{"id":14739,"date":"2018-04-21T23:04:56","date_gmt":"2018-04-21T22:04:56","guid":{"rendered":"https:\/\/www.acasinhadamatematica.pt\/?p=14739"},"modified":"2022-01-09T23:15:31","modified_gmt":"2022-01-09T23:15:31","slug":"pressao-exercida-sobre-o-embolo-de-uma-seringa","status":"publish","type":"post","link":"https:\/\/www.acasinhadamatematica.pt\/?p=14739","title":{"rendered":"Press\u00e3o exercida sobre o \u00eambolo de uma seringa"},"content":{"rendered":"<p><ul id='GTTabs_ul_14739' class='GTTabs' style='display:none'>\n<li id='GTTabs_li_0_14739' class='GTTabs_curr'><a  id=\"14739_0\" onMouseOver=\"GTTabsShowLinks('Enunciado'); return true;\"  onMouseOut=\"GTTabsShowLinks();\"  class='GTTabsLinks'>Enunciado<\/a><\/li>\n<li id='GTTabs_li_1_14739' ><a  id=\"14739_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_14739'>\n<span class='GTTabs_titles'><b>Enunciado<\/b><\/span><\/p>\n<p><a href=\"https:\/\/www.acasinhadamatematica.pt\/wp-content\/uploads\/2018\/04\/9V2Pag115-6.png\"><img loading=\"lazy\" decoding=\"async\" data-attachment-id=\"14740\" data-permalink=\"https:\/\/www.acasinhadamatematica.pt\/?attachment_id=14740\" data-orig-file=\"https:\/\/www.acasinhadamatematica.pt\/wp-content\/uploads\/2018\/04\/9V2Pag115-6.png\" data-orig-size=\"351,564\" 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=\"Tabela\" data-image-description=\"\" data-image-caption=\"\" data-large-file=\"https:\/\/www.acasinhadamatematica.pt\/wp-content\/uploads\/2018\/04\/9V2Pag115-6.png\" class=\"alignright wp-image-14740\" src=\"https:\/\/www.acasinhadamatematica.pt\/wp-content\/uploads\/2018\/04\/9V2Pag115-6-187x300.png\" alt=\"\" width=\"200\" height=\"321\" srcset=\"https:\/\/www.acasinhadamatematica.pt\/wp-content\/uploads\/2018\/04\/9V2Pag115-6-187x300.png 187w, https:\/\/www.acasinhadamatematica.pt\/wp-content\/uploads\/2018\/04\/9V2Pag115-6.png 351w\" sizes=\"auto, (max-width: 200px) 100vw, 200px\" \/><\/a>Sabemos que, se exercermos press\u00e3o sobre o \u00eambolo de uma seringa tapando o orif\u00edcio com o dedo de modo a n\u00e3o deixar sair o g\u00e1s, o volume diminui \u00e0 medida que a press\u00e3o aumenta. \u00c0 temperatura de 0 \u00b0C registaram-se os valores da tabela.<\/p>\n<ol>\n<li>O volume, \u00e0 temperatura de 0 \u00b0C, \u00e9 inversamente proporcional \u00e0 press\u00e3o sobre ele exercida? Porqu\u00ea?<\/li>\n<li>Escreve uma express\u00e3o que permita obter <em>v<\/em> em fun\u00e7\u00e3o de <em>p<\/em>.<\/li>\n<li>Determina o volume de g\u00e1s correspondente a uma press\u00e3o de 50 atmosferas.<\/li>\n<li>Determina a press\u00e3o correspondente a um volume de g\u00e1s de 3 dm<sup>3<\/sup>.<\/li>\n<\/ol>\n<p><div class='GTTabsNavigation' style='display:none'><span class='GTTabs_nav_next'><a href='#GTTabs_ul_14739' onClick='GTTabs_show(1,14739)'>Resolu\u00e7\u00e3o &gt;&gt;<\/a><\/span><\/div><\/div>\n\n<div class='GTTabs_divs' id='GTTabs_1_14739'>\n<span class='GTTabs_titles'><b>Resolu\u00e7\u00e3o<\/b><\/span><!--more--><\/p>\n<ol>\n<li><a href=\"https:\/\/www.acasinhadamatematica.pt\/wp-content\/uploads\/2018\/04\/9V2Pag115-6.png\"><img loading=\"lazy\" decoding=\"async\" data-attachment-id=\"14740\" data-permalink=\"https:\/\/www.acasinhadamatematica.pt\/?attachment_id=14740\" data-orig-file=\"https:\/\/www.acasinhadamatematica.pt\/wp-content\/uploads\/2018\/04\/9V2Pag115-6.png\" data-orig-size=\"351,564\" 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=\"Tabela\" data-image-description=\"\" data-image-caption=\"\" data-large-file=\"https:\/\/www.acasinhadamatematica.pt\/wp-content\/uploads\/2018\/04\/9V2Pag115-6.png\" class=\"alignright wp-image-14740\" src=\"https:\/\/www.acasinhadamatematica.pt\/wp-content\/uploads\/2018\/04\/9V2Pag115-6-187x300.png\" alt=\"\" width=\"200\" height=\"321\" srcset=\"https:\/\/www.acasinhadamatematica.pt\/wp-content\/uploads\/2018\/04\/9V2Pag115-6-187x300.png 187w, https:\/\/www.acasinhadamatematica.pt\/wp-content\/uploads\/2018\/04\/9V2Pag115-6.png 351w\" sizes=\"auto, (max-width: 200px) 100vw, 200px\" \/><\/a>O volume, \u00e0 temperatura de 0 \u00b0C, \u00e9 inversamente proporcional \u00e0 press\u00e3o sobre ele exercida, pois o produto das medidas correspondentes das duas grandezas \u00e9 constante:\\[\\begin{array}{*{20}{r}}{224 \\times 0,1 = 89,6 \\times 0,25 = 44,8 \\times 0,5 = 22,4 \\times 1 = 22,4}\\\\{11,2 \\times 2 = 5,6 \\times 4 = 2,24 \\times 10 = 0,448 \\times 50 = 22,4}\\end{array}\\]<\/li>\n<li>Como \\(v \\times p = 22,4\\), ent\u00e3o:\\[v = \\frac{{22,4}}{p}\\]<\/li>\n<li>Para \\(p = 50\\), vem:\\[\\begin{array}{*{20}{l}}{v = \\frac{{22,4}}{{50}}}&amp; \\Leftrightarrow &amp;{v = 0,448}\\end{array}\\]O volume de g\u00e1s correspondente a uma press\u00e3o de 50 atmosferas \u00e9 0,448 dm<sup>3<\/sup>.<br \/>\n\u00ad<\/li>\n<li>Para\u00a0\\(v = 3\\), vem:\\[\\begin{array}{*{20}{l}}{3 = \\frac{{22,4}}{p}}&amp; \\Leftrightarrow &amp;{p = \\frac{{22,4}}{3}}\\\\{}&amp; \\Leftrightarrow &amp;{p = 7,4\\left( 6 \\right)}\\end{array}\\]<br \/>\n\u00c9 de 7,4(6) atmosferas a press\u00e3o correspondente a um volume de g\u00e1s de 3 dm<sup>3<\/sup>.<\/li>\n<\/ol>\n<div class='GTTabsNavigation' style='display:none'><span class='GTTabs_nav_prev'><a href='#GTTabs_ul_14739' onClick='GTTabs_show(0,14739)'>&lt;&lt; Enunciado<\/a><\/span><\/div><\/div>\n\n","protected":false},"excerpt":{"rendered":"<p>Enunciado Resolu\u00e7\u00e3o Enunciado Sabemos que, se exercermos press\u00e3o sobre o \u00eambolo de uma seringa tapando o orif\u00edcio com o dedo de modo a n\u00e3o deixar sair o g\u00e1s, o volume diminui \u00e0 medida que&#46;&#46;&#46;<\/p>\n","protected":false},"author":1,"featured_media":14741,"comment_status":"open","ping_status":"open","sticky":false,"template":"","format":"standard","meta":{"_jetpack_newsletter_access":"","_jetpack_dont_email_post_to_subs":false,"_jetpack_newsletter_tier_id":0,"_jetpack_memberships_contains_paywalled_content":false,"_jetpack_feature_clip_id":0,"_jetpack_memberships_contains_paid_content":false,"footnotes":"","jetpack_post_was_ever_published":false},"categories":[213,97,249],"tags":[426,250],"series":[],"class_list":["post-14739","post","type-post","status-publish","format-standard","has-post-thumbnail","hentry","category-9--ano","category-aplicando","category-proporcionalidade-inversa-e-funcoes-algebricas","tag-9-o-ano","tag-proporcionalidade-inversa-2"],"views":1669,"jetpack_featured_media_url":"https:\/\/www.acasinhadamatematica.pt\/wp-content\/uploads\/2018\/04\/9V2Pag115-6a.png","jetpack_sharing_enabled":true,"jetpack_likes_enabled":true,"_links":{"self":[{"href":"https:\/\/www.acasinhadamatematica.pt\/index.php?rest_route=\/wp\/v2\/posts\/14739","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=14739"}],"version-history":[{"count":0,"href":"https:\/\/www.acasinhadamatematica.pt\/index.php?rest_route=\/wp\/v2\/posts\/14739\/revisions"}],"wp:featuredmedia":[{"embeddable":true,"href":"https:\/\/www.acasinhadamatematica.pt\/index.php?rest_route=\/wp\/v2\/media\/14741"}],"wp:attachment":[{"href":"https:\/\/www.acasinhadamatematica.pt\/index.php?rest_route=%2Fwp%2Fv2%2Fmedia&parent=14739"}],"wp:term":[{"taxonomy":"category","embeddable":true,"href":"https:\/\/www.acasinhadamatematica.pt\/index.php?rest_route=%2Fwp%2Fv2%2Fcategories&post=14739"},{"taxonomy":"post_tag","embeddable":true,"href":"https:\/\/www.acasinhadamatematica.pt\/index.php?rest_route=%2Fwp%2Fv2%2Ftags&post=14739"},{"taxonomy":"series","embeddable":true,"href":"https:\/\/www.acasinhadamatematica.pt\/index.php?rest_route=%2Fwp%2Fv2%2Fseries&post=14739"}],"curies":[{"name":"wp","href":"https:\/\/api.w.org\/{rel}","templated":true}]}}