{"id":25576,"date":"2023-05-06T12:49:26","date_gmt":"2023-05-06T11:49:26","guid":{"rendered":"https:\/\/www.acasinhadamatematica.pt\/?p=25576"},"modified":"2023-05-09T19:14:38","modified_gmt":"2023-05-09T18:14:38","slug":"escala-termica","status":"publish","type":"post","link":"https:\/\/www.acasinhadamatematica.pt\/?p=25576","title":{"rendered":"Escala t\u00e9rmica"},"content":{"rendered":"\n<p><ul id='GTTabs_ul_25576' class='GTTabs' style='display:none'>\n<li id='GTTabs_li_0_25576' class='GTTabs_curr'><a  id=\"25576_0\" onMouseOver=\"GTTabsShowLinks('Enunciado'); return true;\"  onMouseOut=\"GTTabsShowLinks();\"  class='GTTabsLinks'>Enunciado<\/a><\/li>\n<li id='GTTabs_li_1_25576' ><a  id=\"25576_1\" onMouseOver=\"GTTabsShowLinks('Resolu\u00e7\u00e3o'); return true;\"  onMouseOut=\"GTTabsShowLinks();\"  class='GTTabsLinks'>Resolu\u00e7\u00e3o<\/a><\/li>\n<\/ul>\n\n<div class='GTTabs_divs GTTabs_curr_div' id='GTTabs_0_25576'>\n<span class='GTTabs_titles'><b>Enunciado<\/b><\/span><\/p>\n<p><a href=\"https:\/\/www.acasinhadamatematica.pt\/wp-content\/uploads\/2023\/05\/8_Pag189-T5.png\"><img loading=\"lazy\" decoding=\"async\" data-attachment-id=\"25577\" data-permalink=\"https:\/\/www.acasinhadamatematica.pt\/?attachment_id=25577\" data-orig-file=\"https:\/\/www.acasinhadamatematica.pt\/wp-content\/uploads\/2023\/05\/8_Pag189-T5.png\" data-orig-size=\"361,495\" data-comments-opened=\"1\" data-image-meta=\"{&quot;aperture&quot;:&quot;0&quot;,&quot;credit&quot;:&quot;&quot;,&quot;camera&quot;:&quot;&quot;,&quot;caption&quot;:&quot;&quot;,&quot;created_timestamp&quot;:&quot;0&quot;,&quot;copyright&quot;:&quot;&quot;,&quot;focal_length&quot;:&quot;0&quot;,&quot;iso&quot;:&quot;0&quot;,&quot;shutter_speed&quot;:&quot;0&quot;,&quot;title&quot;:&quot;&quot;,&quot;orientation&quot;:&quot;0&quot;}\" data-image-title=\"8_Pag189-T5\" data-image-description=\"\" data-image-caption=\"\" data-large-file=\"https:\/\/www.acasinhadamatematica.pt\/wp-content\/uploads\/2023\/05\/8_Pag189-T5.png\" class=\"alignright wp-image-25577\" src=\"https:\/\/www.acasinhadamatematica.pt\/wp-content\/uploads\/2023\/05\/8_Pag189-T5-219x300.png\" alt=\"\" width=\"180\" height=\"247\" srcset=\"https:\/\/www.acasinhadamatematica.pt\/wp-content\/uploads\/2023\/05\/8_Pag189-T5-219x300.png 219w, https:\/\/www.acasinhadamatematica.pt\/wp-content\/uploads\/2023\/05\/8_Pag189-T5.png 361w\" sizes=\"auto, (max-width: 180px) 100vw, 180px\" \/><\/a>A escala t\u00e9rmica usada, por exemplo, em Inglaterra \u00e9 a escala <strong>Fahrenheit<\/strong>.<\/p>\n<p>Quando a \u00e1gua gela, os term\u00f3metros ingleses marcam 32\u00a0\u00b0F.<br \/>Quando a \u00e1gua ferve, esses term\u00f3metros marcam 212\u00a0\u00b0F.<br \/>A rela\u00e7\u00e3o entre graus <strong>Celsius<\/strong> (C) e os graus <strong>Fahrenheit<\/strong> (F) \u00e9 a seguinte:<\/p>\n<p>\\[\\frac{{F &#8211; 32}}{9} = \\frac{C}{5}\\]<\/p>\n<ol>\n<li>A quantos graus Celsius correspondem a 32\u00a0\u00b0F?<\/li>\n<li>E 32\u00a0\u00b0C a quantos graus Fahrenheit correspondem?<\/li>\n<li>Copia e completa a tabela, usando, quando necess\u00e1rio, valores aproximados \u00e0s d\u00e9cimas.<br \/><br \/>\n<table class=\"tabela-2 aligncenter\" style=\"width: 80%;\">\n<tbody>\n<tr>\n<td style=\"background-color: #174b73;\"><span style=\"color: #ffffff;\">Temperatura em graus Fahrenheit<\/span><\/td>\n<td style=\"width: 10%;\">50<\/td>\n<td style=\"width: 10%;\">\u00a0<\/td>\n<td style=\"width: 10%;\">100<\/td>\n<td style=\"width: 10%;\">\u00a0<\/td>\n<td style=\"width: 10%;\">10<\/td>\n<\/tr>\n<tr>\n<td style=\"background-color: #174b73;\"><span style=\"color: #ffffff;\">Temperatura em graus Celsius<\/span><\/td>\n<td style=\"width: 10%;\">\u00a0<\/td>\n<td style=\"width: 10%;\">25<\/td>\n<td style=\"width: 10%;\">\u00a0<\/td>\n<td style=\"width: 10%;\">37<\/td>\n<td style=\"width: 10%;\">\u00a0<\/td>\n<\/tr>\n<\/tbody>\n<\/table>\n<\/li>\n<li>Resolve a equa\u00e7\u00e3o:<br \/>a) em ordem a F (ou seja, considerando F como a inc\u00f3gnita e C como uma constante);<br \/>b) em ordem a C.<\/li>\n<li>Qual \u00e9 a vantagem de cada uma das f\u00f3rmulas obtidas em 4.?<\/li>\n<\/ol>\n<p><div class='GTTabsNavigation' style='display:none'><span class='GTTabs_nav_next'><a href='#GTTabs_ul_25576' onClick='GTTabs_show(1,25576)'>Resolu\u00e7\u00e3o &gt;&gt;<\/a><\/span><\/div><\/div>\n\n<div class='GTTabs_divs' id='GTTabs_1_25576'>\n<span class='GTTabs_titles'><b>Resolu\u00e7\u00e3o<\/b><\/span><!--more--><\/p>\n<blockquote>\n<p><a href=\"https:\/\/www.acasinhadamatematica.pt\/wp-content\/uploads\/2023\/05\/8_Pag189-T5.png\"><img loading=\"lazy\" decoding=\"async\" data-attachment-id=\"25577\" data-permalink=\"https:\/\/www.acasinhadamatematica.pt\/?attachment_id=25577\" data-orig-file=\"https:\/\/www.acasinhadamatematica.pt\/wp-content\/uploads\/2023\/05\/8_Pag189-T5.png\" data-orig-size=\"361,495\" data-comments-opened=\"1\" data-image-meta=\"{&quot;aperture&quot;:&quot;0&quot;,&quot;credit&quot;:&quot;&quot;,&quot;camera&quot;:&quot;&quot;,&quot;caption&quot;:&quot;&quot;,&quot;created_timestamp&quot;:&quot;0&quot;,&quot;copyright&quot;:&quot;&quot;,&quot;focal_length&quot;:&quot;0&quot;,&quot;iso&quot;:&quot;0&quot;,&quot;shutter_speed&quot;:&quot;0&quot;,&quot;title&quot;:&quot;&quot;,&quot;orientation&quot;:&quot;0&quot;}\" data-image-title=\"8_Pag189-T5\" data-image-description=\"\" data-image-caption=\"\" data-large-file=\"https:\/\/www.acasinhadamatematica.pt\/wp-content\/uploads\/2023\/05\/8_Pag189-T5.png\" class=\"alignright wp-image-25577\" src=\"https:\/\/www.acasinhadamatematica.pt\/wp-content\/uploads\/2023\/05\/8_Pag189-T5-219x300.png\" alt=\"\" width=\"180\" height=\"247\" srcset=\"https:\/\/www.acasinhadamatematica.pt\/wp-content\/uploads\/2023\/05\/8_Pag189-T5-219x300.png 219w, https:\/\/www.acasinhadamatematica.pt\/wp-content\/uploads\/2023\/05\/8_Pag189-T5.png 361w\" sizes=\"auto, (max-width: 180px) 100vw, 180px\" \/><\/a>A escala t\u00e9rmica usada, por exemplo, em Inglaterra \u00e9 a escala <strong>Fahrenheit<\/strong>.<\/p>\n<p>Quando a \u00e1gua gela, os term\u00f3metros ingleses marcam 32\u00a0\u00b0F.<br \/>Quando a \u00e1gua ferve, esses term\u00f3metros marcam 212\u00a0\u00b0F.<br \/>A rela\u00e7\u00e3o entre graus <strong>Celsius<\/strong> (C) e os graus <strong>Fahrenheit<\/strong> (F) \u00e9 a seguinte:<\/p>\n<\/blockquote>\n<p>\\[\\frac{{F &#8211; 32}}{9} = \\frac{C}{5}\\]<\/p>\n<ol>\n<li>A 32 \u00b0F correspondem 0 graus Celsius:<br \/>\\[\\begin{array}{*{20}{l}}{\\frac{{32 &#8211; 32}}{9} = \\frac{C}{5}}&amp; \\Leftrightarrow &amp;{\\frac{C}{5} = 0}\\\\{}&amp; \\Leftrightarrow &amp;{C = 0}\\end{array}\\]<\/li>\n<li>E a 32 \u00b0C correspondem 89,6 graus Fahrenheit:<br \/>\\[\\begin{array}{*{20}{l}}{\\frac{{F &#8211; 32}}{9} = \\frac{{32}}{5}}&amp; \\Leftrightarrow &amp;{F &#8211; 32 = \\frac{{32}}{5} \\times 9}\\\\{}&amp; \\Leftrightarrow &amp;{F = \\frac{{32}}{5} \\times 9 + 32}\\\\{}&amp; \\Leftrightarrow &amp;{F = 32 \\times \\frac{{14}}{5}}\\\\{}&amp; \\Leftrightarrow &amp;{F = 89,6}\\end{array}\\]<\/li>\n<li>Completa-se a tabela, usando, quando necess\u00e1rio, valores aproximados \u00e0s d\u00e9cimas:<br \/><br \/>\n<table class=\"tabela-2 aligncenter\" style=\"width: 80%;\">\n<tbody>\n<tr>\n<td style=\"background-color: #174b73;\"><span style=\"color: #ffffff;\">Temperatura em graus Fahrenheit<\/span><\/td>\n<td style=\"width: 10%;\">50<\/td>\n<td style=\"width: 10%;\"><span style=\"color: #0000ff;\">77<\/span><\/td>\n<td style=\"width: 10%;\">100<\/td>\n<td style=\"width: 10%;\"><span style=\"color: #0000ff;\">98,6<\/span><\/td>\n<td style=\"width: 10%;\">10<\/td>\n<\/tr>\n<tr>\n<td style=\"background-color: #174b73;\"><span style=\"color: #ffffff;\">Temperatura em graus Celsius<\/span><\/td>\n<td style=\"width: 10%;\"><span style=\"color: #0000ff;\">10<\/span><\/td>\n<td style=\"width: 10%;\">25<\/td>\n<td style=\"width: 10%;\"><span style=\"color: #0000ff;\">37,8<\/span><\/td>\n<td style=\"width: 10%;\">37<\/td>\n<td style=\"width: 10%;\"><span style=\"color: #0000ff;\">\u221212,2<\/span><\/td>\n<\/tr>\n<\/tbody>\n<\/table>\nC\u00e1lculos:<br \/>\n<table style=\"border-collapse: collapse; width: 100%;\">\n<tbody>\n<tr>\n<td style=\"width: 33.3333%;\">\\[\\begin{array}{*{20}{l}}{\\frac{{F &#8211; 32}}{9} = \\frac{{25}}{5}}&amp; \\Leftrightarrow &amp;{F &#8211; 32 = 9 \\times 5}\\\\{}&amp; \\Leftrightarrow &amp;{F = 45 + 32}\\\\{}&amp; \\Leftrightarrow &amp;{F = 77}\\end{array}\\]<\/td>\n<td style=\"width: 33.3333%;\">\u00a0<\/td>\n<td style=\"width: 33.3333%;\">\\[\\begin{array}{*{20}{l}}{\\frac{{F &#8211; 32}}{9} = \\frac{{37}}{5}}&amp; \\Leftrightarrow &amp;{F &#8211; 32 = \\frac{{9 \\times 37}}{5}}\\\\{}&amp; \\Leftrightarrow &amp;{F = \\frac{{9 \\times 37}}{5} + 32}\\\\{}&amp; \\Leftrightarrow &amp;{F = 98,6}\\end{array}\\]<\/td>\n<\/tr>\n<tr>\n<td style=\"width: 33.3333%;\">\\[\\begin{array}{*{20}{l}}{\\frac{{50 &#8211; 32}}{9} = \\frac{C}{5}}&amp; \\Leftrightarrow &amp;{\\frac{C}{5} = \\frac{{18}}{9}}\\\\{}&amp; \\Leftrightarrow &amp;{C = 5 \\times 2}\\\\{}&amp; \\Leftrightarrow &amp;{C = 10}\\end{array}\\]<\/td>\n<td style=\"width: 33.3333%;\">\\[\\begin{array}{*{20}{l}}{\\frac{{100 &#8211; 32}}{9} = \\frac{C}{5}}&amp; \\Leftrightarrow &amp;{\\frac{C}{5} = \\frac{{68}}{9}}\\\\{}&amp; \\Leftrightarrow &amp;{C = 5 \\times \\frac{{68}}{9}}\\\\{}&amp; \\Leftrightarrow &amp;{C = 37,\\left( 7 \\right)}\\end{array}\\]<\/td>\n<td style=\"width: 33.3333%;\">\\[\\begin{array}{*{20}{l}}{\\frac{{10 &#8211; 32}}{9} = \\frac{C}{5}}&amp; \\Leftrightarrow &amp;{\\frac{C}{5} = &#8211; \\frac{{22}}{9}}\\\\{}&amp; \\Leftrightarrow &amp;{C = &#8211; \\frac{{22}}{9} \\times 5}\\\\{}&amp; \\Leftrightarrow &amp;{C = &#8211; 12,\\left( 2 \\right)}\\end{array}\\]<\/td>\n<\/tr>\n<\/tbody>\n<\/table>\n<\/li>\n<li>Resolvendo a equa\u00e7\u00e3o:<br \/>a) em ordem a F (ou seja, considerando F como a inc\u00f3gnita e C como uma constante);<br \/>\\[\\begin{array}{*{20}{l}}{\\frac{{F &#8211; 32}}{9} = \\frac{C}{5}}&amp; \\Leftrightarrow &amp;{F &#8211; 32 = \\frac{{9 \\times C}}{5}}\\\\{}&amp; \\Leftrightarrow &amp;{F = \\frac{{9C}}{5} + 32}\\\\{}&amp; \\Leftrightarrow &amp;{F = \\frac{{9C + 160}}{5}}\\end{array}\\]<br \/>b) em ordem a C.<br \/>\\[\\begin{array}{*{20}{l}}{\\frac{{F &#8211; 32}}{9} = \\frac{C}{5}}&amp; \\Leftrightarrow &amp;{C = \\frac{{F &#8211; 32}}{9} \\times 5}\\\\{}&amp; \\Leftrightarrow &amp;{C = \\frac{{5F &#8211; 160}}{9}}\\end{array}\\]<\/li>\n<li>A vantagem de cada uma das f\u00f3rmulas, obtidas em 4., \u00e9 podermos <span style=\"text-decoration: underline;\">mais rapidamente<\/span> calcular F em fun\u00e7\u00e3o de C, ou C em fun\u00e7\u00e3o de F.<\/li>\n<\/ol>\n<div class='GTTabsNavigation' style='display:none'><span class='GTTabs_nav_prev'><a href='#GTTabs_ul_25576' onClick='GTTabs_show(0,25576)'>&lt;&lt; Enunciado<\/a><\/span><\/div><\/div>\n\n","protected":false},"excerpt":{"rendered":"<p>Enunciado Resolu\u00e7\u00e3o Enunciado A escala t\u00e9rmica usada, por exemplo, em Inglaterra \u00e9 a escala Fahrenheit. Quando a \u00e1gua gela, os term\u00f3metros ingleses marcam 32\u00a0\u00b0F.Quando a \u00e1gua ferve, esses term\u00f3metros marcam 212\u00a0\u00b0F.A rela\u00e7\u00e3o entre graus&#46;&#46;&#46;<\/p>\n","protected":false},"author":1,"featured_media":25578,"comment_status":"open","ping_status":"open","sticky":false,"template":"","format":"standard","meta":{"_jetpack_memberships_contains_paid_content":false,"footnotes":""},"categories":[100,97,714],"tags":[424,701,192],"series":[],"class_list":["post-25576","post","type-post","status-publish","format-standard","has-post-thumbnail","hentry","category-8--ano","category-aplicando","category-equacoes-literais-e-sistemas","tag-8-o-ano","tag-equacao-do-1-o-grau","tag-equacoes-literais"],"views":128,"jetpack_featured_media_url":"https:\/\/www.acasinhadamatematica.pt\/wp-content\/uploads\/2023\/05\/8_Pag189-T5_520x245.png","jetpack_sharing_enabled":true,"jetpack_likes_enabled":true,"_links":{"self":[{"href":"https:\/\/www.acasinhadamatematica.pt\/index.php?rest_route=\/wp\/v2\/posts\/25576","targetHints":{"allow":["GET"]}}],"collection":[{"href":"https:\/\/www.acasinhadamatematica.pt\/index.php?rest_route=\/wp\/v2\/posts"}],"about":[{"href":"https:\/\/www.acasinhadamatematica.pt\/index.php?rest_route=\/wp\/v2\/types\/post"}],"author":[{"embeddable":true,"href":"https:\/\/www.acasinhadamatematica.pt\/index.php?rest_route=\/wp\/v2\/users\/1"}],"replies":[{"embeddable":true,"href":"https:\/\/www.acasinhadamatematica.pt\/index.php?rest_route=%2Fwp%2Fv2%2Fcomments&post=25576"}],"version-history":[{"count":0,"href":"https:\/\/www.acasinhadamatematica.pt\/index.php?rest_route=\/wp\/v2\/posts\/25576\/revisions"}],"wp:featuredmedia":[{"embeddable":true,"href":"https:\/\/www.acasinhadamatematica.pt\/index.php?rest_route=\/wp\/v2\/media\/25578"}],"wp:attachment":[{"href":"https:\/\/www.acasinhadamatematica.pt\/index.php?rest_route=%2Fwp%2Fv2%2Fmedia&parent=25576"}],"wp:term":[{"taxonomy":"category","embeddable":true,"href":"https:\/\/www.acasinhadamatematica.pt\/index.php?rest_route=%2Fwp%2Fv2%2Fcategories&post=25576"},{"taxonomy":"post_tag","embeddable":true,"href":"https:\/\/www.acasinhadamatematica.pt\/index.php?rest_route=%2Fwp%2Fv2%2Ftags&post=25576"},{"taxonomy":"series","embeddable":true,"href":"https:\/\/www.acasinhadamatematica.pt\/index.php?rest_route=%2Fwp%2Fv2%2Fseries&post=25576"}],"curies":[{"name":"wp","href":"https:\/\/api.w.org\/{rel}","templated":true}]}}