e <strong>calor espec\u00edfico<\/strong>, todos formulados dentro da teoria do cal\u00f3rico.<\/li>\n<\/ul>\n\n\n\n<p>Esses avan\u00e7os foram cruciais para quantificar o calor, mesmo que o modelo explicativo estivesse errado.<\/p>\n\n\n\n<h3 class=\"wp-block-heading\">3. <strong>Primeiros questionamentos<\/strong><\/h3>\n\n\n\n<p>O grande golpe contra a teoria veio com <strong>Benjamin Thompson (Conde Rumford)<\/strong>, que observou a produ\u00e7\u00e3o aparentemente inesgot\u00e1vel de calor durante a perfura\u00e7\u00e3o de canh\u00f5es. Se o calor fosse um fluido, ele deveria se esgotar \u2014 mas n\u00e3o se esgotava.<\/p>\n\n\n\n<h3 class=\"wp-block-heading\">4. <strong>Transi\u00e7\u00e3o para a vis\u00e3o mec\u00e2nica<\/strong><\/h3>\n\n\n\n<p>No in\u00edcio do s\u00e9culo XIX, <strong>Julius Robert Mayer<\/strong>, <strong>James Prescott Joule<\/strong> e outros demonstraram que calor \u00e9 uma forma de energia associada ao movimento microsc\u00f3pico das part\u00edculas \u2014 n\u00e3o um fluido material.<\/p>\n\n\n\n<h2 class=\"wp-block-heading\">\ud83d\udd27 Contribui\u00e7\u00f5es da teoria do cal\u00f3rico para a termodin\u00e2mica<\/h2>\n\n\n\n<p>Mesmo sendo incorreta, a teoria do cal\u00f3rico foi <strong>fundamental<\/strong> para o surgimento da termodin\u00e2mica moderna. Suas contribui\u00e7\u00f5es incluem:<\/p>\n\n\n\n<h3 class=\"wp-block-heading\">\u2714\ufe0f 1. Quantifica\u00e7\u00e3o do calor<\/h3>\n\n\n\n<p>A teoria incentivou medi\u00e7\u00f5es precisas:<\/p>\n\n\n\n<ul class=\"wp-block-list\">\n<li>Calor espec\u00edfico<\/li>\n\n\n\n<li>Calor latente<\/li>\n\n\n\n<li>Capacidade t\u00e9rmica<\/li>\n<\/ul>\n\n\n\n<p>Essas grandezas permanecem at\u00e9 hoje.<\/p>\n\n\n\n<h3 class=\"wp-block-heading\">\u2714\ufe0f 2. Desenvolvimento da calorimetria<\/h3>\n\n\n\n<p>A ideia de que o calor \u00e9 uma quantidade mensur\u00e1vel levou \u00e0 cria\u00e7\u00e3o de instrumentos e m\u00e9todos experimentais que ainda usamos.<\/p>\n\n\n\n<h3 class=\"wp-block-heading\">\u2714\ufe0f 3. Base conceitual para a Primeira Lei da Termodin\u00e2mica<\/h3>\n\n\n\n<p>Ao tratar o calor como algo que pode ser contabilizado, a teoria preparou o terreno para a formula\u00e7\u00e3o da <strong>conserva\u00e7\u00e3o da energia<\/strong>: [<math data-latex=\" \\Delta U = Q - W \"><semantics><mrow><mrow><mi mathvariant=\"normal\">\u0394<\/mi><\/mrow><mi>U<\/mi><mo>=<\/mo><mi>Q<\/mi><mo>\u2212<\/mo><mi>W<\/mi><\/mrow><annotation encoding=\"application\/x-tex\"> \\Delta U = Q &#8211; W <\/annotation><\/semantics><\/math>]<\/p>\n\n\n\n<p>Mesmo que o cal\u00f3rico n\u00e3o existisse, a no\u00e7\u00e3o de \u201cquantidade de calor\u201d foi essencial para essa lei.<\/p>\n\n\n\n<h3 class=\"wp-block-heading\">\u2714\ufe0f 4. Est\u00edmulo ao debate cient\u00edfico<\/h3>\n\n\n\n<p>A inconsist\u00eancia entre a teoria e experimentos como os de Rumford e Joule levou \u00e0 reformula\u00e7\u00e3o completa do conceito de calor \u2014 um exemplo cl\u00e1ssico de como a ci\u00eancia progride ao confrontar modelos com evid\u00eancias.<\/p>\n\n\n\n<h2 class=\"wp-block-heading\">\ud83d\udd25 Rela\u00e7\u00e3o com as leis da termodin\u00e2mica<\/h2>\n\n\n\n<h3 class=\"wp-block-heading\"><strong>Primeira Lei<\/strong><\/h3>\n\n\n\n<p>A teoria do cal\u00f3rico ajudou a estabelecer a ideia de que o calor \u00e9 uma grandeza mensur\u00e1vel, mas falhou ao trat\u00e1-lo como subst\u00e2ncia. A supera\u00e7\u00e3o dessa vis\u00e3o permitiu entender o calor como <strong>energia em tr\u00e2nsito<\/strong>, essencial para a Primeira Lei.<\/p>\n\n\n\n<h3 class=\"wp-block-heading\"><strong>Segunda Lei<\/strong><\/h3>\n\n\n\n<p>A teoria do cal\u00f3rico n\u00e3o explicava irreversibilidade nem efici\u00eancia de m\u00e1quinas t\u00e9rmicas. Foi ao abandon\u00e1-la que cientistas como <strong>Carnot<\/strong>, <strong>Clausius<\/strong> e <strong>Kelvin<\/strong> puderam formular:<\/p>\n\n\n\n<ul class=\"wp-block-list\">\n<li>Entropia<\/li>\n\n\n\n<li>Limites de efici\u00eancia<\/li>\n\n\n\n<li>Direcionalidade dos processos t\u00e9rmicos<\/li>\n<\/ul>\n\n\n\n<p>Curiosamente, Carnot inicialmente trabalhou ainda sob a influ\u00eancia da teoria do cal\u00f3rico, mas suas conclus\u00f5es sobreviveram \u00e0 queda da teoria.<\/p>\n\n\n\n<h2 class=\"wp-block-heading\">\ud83e\udded S\u00edntese final<\/h2>\n\n\n\n<p>A teoria do cal\u00f3rico foi um <strong>modelo transit\u00f3rio<\/strong>, mas extremamente produtivo. Ela:<\/p>\n\n\n\n<ul class=\"wp-block-list\">\n<li>Organizou o estudo do calor<\/li>\n\n\n\n<li>Permitiu medi\u00e7\u00f5es precisas<\/li>\n\n\n\n<li>Inspirou experimentos decisivos<\/li>\n\n\n\n<li>Preparou o terreno para a termodin\u00e2mica moderna<\/li>\n<\/ul>\n\n\n\n<p>Seu colapso foi t\u00e3o importante quanto sua exist\u00eancia, pois abriu caminho para a compreens\u00e3o do calor como energia \u2014 o que fundamenta toda a f\u00edsica t\u00e9rmica atual.<\/p>\n\n\n\n<p>A <strong>capacidade t\u00e9rmica<\/strong> e o <strong>calor espec\u00edfico<\/strong> nasceram como conceitos centrais da calorimetria no s\u00e9culo XVIII, quando cientistas buscavam quantificar o calor \u2014 ainda entendido, na \u00e9poca, como o \u201cfluido cal\u00f3rico\u201d. Esses conceitos evolu\u00edram com a queda da teoria do cal\u00f3rico e se tornaram pilares da termodin\u00e2mica moderna.<\/p>\n\n\n\n<hr class=\"wp-block-separator has-alpha-channel-opacity\"\/>\n\n\n\n<h2 class=\"wp-block-heading\">\ud83d\udd25 Conceitos fundamentais<\/h2>\n\n\n\n<h3 class=\"wp-block-heading\">Capacidade t\u00e9rmica<\/h3>\n\n\n\n<p>\u00c9 a quantidade total de calor necess\u00e1ria para elevar a temperatura de <strong>um corpo inteiro<\/strong> em 1\u202f\u00b0C (ou 1\u202fK).<br>Matematicamente:<br><math data-latex=\"\\displaystyle C = \\frac{Q}{\\Delta T} =\\frac{dQ}{dT}\"><semantics><mstyle scriptlevel=\"0\" displaystyle=\"true\"><mi>C<\/mi><mo>=<\/mo><mfrac><mi>Q<\/mi><mrow><mrow><mi mathvariant=\"normal\">\u0394<\/mi><\/mrow><mi>T<\/mi><\/mrow><\/mfrac><mo>=<\/mo><mfrac><mrow><mi>d<\/mi><mi>Q<\/mi><\/mrow><mrow><mi>d<\/mi><mi>T<\/mi><\/mrow><\/mfrac><\/mstyle><annotation encoding=\"application\/x-tex\">\\displaystyle C = \\frac{Q}{\\Delta T} =\\frac{dQ}{dT}<\/annotation><\/semantics><\/math><br>Ela depende da <strong>massa<\/strong> e da <strong>composi\u00e7\u00e3o<\/strong> do corpo.<\/p>\n\n\n\n<h3 class=\"wp-block-heading\">Calor espec\u00edfico<\/h3>\n\n\n\n<p>\u00c9 a quantidade de calor necess\u00e1ria para elevar a temperatura de <strong>1\u202fg ou 1\u202fkg de uma subst\u00e2ncia<\/strong> em 1\u202f\u00b0C (ou 1\u202fK).<br><math data-latex=\"\\displaystyle c = \\frac{Q}{m \\Delta T} =\\frac{1}{m}\\frac{dQ}{dT}\"><semantics><mstyle scriptlevel=\"0\" displaystyle=\"true\"><mi>c<\/mi><mo>=<\/mo><mfrac><mi>Q<\/mi><mrow><mi>m<\/mi><mrow><mi mathvariant=\"normal\">\u0394<\/mi><\/mrow><mi>T<\/mi><\/mrow><\/mfrac><mo>=<\/mo><mfrac><mn>1<\/mn><mi>m<\/mi><\/mfrac><mfrac><mrow><mi>d<\/mi><mi>Q<\/mi><\/mrow><mrow><mi>d<\/mi><mi>T<\/mi><\/mrow><\/mfrac><\/mstyle><annotation encoding=\"application\/x-tex\">\\displaystyle c = \\frac{Q}{m \\Delta T} =\\frac{1}{m}\\frac{dQ}{dT}<\/annotation><\/semantics><\/math> <\/p>\n\n\n\n<p>\u00c9 uma propriedade <strong>intensiva<\/strong>, caracter\u00edstica de cada material.<\/p>\n\n\n\n<h2 class=\"wp-block-heading\">\ud83e\udded Origem hist\u00f3rica dos conceitos<\/h2>\n\n\n\n<h3 class=\"wp-block-heading\">Joseph Black e o nascimento da calorimetria (s\u00e9culo XVIII)<\/h3>\n\n\n\n<p>O f\u00edsico e qu\u00edmico escoc\u00eas <strong>Joseph Black<\/strong> foi o primeiro a formular claramente os conceitos de:<\/p>\n\n\n\n<ul class=\"wp-block-list\">\n<li>calor latente,<\/li>\n\n\n\n<li>calor sens\u00edvel,<\/li>\n\n\n\n<li>capacidade t\u00e9rmica,<\/li>\n\n\n\n<li>e o embri\u00e3o do que hoje chamamos de calor espec\u00edfico.<\/li>\n<\/ul>\n\n\n\n<p>Black percebeu experimentalmente que diferentes subst\u00e2ncias exigiam quantidades diferentes de calor para sofrer a mesma varia\u00e7\u00e3o de temperatura. Ele chamou essa propriedade de \u201ccapacidade de aquecimento\u201d, que evoluiu para o conceito moderno de calor espec\u00edfico.<\/p>\n\n\n\n<h3 class=\"wp-block-heading\">Consolida\u00e7\u00e3o no s\u00e9culo XIX<\/h3>\n\n\n\n<p>Com o avan\u00e7o da calorimetria, especialmente ap\u00f3s a queda da teoria do cal\u00f3rico, o calor passou a ser entendido como <strong>energia em tr\u00e2nsito<\/strong>, e n\u00e3o como fluido. Isso permitiu:<\/p>\n\n\n\n<ul class=\"wp-block-list\">\n<li>definir rigorosamente (<math data-latex=\"Q = mc\\Delta T\"><semantics><mrow><mi>Q<\/mi><mo>=<\/mo><mi>m<\/mi><mi>c<\/mi><mrow><mi mathvariant=\"normal\">\u0394<\/mi><\/mrow><mi>T<\/mi><\/mrow><annotation encoding=\"application\/x-tex\">Q = mc\\Delta T<\/annotation><\/semantics><\/math>),<\/li>\n\n\n\n<li>padronizar unidades (caloria e, depois, joule),<\/li>\n\n\n\n<li>relacionar calor espec\u00edfico com estrutura molecular.<\/li>\n<\/ul>\n\n\n\n<h3 class=\"wp-block-heading\">A transi\u00e7\u00e3o para a termodin\u00e2mica<\/h3>\n\n\n\n<p>A formula\u00e7\u00e3o da <strong>Primeira Lei da Termodin\u00e2mica<\/strong> (conserva\u00e7\u00e3o da energia) integrou definitivamente esses conceitos ao arcabou\u00e7o energ\u00e9tico da f\u00edsica. A capacidade t\u00e9rmica passou a ser vista como derivada da energia interna, e o calor espec\u00edfico ganhou interpreta\u00e7\u00f5es microsc\u00f3picas (graus de liberdade, teoria cin\u00e9tica).<\/p>\n\n\n\n<h2 class=\"wp-block-heading\">\ud83d\udcda Contribui\u00e7\u00f5es cient\u00edficas e impacto<\/h2>\n\n\n\n<h3 class=\"wp-block-heading\">Para a f\u00edsica experimental<\/h3>\n\n\n\n<ul class=\"wp-block-list\">\n<li>Permitiu medir calor de forma quantitativa e compar\u00e1vel.<\/li>\n\n\n\n<li>Viabilizou a constru\u00e7\u00e3o de calor\u00edmetros e tabelas de propriedades t\u00e9rmicas.<\/li>\n\n\n\n<li>Fundamentou estudos de mudan\u00e7as de estado e equil\u00edbrio t\u00e9rmico.<\/li>\n<\/ul>\n\n\n\n<h3 class=\"wp-block-heading\">Para a termodin\u00e2mica<\/h3>\n\n\n\n<ul class=\"wp-block-list\">\n<li>Foi essencial para Carnot, Clausius e Kelvin ao formular leis t\u00e9rmicas.<\/li>\n\n\n\n<li>Relaciona-se diretamente com a energia interna e com a capacidade calor\u00edfica molar dos gases ideais.<\/li>\n\n\n\n<li>Influenciou a compreens\u00e3o da irreversibilidade e da entropia.<\/li>\n<\/ul>\n\n\n\n<h3 class=\"wp-block-heading\">Para a ci\u00eancia dos materiais e engenharia<\/h3>\n\n\n\n<ul class=\"wp-block-list\">\n<li>Determina como materiais respondem ao aquecimento.<\/li>\n\n\n\n<li>\u00c9 crucial em processos industriais, motores t\u00e9rmicos, climatiza\u00e7\u00e3o, metalurgia e geof\u00edsica.<\/li>\n<\/ul>\n\n\n\n<h2 class=\"wp-block-heading\">\ud83e\uddea Rela\u00e7\u00e3o entre capacidade t\u00e9rmica e calor espec\u00edfico<\/h2>\n\n\n\n<p>A rela\u00e7\u00e3o moderna entre os dois conceitos \u00e9: <\/p>\n\n\n\n<div class=\"wp-block-math\"><math display=\"block\"><semantics><mrow><mi>C<\/mi><mo>=<\/mo><mi>m<\/mi><mi>c<\/mi><\/mrow><annotation encoding=\"application\/x-tex\">C=mc<\/annotation><\/semantics><\/math><\/div>\n\n\n\n<ul class=\"wp-block-list\">\n<li><strong>Capacidade t\u00e9rmica<\/strong>: depende do corpo como um todo.<\/li>\n\n\n\n<li><strong>Calor espec\u00edfico<\/strong>: depende apenas da subst\u00e2ncia.<\/li>\n<\/ul>\n\n\n\n<p>Essa distin\u00e7\u00e3o, hoje trivial, foi um avan\u00e7o conceitual importante no s\u00e9culo XVIII, pois permitiu separar propriedades <strong>extensivas<\/strong> (dependem da quantidade de mat\u00e9ria) de <strong>intensivas<\/strong> (independentes da quantidade).<\/p>\n\n\n\n<h2 class=\"wp-block-heading\">\ud83e\udde9 Refer\u00eancias cient\u00edficas e hist\u00f3ricas (com base nas fontes consultadas)<\/h2>\n\n\n\n<ul class=\"wp-block-list\">\n<li>A origem do conceito de calor espec\u00edfico remonta \u00e0s investiga\u00e7\u00f5es de <strong>Joseph Black<\/strong>, que identificou diferen\u00e7as entre subst\u00e2ncias quanto \u00e0 quantidade de calor necess\u00e1ria para aquec\u00ea-las.<\/li>\n\n\n\n<li>Estudos modernos de calorimetria e defini\u00e7\u00f5es formais de calor espec\u00edfico e capacidade t\u00e9rmica s\u00e3o apresentados em materiais did\u00e1ticos como os da Brasil Escola.<\/li>\n\n\n\n<li>A rela\u00e7\u00e3o entre hist\u00f3ria da ci\u00eancia e ensino desses conceitos \u00e9 discutida em trabalhos acad\u00eamicos recentes.<\/li>\n<\/ul>\n\n\n\n<p>Calor <strong>sens\u00edvel<\/strong> e <strong>latente<\/strong> s\u00e3o dois modos diferentes pelos quais a energia t\u00e9rmica pode ser transferida para uma subst\u00e2ncia. A diferen\u00e7a central \u00e9 <strong>se a temperatura muda ou n\u00e3o<\/strong> durante o processo.<\/p>\n\n\n\n<h2 class=\"wp-block-heading\">\ud83d\udd25 Calor sens\u00edvel: quando a temperatura muda<\/h2>\n\n\n\n<p>O <strong>calor sens\u00edvel<\/strong> \u00e9 a energia t\u00e9rmica que provoca <strong>varia\u00e7\u00e3o de temperatura<\/strong> de um corpo <strong>sem mudar seu estado f\u00edsico<\/strong>.<\/p>\n\n\n\n<p>A rela\u00e7\u00e3o \u00e9 dada por:<\/p>\n\n\n\n<p><math data-latex=\" Q = m \\cdot c \\cdot \\Delta T \"><semantics><mrow><mi>Q<\/mi><mo>=<\/mo><mi>m<\/mi><mo>\u22c5<\/mo><mi>c<\/mi><mo>\u22c5<\/mo><mrow><mi mathvariant=\"normal\">\u0394<\/mi><\/mrow><mi>T<\/mi><\/mrow><annotation encoding=\"application\/x-tex\"> Q = m \\cdot c \\cdot \\Delta T <\/annotation><\/semantics><\/math><\/p>\n\n\n\n<ul class=\"wp-block-list\">\n<li>(Q): calor sens\u00edvel (em J ou cal)<\/li>\n\n\n\n<li>(m): massa<\/li>\n\n\n\n<li>(c): calor espec\u00edfico<\/li>\n\n\n\n<li>(<math data-latex=\"\\Delta T\"><semantics><mrow><mrow><mi mathvariant=\"normal\">\u0394<\/mi><\/mrow><mi>T<\/mi><\/mrow><annotation encoding=\"application\/x-tex\">\\Delta T<\/annotation><\/semantics><\/math>): varia\u00e7\u00e3o de temperatura<\/li>\n<\/ul>\n\n\n\n<h3 class=\"wp-block-heading\">Exemplo num\u00e9rico<\/h3>\n\n\n\n<p>Aque\u00e7a <strong>200 g de \u00e1gua<\/strong> de <strong>25\u00b0C para 70\u00b0C<\/strong>.<br>Calor espec\u00edfico da \u00e1gua: (<math data-latex=\"c = 1,0\\text{cal\/g\u00b0C}\"><semantics><mrow><mi>c<\/mi><mo>=<\/mo><mn>1,0<\/mn><mtext>cal\/g\u00b0C<\/mtext><\/mrow><annotation encoding=\"application\/x-tex\">c = 1,0\\text{cal\/g\u00b0C}<\/annotation><\/semantics><\/math>).<\/p>\n\n\n\n<p><math data-latex=\" Q = 200 \\cdot 1 \\cdot (70 - 25) \"><semantics><mrow><mi>Q<\/mi><mo>=<\/mo><mn>200<\/mn><mo>\u22c5<\/mo><mn>1<\/mn><mo>\u22c5<\/mo><mo form=\"prefix\" stretchy=\"false\">(<\/mo><mn>70<\/mn><mo>\u2212<\/mo><mn>25<\/mn><mo form=\"postfix\" stretchy=\"false\">)<\/mo><\/mrow><annotation encoding=\"application\/x-tex\"> Q = 200 \\cdot 1 \\cdot (70 &#8211; 25) <\/annotation><\/semantics><\/math><\/p>\n\n\n\n<p><math data-latex=\" Q = 200 \\cdot 45 = 9000,\\text{cal} \"><semantics><mrow><mi>Q<\/mi><mo>=<\/mo><mn>200<\/mn><mo>\u22c5<\/mo><mn>45<\/mn><mo>=<\/mo><mn>9000<\/mn><mo separator=\"true\">,<\/mo><mtext>cal<\/mtext><\/mrow><annotation encoding=\"application\/x-tex\"> Q = 200 \\cdot 45 = 9000,\\text{cal} <\/annotation><\/semantics><\/math><\/p>\n\n\n\n<p><strong>Interpreta\u00e7\u00e3o:<\/strong> foram necess\u00e1rias <strong>9.000 calorias<\/strong> para aquecer a \u00e1gua sem mudar seu estado.<\/p>\n\n\n\n<h2 class=\"wp-block-heading\">\u2744\ufe0f Calor latente: quando o estado muda<\/h2>\n\n\n\n<p>O <strong>calor latente<\/strong> \u00e9 a energia t\u00e9rmica usada para <strong>mudar o estado f\u00edsico<\/strong> de uma subst\u00e2ncia <strong>sem alterar a temperatura<\/strong>.<\/p>\n\n\n\n<p>A rela\u00e7\u00e3o \u00e9:<\/p>\n\n\n\n<p><math data-latex=\" Q = m \\cdot L \"><semantics><mrow><mi>Q<\/mi><mo>=<\/mo><mi>m<\/mi><mo>\u22c5<\/mo><mi>L<\/mi><\/mrow><annotation encoding=\"application\/x-tex\"> Q = m \\cdot L <\/annotation><\/semantics><\/math><\/p>\n\n\n\n<ul class=\"wp-block-list\">\n<li>(Q): calor latente<\/li>\n\n\n\n<li>(m): massa<\/li>\n\n\n\n<li>(L): calor latente (de fus\u00e3o, vaporiza\u00e7\u00e3o etc.)<\/li>\n<\/ul>\n\n\n\n<h3 class=\"wp-block-heading\">Tipos comuns<\/h3>\n\n\n\n<ul class=\"wp-block-list\">\n<li><strong>Latente de fus\u00e3o (Lf):<\/strong> s\u00f3lido \u2192 l\u00edquido<\/li>\n\n\n\n<li><strong>Latente de vaporiza\u00e7\u00e3o (Lv):<\/strong> l\u00edquido \u2192 vapor<\/li>\n<\/ul>\n\n\n\n<h3 class=\"wp-block-heading\">Exemplo num\u00e9rico<\/h3>\n\n\n\n<p>Derreter <strong>500 g de gelo<\/strong> a 0\u00b0C.<br>Calor latente de fus\u00e3o da \u00e1gua: <math data-latex=\"(L_f = 80,\\text{cal\/g})\"><semantics><mrow><mo form=\"prefix\" stretchy=\"false\">(<\/mo><msub><mi>L<\/mi><mi>f<\/mi><\/msub><mo>=<\/mo><mn>80<\/mn><mo separator=\"true\">,<\/mo><mtext>cal\/g<\/mtext><mo form=\"postfix\" stretchy=\"false\">)<\/mo><\/mrow><annotation encoding=\"application\/x-tex\">(L_f = 80,\\text{cal\/g})<\/annotation><\/semantics><\/math>.<\/p>\n\n\n\n<p><math data-latex=\" Q = 500 \\cdot 80 = 40,000,\\text{cal} \"><semantics><mrow><mi>Q<\/mi><mo>=<\/mo><mn>500<\/mn><mo>\u22c5<\/mo><mn>80<\/mn><mo>=<\/mo><mn>40,000<\/mn><mo separator=\"true\">,<\/mo><mtext>cal<\/mtext><\/mrow><annotation encoding=\"application\/x-tex\"> Q = 500 \\cdot 80 = 40,000,\\text{cal} <\/annotation><\/semantics><\/math><\/p>\n\n\n\n<p><strong>Interpreta\u00e7\u00e3o:<\/strong> s\u00e3o necess\u00e1rias <strong>40.000 calorias<\/strong> para transformar o gelo em \u00e1gua <strong>sem mudar a temperatura<\/strong> (continua em 0\u00b0C durante todo o processo).<\/p>\n\n\n\n<h2 class=\"wp-block-heading\">\ud83c\udf21\ufe0f Compara\u00e7\u00e3o direta<\/h2>\n\n\n\n<figure class=\"wp-block-table\"><table class=\"has-fixed-layout\"><thead><tr><th>Caracter\u00edstica<\/th><th>Calor Sens\u00edvel<\/th><th>Calor Latente<\/th><\/tr><\/thead><tbody><tr><td>Muda a temperatura?<\/td><td>\u2714\ufe0f Sim<\/td><td>\u274c N\u00e3o<\/td><\/tr><tr><td>Muda o estado f\u00edsico?<\/td><td>\u274c N\u00e3o<\/td><td>\u2714\ufe0f Sim<\/td><\/tr><tr><td>F\u00f3rmula<\/td><td>(<math data-latex=\"Q = m c \\Delta T\"><semantics><mrow><mi>Q<\/mi><mo>=<\/mo><mi>m<\/mi><mi>c<\/mi><mrow><mi mathvariant=\"normal\">\u0394<\/mi><\/mrow><mi>T<\/mi><\/mrow><annotation encoding=\"application\/x-tex\">Q = m c \\Delta T<\/annotation><\/semantics><\/math>)<\/td><td>(Q = m L)<\/td><\/tr><tr><td>Exemplo t\u00edpico<\/td><td>Aquecer \u00e1gua<\/td><td>Derreter gelo<\/td><\/tr><\/tbody><\/table><\/figure>\n\n\n\n<hr class=\"wp-block-separator has-alpha-channel-opacity\"\/>\n\n\n\n<h2 class=\"wp-block-heading\">Um detalhe importante que muita gente esquece<\/h2>\n\n\n\n<p>Durante mudan\u00e7as de fase, <strong>toda energia fornecida vai para quebrar liga\u00e7\u00f5es<\/strong>, n\u00e3o para aumentar a temperatura. Por isso, ao ferver \u00e1gua, ela fica <strong>parada em 100\u00b0C<\/strong> at\u00e9 evaporar completamente \u2014 mesmo recebendo calor continuamente.<\/p>\n\n\n\n<p>O uso de <strong>calor sens\u00edvel<\/strong> e <strong>calor latente<\/strong> em <strong>F\u00edsico\u2011Qu\u00edmica<\/strong> vai al\u00e9m da defini\u00e7\u00e3o b\u00e1sica e aparece em temas como <strong>termodin\u00e2mica<\/strong>, <strong>transi\u00e7\u00f5es de fase<\/strong>, <strong>entalpia<\/strong>, <strong>diagramas de aquecimento<\/strong>, <strong>equil\u00edbrio de fases<\/strong> e <strong>propriedades coligativas<\/strong>. A ideia central continua a mesma, mas o foco passa a ser <strong>como a energia t\u00e9rmica altera a estrutura molecular e o estado energ\u00e9tico de uma subst\u00e2ncia<\/strong>.<\/p>\n\n\n\n<h2 class=\"wp-block-heading\">\ud83c\udf21\ufe0f Calor sens\u00edvel em F\u00edsico\u2011Qu\u00edmica<\/h2>\n\n\n\n<p>O calor sens\u00edvel \u00e9 interpretado como <strong>varia\u00e7\u00e3o de energia interna associada ao movimento das part\u00edculas<\/strong>, sem mudan\u00e7a de fase. Em termos termodin\u00e2micos, ele est\u00e1 ligado \u00e0 <strong>capacidade calor\u00edfica<\/strong> e \u00e0 <strong>entalpia<\/strong>.<\/p>\n\n\n\n<h3 class=\"wp-block-heading\">Como aparece em F\u00edsico\u2011Qu\u00edmica<\/h3>\n\n\n\n<ul class=\"wp-block-list\">\n<li><strong>Capacidade calor\u00edfica molar<\/strong>: usa-se (<math data-latex=\"C_m\"><semantics><msub><mi>C<\/mi><mi>m<\/mi><\/msub><annotation encoding=\"application\/x-tex\">C_m<\/annotation><\/semantics><\/math>) em vez de (c).<\/li>\n\n\n\n<li><strong>Processos a press\u00e3o constante<\/strong>: o calor sens\u00edvel \u00e9 igual \u00e0 varia\u00e7\u00e3o de entalpia:<br><math data-latex=\" Q = n \\cdot C_p \\cdot \\Delta T \"><semantics><mrow><mi>Q<\/mi><mo>=<\/mo><mi>n<\/mi><mo>\u22c5<\/mo><msub><mi>C<\/mi><mi>p<\/mi><\/msub><mo>\u22c5<\/mo><mrow><mi mathvariant=\"normal\">\u0394<\/mi><\/mrow><mi>T<\/mi><\/mrow><annotation encoding=\"application\/x-tex\"> Q = n \\cdot C_p \\cdot \\Delta T <\/annotation><\/semantics><\/math><\/li>\n\n\n\n<li><strong>Interpreta\u00e7\u00e3o molecular<\/strong>: aumento de temperatura significa aumento da energia cin\u00e9tica m\u00e9dia.<\/li>\n<\/ul>\n\n\n\n<h3 class=\"wp-block-heading\">Exemplo num\u00e9rico (agora em termos f\u00edsico\u2011qu\u00edmicos)<\/h3>\n\n\n\n<p>Aque\u00e7a <strong>2 mol de etanol l\u00edquido<\/strong> de <strong>20\u00b0C para 50\u00b0C<\/strong>.<br>Capacidade calor\u00edfica molar do etanol: <\/p>\n\n\n\n<p><math data-latex=\"(C_p = 112,0\\text{J\u00b7mol}^{-1}\\text{\u00b7\u00b0C}^{-1}).\"><semantics><mrow><mo form=\"prefix\" stretchy=\"false\">(<\/mo><msub><mi>C<\/mi><mi>p<\/mi><\/msub><mo>=<\/mo><mn>112,0<\/mn><msup><mtext>J\u00b7mol<\/mtext><mrow><mo lspace=\"0em\" rspace=\"0em\">\u2212<\/mo><mn>1<\/mn><\/mrow><\/msup><msup><mtext>\u00b7\u00b0C<\/mtext><mrow><mo lspace=\"0em\" rspace=\"0em\">\u2212<\/mo><mn>1<\/mn><\/mrow><\/msup><mo form=\"postfix\" stretchy=\"false\">)<\/mo><mi>.<\/mi><\/mrow><annotation encoding=\"application\/x-tex\">(C_p = 112,0\\text{J\u00b7mol}^{-1}\\text{\u00b7\u00b0C}^{-1}).<\/annotation><\/semantics><\/math><\/p>\n\n\n\n<p><math data-latex=\" Q = n C_p \\Delta T = 2 \\cdot 112 \\cdot (50 - 20) \"><semantics><mrow><mi>Q<\/mi><mo>=<\/mo><mi>n<\/mi><msub><mi>C<\/mi><mi>p<\/mi><\/msub><mrow><mi mathvariant=\"normal\">\u0394<\/mi><\/mrow><mi>T<\/mi><mo>=<\/mo><mn>2<\/mn><mo>\u22c5<\/mo><mn>112<\/mn><mo>\u22c5<\/mo><mo form=\"prefix\" stretchy=\"false\">(<\/mo><mn>50<\/mn><mo>\u2212<\/mo><mn>20<\/mn><mo form=\"postfix\" stretchy=\"false\">)<\/mo><\/mrow><annotation encoding=\"application\/x-tex\"> Q = n C_p \\Delta T = 2 \\cdot 112 \\cdot (50 &#8211; 20) <\/annotation><\/semantics><\/math><\/p>\n\n\n\n<p><math data-latex=\" Q = 2 \\cdot 112 \\cdot 30 = 6720,\\text{J} \"><semantics><mrow><mi>Q<\/mi><mo>=<\/mo><mn>2<\/mn><mo>\u22c5<\/mo><mn>112<\/mn><mo>\u22c5<\/mo><mn>30<\/mn><mo>=<\/mo><mn>6720<\/mn><mo separator=\"true\">,<\/mo><mtext>J<\/mtext><\/mrow><annotation encoding=\"application\/x-tex\"> Q = 2 \\cdot 112 \\cdot 30 = 6720,\\text{J} <\/annotation><\/semantics><\/math><\/p>\n\n\n\n<p>Esse calor corresponde \u00e0 <strong>varia\u00e7\u00e3o de entalpia<\/strong> do etanol nesse intervalo.<\/p>\n\n\n\n<h2 class=\"wp-block-heading\">\u2744\ufe0f Calor latente em F\u00edsico\u2011Qu\u00edmica<\/h2>\n\n\n\n<p>O calor latente passa a ser tratado como <strong>entalpia de mudan\u00e7a de fase<\/strong>, como:<\/p>\n\n\n\n<ul class=\"wp-block-list\">\n<li><strong>entalpia molar de fus\u00e3o<\/strong> <math data-latex=\"(\\Delta H_\\text{fus})\"><semantics><mrow><mo form=\"prefix\" stretchy=\"false\">(<\/mo><mrow><mi mathvariant=\"normal\">\u0394<\/mi><\/mrow><msub><mi>H<\/mi><mtext>fus<\/mtext><\/msub><mo form=\"postfix\" stretchy=\"false\">)<\/mo><\/mrow><annotation encoding=\"application\/x-tex\">(\\Delta H_\\text{fus})<\/annotation><\/semantics><\/math><\/li>\n\n\n\n<li><strong>entalpia molar de vaporiza\u00e7\u00e3o<\/strong> <math data-latex=\"(\\Delta H_\\text{vap})\"><semantics><mrow><mo form=\"prefix\" stretchy=\"false\">(<\/mo><mrow><mi mathvariant=\"normal\">\u0394<\/mi><\/mrow><msub><mi>H<\/mi><mtext>vap<\/mtext><\/msub><mo form=\"postfix\" stretchy=\"false\">)<\/mo><\/mrow><annotation encoding=\"application\/x-tex\">(\\Delta H_\\text{vap})<\/annotation><\/semantics><\/math><\/li>\n\n\n\n<li><strong>entalpia de sublima\u00e7\u00e3o<\/strong> <math data-latex=\"(\\Delta H_\\text{sub})\"><semantics><mrow><mo form=\"prefix\" stretchy=\"false\">(<\/mo><mrow><mi mathvariant=\"normal\">\u0394<\/mi><\/mrow><msub><mi>H<\/mi><mtext>sub<\/mtext><\/msub><mo form=\"postfix\" stretchy=\"false\">)<\/mo><\/mrow><annotation encoding=\"application\/x-tex\">(\\Delta H_\\text{sub})<\/annotation><\/semantics><\/math><\/li>\n<\/ul>\n\n\n\n<p>A temperatura permanece constante porque a energia \u00e9 usada para <strong>romper ou formar intera\u00e7\u00f5es intermoleculares<\/strong>, n\u00e3o para aumentar energia cin\u00e9tica.<\/p>\n\n\n\n<h3 class=\"wp-block-heading\">Como aparece em F\u00edsico\u2011Qu\u00edmica<\/h3>\n\n\n\n<ul class=\"wp-block-list\">\n<li>Em <strong>diagramas de fase<\/strong> (P \u00d7 T), o calor latente est\u00e1 relacionado \u00e0s linhas de equil\u00edbrio.<\/li>\n\n\n\n<li>Na <strong>equa\u00e7\u00e3o de Clausius\u2013Clapeyron<\/strong>, a entalpia de vaporiza\u00e7\u00e3o determina a inclina\u00e7\u00e3o da curva l\u00edquido\u2011vapor.<\/li>\n\n\n\n<li>Em <strong>equil\u00edbrio qu\u00edmico<\/strong>, mudan\u00e7as de fase podem alterar press\u00f5es parciais e constantes de equil\u00edbrio.<\/li>\n<\/ul>\n\n\n\n<h3 class=\"wp-block-heading\">Exemplo num\u00e9rico (com entalpia molar)<\/h3>\n\n\n\n<p>Vaporizar <strong>0,5 mol de \u00e1gua<\/strong> a 100\u00b0C.<br>Entalpia molar de vaporiza\u00e7\u00e3o: <math data-latex=\"(\\Delta H_\\text{vap} = 40,7\\text{kJ\/mol}).\"><semantics><mrow><mo form=\"prefix\" stretchy=\"false\">(<\/mo><mrow><mi mathvariant=\"normal\">\u0394<\/mi><\/mrow><msub><mi>H<\/mi><mtext>vap<\/mtext><\/msub><mo>=<\/mo><mn>40,7<\/mn><mtext>kJ\/mol<\/mtext><mo form=\"postfix\" stretchy=\"false\">)<\/mo><mi>.<\/mi><\/mrow><annotation encoding=\"application\/x-tex\">(\\Delta H_\\text{vap} = 40,7\\text{kJ\/mol}).<\/annotation><\/semantics><\/math><\/p>\n\n\n\n<p><math data-latex=\" Q = n \\cdot \\Delta H_\\text{vap} = 0,5 \\cdot 40,7 \"><semantics><mrow><mi>Q<\/mi><mo>=<\/mo><mi>n<\/mi><mo>\u22c5<\/mo><mrow><mi mathvariant=\"normal\">\u0394<\/mi><\/mrow><msub><mi>H<\/mi><mtext>vap<\/mtext><\/msub><mo>=<\/mo><mn>0,5<\/mn><mo>\u22c5<\/mo><mn>40,7<\/mn><\/mrow><annotation encoding=\"application\/x-tex\"> Q = n \\cdot \\Delta H_\\text{vap} = 0,5 \\cdot 40,7 <\/annotation><\/semantics><\/math><\/p>\n\n\n\n<p><math data-latex=\" Q = 20,35\\text{kJ} \"><semantics><mrow><mi>Q<\/mi><mo>=<\/mo><mn>20,35<\/mn><mtext>kJ<\/mtext><\/mrow><annotation encoding=\"application\/x-tex\"> Q = 20,35\\text{kJ} <\/annotation><\/semantics><\/math><\/p>\n\n\n\n<p>Esse calor \u00e9 usado exclusivamente para <strong>romper liga\u00e7\u00f5es de hidrog\u00eanio<\/strong> entre as mol\u00e9culas.<\/p>\n\n\n\n<h2 class=\"wp-block-heading\">\ud83d\udd2c Compara\u00e7\u00e3o f\u00edsico\u2011qu\u00edmica: o que muda no n\u00edvel molecular<\/h2>\n\n\n\n<h3 class=\"wp-block-heading\">Calor sens\u00edvel<\/h3>\n\n\n\n<ul class=\"wp-block-list\">\n<li>Aumenta a energia cin\u00e9tica m\u00e9dia.<\/li>\n\n\n\n<li>Mol\u00e9culas vibram, rotacionam e se movem mais rapidamente.<\/li>\n\n\n\n<li>N\u00e3o h\u00e1 reorganiza\u00e7\u00e3o estrutural significativa.<\/li>\n<\/ul>\n\n\n\n<h3 class=\"wp-block-heading\">Calor latente<\/h3>\n\n\n\n<ul class=\"wp-block-list\">\n<li>A energia vai para <strong>romper ou formar intera\u00e7\u00f5es intermoleculares<\/strong> (dipolo\u2011dipolo, liga\u00e7\u00f5es de hidrog\u00eanio, for\u00e7as de London).<\/li>\n\n\n\n<li>A temperatura fica constante porque a energia n\u00e3o aumenta o movimento t\u00e9rmico, mas sim a <strong>configura\u00e7\u00e3o estrutural<\/strong>.<\/li>\n<\/ul>\n\n\n\n<h2 class=\"wp-block-heading\">\ud83d\udcc8 Onde esses conceitos aparecem juntos<\/h2>\n\n\n\n<p>Em F\u00edsico\u2011Qu\u00edmica, eles se combinam em:<\/p>\n\n\n\n<h3 class=\"wp-block-heading\">1. Curvas de aquecimento e resfriamento<\/h3>\n\n\n\n<p>Mostram trechos inclinados (calor sens\u00edvel) e trechos horizontais (calor latente).<br>Permitem calcular a energia total de processos complexos.<\/p>\n\n\n\n<h3 class=\"wp-block-heading\">2. C\u00e1lculo de entalpia total de processos<\/h3>\n\n\n\n<p>Exemplo: transformar gelo a \u201310\u00b0C em vapor a 120\u00b0C envolve <strong>cinco etapas<\/strong>, alternando calor sens\u00edvel e latente.<\/p>\n\n\n\n<h3 class=\"wp-block-heading\">3. Termodin\u00e2mica de solu\u00e7\u00f5es<\/h3>\n\n\n\n<p>A vaporiza\u00e7\u00e3o e fus\u00e3o influenciam:<\/p>\n\n\n\n<ul class=\"wp-block-list\">\n<li>press\u00e3o de vapor<\/li>\n\n\n\n<li>ponto de ebuli\u00e7\u00e3o<\/li>\n\n\n\n<li>ponto de congelamento<\/li>\n\n\n\n<li>entalpia de dissolu\u00e7\u00e3o<\/li>\n<\/ul>\n\n\n\n<h3 class=\"wp-block-heading\">4. Cin\u00e9tica e equil\u00edbrio<\/h3>\n\n\n\n<p>Mudan\u00e7as de fase alteram:<\/p>\n\n\n\n<ul class=\"wp-block-list\">\n<li>press\u00f5es parciais<\/li>\n\n\n\n<li>constantes de equil\u00edbrio<\/li>\n\n\n\n<li>velocidades de rea\u00e7\u00e3o em sistemas heterog\u00eaneos<\/li>\n<\/ul>\n\n\n\n<h2 class=\"wp-block-heading\">\ud83e\udde0 S\u00edntese final<\/h2>\n\n\n\n<ul class=\"wp-block-list\">\n<li><strong>Calor sens\u00edvel<\/strong>: muda temperatura; ligado \u00e0 capacidade calor\u00edfica e \u00e0 energia cin\u00e9tica.<\/li>\n\n\n\n<li><strong>Calor latente<\/strong>: muda fase; ligado \u00e0 entalpia de transi\u00e7\u00e3o e \u00e0 estrutura molecular.<\/li>\n\n\n\n<li>Em F\u00edsico\u2011Qu\u00edmica, esses conceitos se conectam a entalpia, diagramas de fase, equil\u00edbrio e propriedades coligativas.<\/li>\n<\/ul>\n\n\n\n<p>Vomos pensar em um cen\u00e1rio envolvendo gelo a -20\u00b0C sendo aquecido at\u00e9 vapor a 120\u00b0C. Vou usar as f\u00f3rmulas de calor espec\u00edfico (c), fus\u00e3o (Lf) e vaporiza\u00e7\u00e3o (Lv). A ideia \u00e9 dividir o processo em etapas: aquecer o gelo at\u00e9 0\u00b0C, derreter, aquecer a \u00e1gua at\u00e9 100\u00b0C, vaporizar e, finalmente, aquecer o vapor at\u00e9 120\u00b0C. Vou organizar tudo direitinho! Beleza, vamos montar um problem\u00e3o cl\u00e1ssico de F\u00edsico\u2011Qu\u00edmica, com tudo: calor sens\u00edvel + latente, v\u00e1rias etapas e resolu\u00e7\u00e3o completa.<\/p>\n\n\n\n<hr class=\"wp-block-separator has-alpha-channel-opacity\"\/>\n\n\n\n<h3 class=\"wp-block-heading\">Problema<\/h3>\n\n\n\n<p>Calcule o <strong>calor total<\/strong> necess\u00e1rio para transformar <strong>100 g de \u00e1gua<\/strong> na forma de <strong>gelo a \u201320\u00b0C<\/strong> em <strong>vapor a 120\u00b0C<\/strong>, \u00e0 press\u00e3o de 1 atm.<\/p>\n\n\n\n<p>Use os seguintes dados:<\/p>\n\n\n\n<ul class=\"wp-block-list\">\n<li><strong>Calor espec\u00edfico do gelo:<\/strong> <math data-latex=\"(c_{\\text{gelo}} = 0{,}5\\text{cal\/g\u00b7\u00b0C})\"><semantics><mrow><mo form=\"prefix\" stretchy=\"false\">(<\/mo><msub><mi>c<\/mi><mtext>gelo<\/mtext><\/msub><mo>=<\/mo><mn>0,5<\/mn><mtext>cal\/g\u00b7\u00b0C<\/mtext><mo form=\"postfix\" stretchy=\"false\">)<\/mo><\/mrow><annotation encoding=\"application\/x-tex\">(c_{\\text{gelo}} = 0{,}5\\text{cal\/g\u00b7\u00b0C})<\/annotation><\/semantics><\/math><\/li>\n\n\n\n<li><strong>Calor espec\u00edfico da \u00e1gua l\u00edquida:<\/strong> <math data-latex=\"(c_{\\text{\u00e1gua}} = 1{,}0\\text{cal\/g\u00b7\u00b0C})\"><semantics><mrow><mo form=\"prefix\" stretchy=\"false\">(<\/mo><msub><mi>c<\/mi><mtext>\u00e1gua<\/mtext><\/msub><mo>=<\/mo><mn>1,0<\/mn><mtext>cal\/g\u00b7\u00b0C<\/mtext><mo form=\"postfix\" stretchy=\"false\">)<\/mo><\/mrow><annotation encoding=\"application\/x-tex\">(c_{\\text{\u00e1gua}} = 1{,}0\\text{cal\/g\u00b7\u00b0C})<\/annotation><\/semantics><\/math><\/li>\n\n\n\n<li><strong>Calor espec\u00edfico do vapor:<\/strong> <math data-latex=\"(c_{\\text{vapor}} = 0{,}5\\text{cal\/g\u00b7\u00b0C})\"><semantics><mrow><mo form=\"prefix\" stretchy=\"false\">(<\/mo><msub><mi>c<\/mi><mtext>vapor<\/mtext><\/msub><mo>=<\/mo><mn>0,5<\/mn><mtext>cal\/g\u00b7\u00b0C<\/mtext><mo form=\"postfix\" stretchy=\"false\">)<\/mo><\/mrow><annotation encoding=\"application\/x-tex\">(c_{\\text{vapor}} = 0{,}5\\text{cal\/g\u00b7\u00b0C})<\/annotation><\/semantics><\/math><\/li>\n\n\n\n<li><strong>Calor latente de fus\u00e3o da \u00e1gua:<\/strong> <math data-latex=\"(L_f = 80\\text{cal\/g})\"><semantics><mrow><mo form=\"prefix\" stretchy=\"false\">(<\/mo><msub><mi>L<\/mi><mi>f<\/mi><\/msub><mo>=<\/mo><mn>80<\/mn><mtext>cal\/g<\/mtext><mo form=\"postfix\" stretchy=\"false\">)<\/mo><\/mrow><annotation encoding=\"application\/x-tex\">(L_f = 80\\text{cal\/g})<\/annotation><\/semantics><\/math><\/li>\n\n\n\n<li><strong>Calor latente de vaporiza\u00e7\u00e3o da \u00e1gua:<\/strong> <math data-latex=\"(L_v = 540\\text{cal\/g})\"><semantics><mrow><mo form=\"prefix\" stretchy=\"false\">(<\/mo><msub><mi>L<\/mi><mi>v<\/mi><\/msub><mo>=<\/mo><mn>540<\/mn><mtext>cal\/g<\/mtext><mo form=\"postfix\" stretchy=\"false\">)<\/mo><\/mrow><annotation encoding=\"application\/x-tex\">(L_v = 540\\text{cal\/g})<\/annotation><\/semantics><\/math><\/li>\n<\/ul>\n\n\n\n<p>Considere:<br><math data-latex=\"m = 100,\\text{g} \"><semantics><mrow><mi>m<\/mi><mo>=<\/mo><mn>100<\/mn><mo separator=\"true\">,<\/mo><mtext>g<\/mtext><\/mrow><annotation encoding=\"application\/x-tex\">m = 100,\\text{g} <\/annotation><\/semantics><\/math><\/p>\n\n\n\n<hr class=\"wp-block-separator has-alpha-channel-opacity\"\/>\n\n\n\n<h3 class=\"wp-block-heading\">Estrat\u00e9gia<\/h3>\n\n\n\n<p>O processo completo tem <strong>5 etapas<\/strong>:<\/p>\n\n\n\n<ol class=\"wp-block-list\">\n<li>Aquecer o gelo de \u201320\u00b0C at\u00e9 0\u00b0C (<strong>calor sens\u00edvel<\/strong> no gelo)<\/li>\n\n\n\n<li>Fundir o gelo a 0\u00b0C (<strong>calor latente de fus\u00e3o<\/strong>)<\/li>\n\n\n\n<li>Aquecer a \u00e1gua l\u00edquida de 0\u00b0C at\u00e9 100\u00b0C (<strong>calor sens\u00edvel<\/strong> na \u00e1gua)<\/li>\n\n\n\n<li>Vaporizar a \u00e1gua a 100\u00b0C (<strong>calor latente de vaporiza\u00e7\u00e3o<\/strong>)<\/li>\n\n\n\n<li>Aquecer o vapor de 100\u00b0C at\u00e9 120\u00b0C (<strong>calor sens\u00edvel<\/strong> no vapor)<\/li>\n<\/ol>\n\n\n\n<p>O calor total ser\u00e1:<\/p>\n\n\n\n<p><math data-latex=\" Q_{\\text{total}} = Q_1 + Q_2 + Q_3 + Q_4 + Q_5 \"><semantics><mrow><msub><mi>Q<\/mi><mtext>total<\/mtext><\/msub><mo>=<\/mo><msub><mi>Q<\/mi><mn>1<\/mn><\/msub><mo>+<\/mo><msub><mi>Q<\/mi><mn>2<\/mn><\/msub><mo>+<\/mo><msub><mi>Q<\/mi><mn>3<\/mn><\/msub><mo>+<\/mo><msub><mi>Q<\/mi><mn>4<\/mn><\/msub><mo>+<\/mo><msub><mi>Q<\/mi><mn>5<\/mn><\/msub><\/mrow><annotation encoding=\"application\/x-tex\"> Q_{\\text{total}} = Q_1 + Q_2 + Q_3 + Q_4 + Q_5 <\/annotation><\/semantics><\/math><\/p>\n\n\n\n<hr class=\"wp-block-separator has-alpha-channel-opacity\"\/>\n\n\n\n<h3 class=\"wp-block-heading\">Etapa 1 \u2013 Aquecer o gelo de \u201320\u00b0C at\u00e9 0\u00b0C<\/h3>\n\n\n\n<p><math data-latex=\"Q_1 = m \\cdot c_{\\text{gelo}} \\cdot \\Delta T \"><semantics><mrow><msub><mi>Q<\/mi><mn>1<\/mn><\/msub><mo>=<\/mo><mi>m<\/mi><mo>\u22c5<\/mo><msub><mi>c<\/mi><mtext>gelo<\/mtext><\/msub><mo>\u22c5<\/mo><mrow><mi mathvariant=\"normal\">\u0394<\/mi><\/mrow><mi>T<\/mi><\/mrow><annotation encoding=\"application\/x-tex\">Q_1 = m \\cdot c_{\\text{gelo}} \\cdot \\Delta T <\/annotation><\/semantics><\/math><\/p>\n\n\n\n<p><math data-latex=\" \\Delta T = 0 - (-20) = 20,\u00b0C \"><semantics><mrow><mrow><mi mathvariant=\"normal\">\u0394<\/mi><\/mrow><mi>T<\/mi><mo>=<\/mo><mn>0<\/mn><mo>\u2212<\/mo><mo form=\"prefix\" stretchy=\"false\">(<\/mo><mo form=\"prefix\" stretchy=\"false\">\u2212<\/mo><mn>20<\/mn><mo form=\"postfix\" stretchy=\"false\">)<\/mo><mo>=<\/mo><mn>20<\/mn><mo separator=\"true\">,<\/mo><mi>\u00b0<\/mi><mi>C<\/mi><\/mrow><annotation encoding=\"application\/x-tex\"> \\Delta T = 0 &#8211; (-20) = 20,\u00b0C <\/annotation><\/semantics><\/math><\/p>\n\n\n\n<p><math data-latex=\" Q_1 = 100 \\cdot 0{,}5 \\cdot 20 = 1000\\text{cal} \"><semantics><mrow><msub><mi>Q<\/mi><mn>1<\/mn><\/msub><mo>=<\/mo><mn>100<\/mn><mo>\u22c5<\/mo><mn>0,5<\/mn><mo>\u22c5<\/mo><mn>20<\/mn><mo>=<\/mo><mn>1000<\/mn><mtext>cal<\/mtext><\/mrow><annotation encoding=\"application\/x-tex\"> Q_1 = 100 \\cdot 0{,}5 \\cdot 20 = 1000\\text{cal} <\/annotation><\/semantics><\/math><\/p>\n\n\n\n<hr class=\"wp-block-separator has-alpha-channel-opacity\"\/>\n\n\n\n<h3 class=\"wp-block-heading\">Etapa 2 \u2013 Fus\u00e3o do gelo a 0\u00b0C<\/h3>\n\n\n\n<p><math data-latex=\" Q_2 = m \\cdot L_f \"><semantics><mrow><msub><mi>Q<\/mi><mn>2<\/mn><\/msub><mo>=<\/mo><mi>m<\/mi><mo>\u22c5<\/mo><msub><mi>L<\/mi><mi>f<\/mi><\/msub><\/mrow><annotation encoding=\"application\/x-tex\"> Q_2 = m \\cdot L_f <\/annotation><\/semantics><\/math><\/p>\n\n\n\n<p><math data-latex=\"Q_2 = 100 \\cdot 80 = 8000\\text{cal} \"><semantics><mrow><msub><mi>Q<\/mi><mn>2<\/mn><\/msub><mo>=<\/mo><mn>100<\/mn><mo>\u22c5<\/mo><mn>80<\/mn><mo>=<\/mo><mn>8000<\/mn><mtext>cal<\/mtext><\/mrow><annotation encoding=\"application\/x-tex\">Q_2 = 100 \\cdot 80 = 8000\\text{cal} <\/annotation><\/semantics><\/math><\/p>\n\n\n\n<hr class=\"wp-block-separator has-alpha-channel-opacity\"\/>\n\n\n\n<h3 class=\"wp-block-heading\">Etapa 3 \u2013 Aquecer a \u00e1gua de 0\u00b0C at\u00e9 100\u00b0C<\/h3>\n\n\n\n<p><math data-latex=\" Q_3 = m \\cdot c_{\\text{\u00e1gua}} \\cdot \\Delta T \"><semantics><mrow><msub><mi>Q<\/mi><mn>3<\/mn><\/msub><mo>=<\/mo><mi>m<\/mi><mo>\u22c5<\/mo><msub><mi>c<\/mi><mtext>\u00e1gua<\/mtext><\/msub><mo>\u22c5<\/mo><mrow><mi mathvariant=\"normal\">\u0394<\/mi><\/mrow><mi>T<\/mi><\/mrow><annotation encoding=\"application\/x-tex\"> Q_3 = m \\cdot c_{\\text{\u00e1gua}} \\cdot \\Delta T <\/annotation><\/semantics><\/math><\/p>\n\n\n\n<p><math data-latex=\"\\Delta T = 100 - 0 = 100\u00b0C \"><semantics><mrow><mrow><mi mathvariant=\"normal\">\u0394<\/mi><\/mrow><mi>T<\/mi><mo>=<\/mo><mn>100<\/mn><mo>\u2212<\/mo><mn>0<\/mn><mo>=<\/mo><mn>100<\/mn><mi>\u00b0<\/mi><mi>C<\/mi><\/mrow><annotation encoding=\"application\/x-tex\">\\Delta T = 100 &#8211; 0 = 100\u00b0C <\/annotation><\/semantics><\/math><\/p>\n\n\n\n<p><math data-latex=\" Q_3 = 100 \\cdot 1{,}0 \\cdot 100 = 10,000\\text{cal} \"><semantics><mrow><msub><mi>Q<\/mi><mn>3<\/mn><\/msub><mo>=<\/mo><mn>100<\/mn><mo>\u22c5<\/mo><mn>1,0<\/mn><mo>\u22c5<\/mo><mn>100<\/mn><mo>=<\/mo><mn>10,000<\/mn><mtext>cal<\/mtext><\/mrow><annotation encoding=\"application\/x-tex\"> Q_3 = 100 \\cdot 1{,}0 \\cdot 100 = 10,000\\text{cal} <\/annotation><\/semantics><\/math><\/p>\n\n\n\n<hr class=\"wp-block-separator has-alpha-channel-opacity\"\/>\n\n\n\n<h3 class=\"wp-block-heading\">Etapa 4 \u2013 Vaporiza\u00e7\u00e3o da \u00e1gua a 100\u00b0C<\/h3>\n\n\n\n<p><math data-latex=\"Q_4 = m \\cdot L_v \"><semantics><mrow><msub><mi>Q<\/mi><mn>4<\/mn><\/msub><mo>=<\/mo><mi>m<\/mi><mo>\u22c5<\/mo><msub><mi>L<\/mi><mi>v<\/mi><\/msub><\/mrow><annotation encoding=\"application\/x-tex\">Q_4 = m \\cdot L_v <\/annotation><\/semantics><\/math><\/p>\n\n\n\n<p><math data-latex=\"Q_4 = 100 \\cdot 540 = 54,000\\text{cal}\"><semantics><mrow><msub><mi>Q<\/mi><mn>4<\/mn><\/msub><mo>=<\/mo><mn>100<\/mn><mo>\u22c5<\/mo><mn>540<\/mn><mo>=<\/mo><mn>54,000<\/mn><mtext>cal<\/mtext><\/mrow><annotation encoding=\"application\/x-tex\">Q_4 = 100 \\cdot 540 = 54,000\\text{cal}<\/annotation><\/semantics><\/math><\/p>\n\n\n\n<hr class=\"wp-block-separator has-alpha-channel-opacity\"\/>\n\n\n\n<h3 class=\"wp-block-heading\">Etapa 5 \u2013 Aquecer o vapor de 100\u00b0C at\u00e9 120\u00b0C<\/h3>\n\n\n\n<p><math data-latex=\"Q_5 = m \\cdot c_{\\text{vapor}} \\cdot \\Delta T \"><semantics><mrow><msub><mi>Q<\/mi><mn>5<\/mn><\/msub><mo>=<\/mo><mi>m<\/mi><mo>\u22c5<\/mo><msub><mi>c<\/mi><mtext>vapor<\/mtext><\/msub><mo>\u22c5<\/mo><mrow><mi mathvariant=\"normal\">\u0394<\/mi><\/mrow><mi>T<\/mi><\/mrow><annotation encoding=\"application\/x-tex\">Q_5 = m \\cdot c_{\\text{vapor}} \\cdot \\Delta T <\/annotation><\/semantics><\/math><\/p>\n\n\n\n<p><math data-latex=\"\\Delta T = 120 - 100 = 20\u00b0C \"><semantics><mrow><mrow><mi mathvariant=\"normal\">\u0394<\/mi><\/mrow><mi>T<\/mi><mo>=<\/mo><mn>120<\/mn><mo>\u2212<\/mo><mn>100<\/mn><mo>=<\/mo><mn>20<\/mn><mi>\u00b0<\/mi><mi>C<\/mi><\/mrow><annotation encoding=\"application\/x-tex\">\\Delta T = 120 &#8211; 100 = 20\u00b0C <\/annotation><\/semantics><\/math><\/p>\n\n\n\n<p><math data-latex=\" Q_5 = 100 \\cdot 0{,}5 \\cdot 20 = 1000\\text{cal} \"><semantics><mrow><msub><mi>Q<\/mi><mn>5<\/mn><\/msub><mo>=<\/mo><mn>100<\/mn><mo>\u22c5<\/mo><mn>0,5<\/mn><mo>\u22c5<\/mo><mn>20<\/mn><mo>=<\/mo><mn>1000<\/mn><mtext>cal<\/mtext><\/mrow><annotation encoding=\"application\/x-tex\"> Q_5 = 100 \\cdot 0{,}5 \\cdot 20 = 1000\\text{cal} <\/annotation><\/semantics><\/math><\/p>\n\n\n\n<hr class=\"wp-block-separator has-alpha-channel-opacity\"\/>\n\n\n\n<h3 class=\"wp-block-heading\">Soma total<\/h3>\n\n\n\n<p><math data-latex=\"Q_{\\text{total}} = Q_1 + Q_2 + Q_3 + Q_4 + Q_5 \"><semantics><mrow><msub><mi>Q<\/mi><mtext>total<\/mtext><\/msub><mo>=<\/mo><msub><mi>Q<\/mi><mn>1<\/mn><\/msub><mo>+<\/mo><msub><mi>Q<\/mi><mn>2<\/mn><\/msub><mo>+<\/mo><msub><mi>Q<\/mi><mn>3<\/mn><\/msub><mo>+<\/mo><msub><mi>Q<\/mi><mn>4<\/mn><\/msub><mo>+<\/mo><msub><mi>Q<\/mi><mn>5<\/mn><\/msub><\/mrow><annotation encoding=\"application\/x-tex\">Q_{\\text{total}} = Q_1 + Q_2 + Q_3 + Q_4 + Q_5 <\/annotation><\/semantics><\/math><\/p>\n\n\n\n<p><math data-latex=\"Q_{\\text{total}} = 1000 + 8000 + 10,000 + 54,000 + 1000 \"><semantics><mrow><msub><mi>Q<\/mi><mtext>total<\/mtext><\/msub><mo>=<\/mo><mn>1000<\/mn><mo>+<\/mo><mn>8000<\/mn><mo>+<\/mo><mn>10,000<\/mn><mo>+<\/mo><mn>54,000<\/mn><mo>+<\/mo><mn>1000<\/mn><\/mrow><annotation encoding=\"application\/x-tex\">Q_{\\text{total}} = 1000 + 8000 + 10,000 + 54,000 + 1000 <\/annotation><\/semantics><\/math><\/p>\n\n\n\n<p><math data-latex=\"Q_{\\text{total}} = 74,000\\text{cal}\"><semantics><mrow><msub><mi>Q<\/mi><mtext>total<\/mtext><\/msub><mo>=<\/mo><mn>74,000<\/mn><mtext>cal<\/mtext><\/mrow><annotation encoding=\"application\/x-tex\">Q_{\\text{total}} = 74,000\\text{cal}<\/annotation><\/semantics><\/math><\/p>\n\n\n\n<hr class=\"wp-block-separator has-alpha-channel-opacity\"\/>\n\n\n\n<h3 class=\"wp-block-heading\">Interpreta\u00e7\u00e3o f\u00edsico\u2011qu\u00edmica<\/h3>\n\n\n\n<ul class=\"wp-block-list\">\n<li><strong>Calor sens\u00edvel:<\/strong>\n<ul class=\"wp-block-list\">\n<li><math data-latex=\"(Q_1), (Q_3), (Q_5)\"><semantics><mrow><mo form=\"prefix\" stretchy=\"false\">(<\/mo><msub><mi>Q<\/mi><mn>1<\/mn><\/msub><mo form=\"postfix\" stretchy=\"false\">)<\/mo><mo separator=\"true\">,<\/mo><mo form=\"prefix\" stretchy=\"false\">(<\/mo><msub><mi>Q<\/mi><mn>3<\/mn><\/msub><mo form=\"postfix\" stretchy=\"false\">)<\/mo><mo separator=\"true\">,<\/mo><mo form=\"prefix\" stretchy=\"false\">(<\/mo><msub><mi>Q<\/mi><mn>5<\/mn><\/msub><mo form=\"postfix\" stretchy=\"false\">)<\/mo><\/mrow><annotation encoding=\"application\/x-tex\">(Q_1), (Q_3), (Q_5)<\/annotation><\/semantics><\/math>: mudan\u00e7as de temperatura (energia cin\u00e9tica m\u00e9dia das mol\u00e9culas aumenta).<\/li>\n<\/ul>\n<\/li>\n\n\n\n<li><strong>Calor latente:<\/strong>\n<ul class=\"wp-block-list\">\n<li><math data-latex=\"(Q_2), (Q_4)\"><semantics><mrow><mo form=\"prefix\" stretchy=\"false\">(<\/mo><msub><mi>Q<\/mi><mn>2<\/mn><\/msub><mo form=\"postfix\" stretchy=\"false\">)<\/mo><mo separator=\"true\">,<\/mo><mo form=\"prefix\" stretchy=\"false\">(<\/mo><msub><mi>Q<\/mi><mn>4<\/mn><\/msub><mo form=\"postfix\" stretchy=\"false\">)<\/mo><\/mrow><annotation encoding=\"application\/x-tex\">(Q_2), (Q_4)<\/annotation><\/semantics><\/math>: mudan\u00e7as de fase (rompendo\/organizando intera\u00e7\u00f5es intermoleculares, sem mudar a temperatura).<\/li>\n<\/ul>\n<\/li>\n<\/ul>\n\n\n\n<p>O processo mostra bem como, em F\u00edsico\u2011Qu\u00edmica, a energia t\u00e9rmica se reparte entre <strong>movimento<\/strong> (sens\u00edvel) e <strong>reorganiza\u00e7\u00e3o estrutural<\/strong> (latente).<\/p>\n\n\n\n<h2 class=\"wp-block-heading\">Transfer\u00eancia de Calor<\/h2>\n\n\n\n<p>A <strong>transfer\u00eancia de calor <\/strong>\u00e9 o conjunto de mecanismos pelos quais a energia t\u00e9rmica flui de regi\u00f5es mais quentes para regi\u00f5es mais frias. Ela ocorre por condu\u00e7\u00e3o, convec\u00e7\u00e3o e radia\u00e7\u00e3o, cada uma descrita por leis f\u00edsicas bem estabelecidas e amplamente documentadas na literatura cient\u00edfica.<\/p>\n\n\n\n<p>A transfer\u00eancia de calor \u00e9 o processo pelo qual energia t\u00e9rmica se move devido a uma diferen\u00e7a de temperatura. O calor sempre flui espontaneamente do corpo mais quente para o mais frio at\u00e9 atingir o <strong>equil\u00edbrio t\u00e9rmico<\/strong>.<\/p>\n\n\n\n<p>A hist\u00f3ria da transfer\u00eancia de calor \u00e9 uma jornada fascinante que vai desde explica\u00e7\u00f5es filos\u00f3ficas da Antiguidade at\u00e9 a formula\u00e7\u00e3o matem\u00e1tica rigorosa no s\u00e9culo XIX e o desenvolvimento da termodin\u00e2mica moderna.<\/p>\n\n\n\n<h1 class=\"wp-block-heading\">\ud83d\udd25 1. Origem hist\u00f3rica do conceito de calor<\/h1>\n\n\n\n<p>A compreens\u00e3o do calor evoluiu lentamente ao longo dos s\u00e9culos. Os registros mais antigos mostram que o ser humano j\u00e1 dominava o fogo por volta de <strong>1200 a.C.<\/strong>, usando-o para aquecimento, ilumina\u00e7\u00e3o e metalurgia .<\/p>\n\n\n\n<h2 class=\"wp-block-heading\">\ud83c\udffa Antiguidade<\/h2>\n\n\n\n<ul class=\"wp-block-list\">\n<li><strong>Filosofia grega:<\/strong> Arist\u00f3teles e outros fil\u00f3sofos acreditavam que o calor era uma qualidade associada ao elemento \u201cfogo\u201d dentro dos quatro elementos cl\u00e1ssicos (terra, \u00e1gua, ar e fogo) .<\/li>\n\n\n\n<li><strong>Heron de Alexandria (s\u00e9culo I d.C.):<\/strong> Desenvolveu dispositivos a vapor e estudou princ\u00edpios de aquecimento, sendo um dos primeiros a tratar calor como fen\u00f4meno f\u00edsico sistem\u00e1tico .<\/li>\n<\/ul>\n\n\n\n<h2 class=\"wp-block-heading\">\u2697\ufe0f Idade M\u00e9dia e Renascimento<\/h2>\n\n\n\n<ul class=\"wp-block-list\">\n<li><strong>Alquimistas:<\/strong> A busca por transformar metais levou ao estudo sistem\u00e1tico da temperatura e dos processos de aquecimento.<\/li>\n\n\n\n<li><strong>Teoria do flogisto (s\u00e9culo XVII):<\/strong> Proposta por George Stahl, afirmava que materiais combust\u00edveis continham uma subst\u00e2ncia chamada <em>flogisto<\/em>, liberada durante a combust\u00e3o. Essa teoria dominou por mais de 50 anos at\u00e9 ser refutada por Lavoisier .<\/li>\n<\/ul>\n\n\n\n<h2 class=\"wp-block-heading\">\ud83d\udd2c S\u00e9culo XVIII \u2013 A virada cient\u00edfica<\/h2>\n\n\n\n<ul class=\"wp-block-list\">\n<li><strong>Joseph Black:<\/strong> Introduziu o conceito de <em>cal\u00f3rico<\/em>, um fluido hipot\u00e9tico respons\u00e1vel pela transfer\u00eancia de calor.<\/li>\n\n\n\n<li><strong>Benjamin Thompson (Conde de Rumford):<\/strong> Demonstrou experimentalmente que o calor podia ser gerado indefinidamente por atrito, contrariando a teoria do cal\u00f3rico e sugerindo que o calor era uma forma de energia .<\/li>\n<\/ul>\n\n\n\n<h2 class=\"wp-block-heading\">\ud83d\udcd0 S\u00e9culo XIX \u2013 Consolida\u00e7\u00e3o cient\u00edfica<\/h2>\n\n\n\n<ul class=\"wp-block-list\">\n<li><strong>Joseph Fourier (1768\u20131830):<\/strong> Criou a teoria matem\u00e1tica da condu\u00e7\u00e3o de calor e formulou a <strong>Lei de Fourier<\/strong>, marco fundamental da engenharia t\u00e9rmica .<\/li>\n\n\n\n<li><strong>Isaac Newton:<\/strong> Desenvolveu a <strong>Lei do Resfriamento de Newton<\/strong>, base da convec\u00e7\u00e3o.<\/li>\n\n\n\n<li><strong>James Clerk Maxwell:<\/strong> Contribuiu para a compreens\u00e3o da radia\u00e7\u00e3o t\u00e9rmica e fundamentou a f\u00edsica eletromagn\u00e9tica, que levou \u00e0 formula\u00e7\u00e3o da Lei de Stefan\u2013Boltzmann .<\/li>\n<\/ul>\n\n\n\n<h2 class=\"wp-block-heading\">\ud83c\udf21\ufe0f S\u00e9culo XX \u2013 Termodin\u00e2mica moderna<\/h2>\n\n\n\n<ul class=\"wp-block-list\">\n<li>A teoria cin\u00e9tica dos gases e a mec\u00e2nica estat\u00edstica consolidaram o calor como <strong>energia associada ao movimento microsc\u00f3pico das part\u00edculas<\/strong>.<\/li>\n\n\n\n<li>Estudos sobre radia\u00e7\u00e3o t\u00e9rmica e camada limite (Prandtl) permitiram avan\u00e7os em aerodin\u00e2mica, motores e sistemas t\u00e9rmicos modernos .<\/li>\n<\/ul>\n\n\n\n<h1 class=\"wp-block-heading\">\ud83d\udcd8 2. Fundamentos f\u00edsicos da transfer\u00eancia de calor<\/h1>\n\n\n\n<p>A transfer\u00eancia de calor ocorre por <strong>condu\u00e7\u00e3o<\/strong>, <strong>convec\u00e7\u00e3o<\/strong> e <strong>radia\u00e7\u00e3o<\/strong>. Cada mecanismo possui leis pr\u00f3prias.<\/p>\n\n\n\n<h2 class=\"wp-block-heading\">\ud83e\uddf1 2.1 Condu\u00e7\u00e3o \u2013 Lei de Fourier<\/h2>\n\n\n\n<p><br><math data-latex=\"\\dot{Q}=\\frac{dQ}{dt} = k \\cdot A \\cdot \\frac{dT}{dx}\"><semantics><mrow><mover><mi>Q<\/mi><mo stretchy=\"false\" class=\"tml-capshift\" style=\"math-style:normal;math-depth:0;\">\u02d9<\/mo><\/mover><mo>=<\/mo><mfrac><mrow><mi>d<\/mi><mi>Q<\/mi><\/mrow><mrow><mi>d<\/mi><mi>t<\/mi><\/mrow><\/mfrac><mo>=<\/mo><mi>k<\/mi><mo>\u22c5<\/mo><mi>A<\/mi><mo>\u22c5<\/mo><mfrac><mrow><mi>d<\/mi><mi>T<\/mi><\/mrow><mrow><mi>d<\/mi><mi>x<\/mi><\/mrow><\/mfrac><\/mrow><annotation encoding=\"application\/x-tex\">\\dot{Q}=\\frac{dQ}{dt} = k \\cdot A \\cdot \\frac{dT}{dx}<\/annotation><\/semantics><\/math><\/p>\n\n\n\n<ul class=\"wp-block-list\">\n<li>(<math data-latex=\"\\dot{Q}\"><semantics><mover><mi>Q<\/mi><mo stretchy=\"false\" class=\"tml-capshift\" style=\"math-style:normal;math-depth:0;\">\u02d9<\/mo><\/mover><annotation encoding=\"application\/x-tex\">\\dot{Q}<\/annotation><\/semantics><\/math>): fluxo de calor (W)<\/li>\n\n\n\n<li>(k): condutividade t\u00e9rmica<\/li>\n\n\n\n<li>(A): \u00e1rea<\/li>\n\n\n\n<li>(<math data-latex=\"\\frac{dT}{dx}\"><semantics><mfrac><mrow><mi>d<\/mi><mi>T<\/mi><\/mrow><mrow><mi>d<\/mi><mi>x<\/mi><\/mrow><\/mfrac><annotation encoding=\"application\/x-tex\">\\frac{dT}{dx}<\/annotation><\/semantics><\/math>): gradiente de temperatura<\/li>\n<\/ul>\n\n\n\n<p><strong>Exemplo num\u00e9rico:<\/strong><br>Uma parede de concreto (k = 1.4 W\/(m\u00b7K)), espessura 0.1 m, \u00e1rea 5 m\u00b2, temperaturas 40\u00b0C e 20\u00b0C:<br><br><math data-latex=\"\\dot{Q} = 1.4 \\cdot 5 \\cdot \\frac{20}{0.1} = 1400  W\"><semantics><mrow><mover><mi>Q<\/mi><mo stretchy=\"false\" class=\"tml-capshift\" style=\"math-style:normal;math-depth:0;\">\u02d9<\/mo><\/mover><mo>=<\/mo><mn>1.4<\/mn><mo>\u22c5<\/mo><mn>5<\/mn><mo>\u22c5<\/mo><mfrac><mn>20<\/mn><mn>0.1<\/mn><\/mfrac><mo>=<\/mo><mn>1400<\/mn><mi>W<\/mi><\/mrow><annotation encoding=\"application\/x-tex\">\\dot{Q} = 1.4 \\cdot 5 \\cdot \\frac{20}{0.1} = 1400  W<\/annotation><\/semantics><\/math><\/p>\n\n\n\n<hr class=\"wp-block-separator has-alpha-channel-opacity\"\/>\n\n\n\n<h2 class=\"wp-block-heading\">\ud83c\udf2c\ufe0f 2.2 Convec\u00e7\u00e3o \u2013 Lei de Resfriamento de Newton<\/h2>\n\n\n\n<p><br><math data-latex=\"\\dot{Q}=\\frac{dQ}{dt} = h \\cdot A \\cdot (T_s - T_f)\"><semantics><mrow><mover><mi>Q<\/mi><mo stretchy=\"false\" class=\"tml-capshift\" style=\"math-style:normal;math-depth:0;\">\u02d9<\/mo><\/mover><mo>=<\/mo><mfrac><mrow><mi>d<\/mi><mi>Q<\/mi><\/mrow><mrow><mi>d<\/mi><mi>t<\/mi><\/mrow><\/mfrac><mo>=<\/mo><mi>h<\/mi><mo>\u22c5<\/mo><mi>A<\/mi><mo>\u22c5<\/mo><mo form=\"prefix\" stretchy=\"false\">(<\/mo><msub><mi>T<\/mi><mi>s<\/mi><\/msub><mo>\u2212<\/mo><msub><mi>T<\/mi><mi>f<\/mi><\/msub><mo form=\"postfix\" stretchy=\"false\">)<\/mo><\/mrow><annotation encoding=\"application\/x-tex\">\\dot{Q}=\\frac{dQ}{dt} = h \\cdot A \\cdot (T_s &#8211; T_f)<\/annotation><\/semantics><\/math><\/p>\n\n\n\n<ul class=\"wp-block-list\">\n<li>(h): coeficiente convectivo<\/li>\n\n\n\n<li>(<math data-latex=\"T_s\"><semantics><msub><mi>T<\/mi><mi>s<\/mi><\/msub><annotation encoding=\"application\/x-tex\">T_s<\/annotation><\/semantics><\/math>): temperatura da superf\u00edcie<\/li>\n\n\n\n<li>(<math data-latex=\"T_f)\"><semantics><mrow><msub><mi>T<\/mi><mi>f<\/mi><\/msub><mo form=\"postfix\" stretchy=\"false\">)<\/mo><\/mrow><annotation encoding=\"application\/x-tex\">T_f)<\/annotation><\/semantics><\/math>: temperatura do fluido<\/li>\n<\/ul>\n\n\n\n<p><strong>Exemplo:<\/strong><br>Placa a 120\u00b0C em ar a 25\u00b0C, \u00e1rea 0.2 m\u00b2, (h = 15):<br><br><math data-latex=\"\\dot{Q} = 15 \\cdot 0.2 \\cdot 95 = 285 \\, W\"><semantics><mrow><mover><mi>Q<\/mi><mo stretchy=\"false\" class=\"tml-capshift\" style=\"math-style:normal;math-depth:0;\">\u02d9<\/mo><\/mover><mo>=<\/mo><mn>15<\/mn><mo>\u22c5<\/mo><mn>0.2<\/mn><mo>\u22c5<\/mo><mn>95<\/mn><mo>=<\/mo><mn>285<\/mn><mspace width=\"0.1667em\"><\/mspace><mi>W<\/mi><\/mrow><annotation encoding=\"application\/x-tex\">\\dot{Q} = 15 \\cdot 0.2 \\cdot 95 = 285 \\, W<\/annotation><\/semantics><\/math><\/p>\n\n\n\n<hr class=\"wp-block-separator has-alpha-channel-opacity\"\/>\n\n\n\n<h2 class=\"wp-block-heading\">\u2600\ufe0f 2.3 Radia\u00e7\u00e3o \u2013 Lei de Stefan\u2013Boltzmann<\/h2>\n\n\n\n<p><br><math data-latex=\"\\dot{Q}=\\frac{dQ}{dt} = \\varepsilon \\cdot \\sigma \\cdot A \\cdot (T_s^4 - T_{amb}^4)\"><semantics><mrow><mover><mi>Q<\/mi><mo stretchy=\"false\" class=\"tml-capshift\" style=\"math-style:normal;math-depth:0;\">\u02d9<\/mo><\/mover><mo>=<\/mo><mfrac><mrow><mi>d<\/mi><mi>Q<\/mi><\/mrow><mrow><mi>d<\/mi><mi>t<\/mi><\/mrow><\/mfrac><mo>=<\/mo><mi>\u03b5<\/mi><mo>\u22c5<\/mo><mi>\u03c3<\/mi><mo>\u22c5<\/mo><mi>A<\/mi><mo>\u22c5<\/mo><mo form=\"prefix\" stretchy=\"false\">(<\/mo><msubsup><mi>T<\/mi><mi>s<\/mi><mn>4<\/mn><\/msubsup><mo>\u2212<\/mo><msubsup><mi>T<\/mi><mrow><mi>a<\/mi><mi>m<\/mi><mi>b<\/mi><\/mrow><mn>4<\/mn><\/msubsup><mo form=\"postfix\" stretchy=\"false\">)<\/mo><\/mrow><annotation encoding=\"application\/x-tex\">\\dot{Q}=\\frac{dQ}{dt} = \\varepsilon \\cdot \\sigma \\cdot A \\cdot (T_s^4 &#8211; T_{amb}^4)<\/annotation><\/semantics><\/math><\/p>\n\n\n\n<ul class=\"wp-block-list\">\n<li>(<math data-latex=\"\\sigma = 5.67 \\times 10^{-8}\"><semantics><mrow><mi>\u03c3<\/mi><mo>=<\/mo><mn>5.67<\/mn><mo>\u00d7<\/mo><msup><mn>10<\/mn><mrow><mo lspace=\"0em\" rspace=\"0em\">\u2212<\/mo><mn>8<\/mn><\/mrow><\/msup><\/mrow><annotation encoding=\"application\/x-tex\">\\sigma = 5.67 \\times 10^{-8}<\/annotation><\/semantics><\/math>) W\/(m\u00b2\u00b7K\u2074)<\/li>\n\n\n\n<li>(<math data-latex=\"\\varepsilon\"><semantics><mi>\u03b5<\/mi><annotation encoding=\"application\/x-tex\">\\varepsilon<\/annotation><\/semantics><\/math>): emissividade<\/li>\n<\/ul>\n\n\n\n<hr class=\"wp-block-separator has-alpha-channel-opacity\"\/>\n\n\n\n<h1 class=\"wp-block-heading\">\ud83e\uddee 3. Calorimetria \u2013 Quantidade de calor<\/h1>\n\n\n\n<p><br><math data-latex=\"Q = m \\cdot c \\cdot \\Delta T\"><semantics><mrow><mi>Q<\/mi><mo>=<\/mo><mi>m<\/mi><mo>\u22c5<\/mo><mi>c<\/mi><mo>\u22c5<\/mo><mrow><mi mathvariant=\"normal\">\u0394<\/mi><\/mrow><mi>T<\/mi><\/mrow><annotation encoding=\"application\/x-tex\">Q = m \\cdot c \\cdot \\Delta T<\/annotation><\/semantics><\/math><\/p>\n\n\n\n<p><strong>Exemplo:<\/strong><br>Aquecimento de 1 kg de \u00e1gua de 20\u00b0C para 100\u00b0C:<br><br><math data-latex=\"Q = 1 \\cdot 4180 \\cdot 80 = 334\\,400 J\"><semantics><mrow><mi>Q<\/mi><mo>=<\/mo><mn>1<\/mn><mo>\u22c5<\/mo><mn>4180<\/mn><mo>\u22c5<\/mo><mn>80<\/mn><mo>=<\/mo><mn>334<\/mn><mspace width=\"0.1667em\"><\/mspace><mn>400<\/mn><mi>J<\/mi><\/mrow><annotation encoding=\"application\/x-tex\">Q = 1 \\cdot 4180 \\cdot 80 = 334\\,400 J<\/annotation><\/semantics><\/math><\/p>\n\n\n\n<hr class=\"wp-block-separator has-alpha-channel-opacity\"\/>\n\n\n\n<h1 class=\"wp-block-heading\">\ud83e\udded 4. Linha do tempo resumida<\/h1>\n\n\n\n<figure class=\"wp-block-table\"><table class=\"has-fixed-layout\"><thead><tr><th>Per\u00edodo<\/th><th>Contribui\u00e7\u00f5es<\/th><\/tr><\/thead><tbody><tr><td>Antiguidade<\/td><td>Filosofia dos quatro elementos; Heron e dispositivos t\u00e9rmicos<\/td><\/tr><tr><td>S\u00e9culo XVII<\/td><td>Teoria do flogisto<\/td><\/tr><tr><td>S\u00e9culo XVIII<\/td><td>Cal\u00f3rico; Rumford refuta o cal\u00f3rico<\/td><\/tr><tr><td>S\u00e9culo XIX<\/td><td>Fourier, Newton, Maxwell; formula\u00e7\u00e3o matem\u00e1tica<\/td><\/tr><tr><td>S\u00e9culo XX<\/td><td>Termodin\u00e2mica moderna; radia\u00e7\u00e3o e camada limite<\/td><\/tr><\/tbody><\/table><\/figure>\n\n\n\n<hr class=\"wp-block-separator has-alpha-channel-opacity\"\/>\n\n\n\n<p><\/p>\n","protected":false},"excerpt":{"rendered":"<p>Os termos \u201ctemperatura\u201d e \u201ccalor\u201d costumam ser usados como sin\u00f4nimos na linguagem cotidiana. Em F\u00edsica, contudo, esses dois termos t\u00eam significados muito diferentes. O conceito de calor, utilizado no cotidiano \u00e9 confundido com a sensa\u00e7\u00e3o t\u00e9rmica. Podemos definir calor como: Calor \u00e9 a energia em tr\u00e2nsito transferida entre sistemas devido exclusivamente a uma diferen\u00e7a de&hellip; <br \/> <a class=\"read-more\" href=\"https:\/\/fiziko.net\/?page_id=1324\">Leia mais<\/a><\/p>\n","protected":false},"author":1,"featured_media":0,"parent":0,"menu_order":0,"comment_status":"closed","ping_status":"closed","template":"","meta":{"footnotes":""},"class_list":["post-1324","page","type-page","status-publish","hentry"],"_links":{"self":[{"href":"https:\/\/fiziko.net\/index.php?rest_route=\/wp\/v2\/pages\/1324","targetHints":{"allow":["GET"]}}],"collection":[{"href":"https:\/\/fiziko.net\/index.php?rest_route=\/wp\/v2\/pages"}],"about":[{"href":"https:\/\/fiziko.net\/index.php?rest_route=\/wp\/v2\/types\/page"}],"author":[{"embeddable":true,"href":"https:\/\/fiziko.net\/index.php?rest_route=\/wp\/v2\/users\/1"}],"replies":[{"embeddable":true,"href":"https:\/\/fiziko.net\/index.php?rest_route=%2Fwp%2Fv2%2Fcomments&post=1324"}],"version-history":[{"count":11,"href":"https:\/\/fiziko.net\/index.php?rest_route=\/wp\/v2\/pages\/1324\/revisions"}],"predecessor-version":[{"id":1348,"href":"https:\/\/fiziko.net\/index.php?rest_route=\/wp\/v2\/pages\/1324\/revisions\/1348"}],"wp:attachment":[{"href":"https:\/\/fiziko.net\/index.php?rest_route=%2Fwp%2Fv2%2Fmedia&parent=1324"}],"curies":[{"name":"wp","href":"https:\/\/api.w.org\/{rel}","templated":true}]}}