{"id":6557,"date":"2011-03-01T18:17:40","date_gmt":"2011-03-01T18:17:40","guid":{"rendered":"https:\/\/www.acasinhadamatematica.pt\/?p=6557"},"modified":"2022-01-23T16:34:14","modified_gmt":"2022-01-23T16:34:14","slug":"a-lei-de-boyle","status":"publish","type":"post","link":"https:\/\/www.acasinhadamatematica.pt\/?p=6557","title":{"rendered":"A lei de Boyle"},"content":{"rendered":"<p><ul id='GTTabs_ul_6557' class='GTTabs' style='display:none'>\n<li id='GTTabs_li_0_6557' class='GTTabs_curr'><a  id=\"6557_0\" onMouseOver=\"GTTabsShowLinks('Enunciado'); return true;\"  onMouseOut=\"GTTabsShowLinks();\"  class='GTTabsLinks'>Enunciado<\/a><\/li>\n<li id='GTTabs_li_1_6557' ><a  id=\"6557_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_6557'>\n<span class='GTTabs_titles'><b>Enunciado<\/b><\/span><\/p>\n<p>A lei de Boyle afirma que, se a temperatura permanece constante, a press\u00e3o $p$ e o volume $v$ (em m<sup>3<\/sup>) de um certo g\u00e1s dentro de um recipiente est\u00e3o relacionados pela express\u00e3o<br \/>\n\\[p=\\frac{200}{v}\\]<\/p>\n<p>Determine a taxa de varia\u00e7\u00e3o de $p$ em rela\u00e7\u00e3o a $v$ para um volume:<\/p>\n<ol>\n<li>de $10\\,{{m}^{3}}$;<\/li>\n<li>${{v}_{0}}$ qualquer.<\/li>\n<\/ol>\n<p><div class='GTTabsNavigation' style='display:none'><span class='GTTabs_nav_next'><a href='#GTTabs_ul_6557' onClick='GTTabs_show(1,6557)'>Resolu\u00e7\u00e3o &gt;&gt;<\/a><\/span><\/div><\/div>\n\n<div class='GTTabs_divs' id='GTTabs_1_6557'>\n<span class='GTTabs_titles'><b>Resolu\u00e7\u00e3o<\/b><\/span><!--more--><\/p>\n<ol>\n<li>Ora, \\[\\frac{dp}{dv}={{\\left( \\frac{200}{v} \\right)}^{&#8216;}}=-\\frac{200}{{{v}^{2}}}\\]<br \/>\nLogo, \\[{{\\left( \\frac{dp}{dv} \\right)}_{v=10}}=-\\frac{200}{{{10}^{2}}}=-2\\]<br \/>\nunidades de press\u00e3o por\u00a0m<sup>3<\/sup>.<\/li>\n<li>Nesta situa\u00e7\u00e3o ser\u00e1:<br \/>\n\\[{{\\left( \\frac{dp}{dv} \\right)}_{v={{v}_{0}}}}=-\\frac{200}{{{v}_{0}}^{2}}\\]\u00a0\u00a0unidades de press\u00e3o por m<sup>3<\/sup>.<\/li>\n<\/ol>\n<div class='GTTabsNavigation' style='display:none'><span class='GTTabs_nav_prev'><a href='#GTTabs_ul_6557' onClick='GTTabs_show(0,6557)'>&lt;&lt; Enunciado<\/a><\/span><\/div><\/div>\n\n","protected":false},"excerpt":{"rendered":"<p>Enunciado Resolu\u00e7\u00e3o Enunciado A lei de Boyle afirma que, se a temperatura permanece constante, a press\u00e3o $p$ e o volume $v$ (em m3) de um certo g\u00e1s dentro de um recipiente est\u00e3o relacionados pela&#46;&#46;&#46;<\/p>\n","protected":false},"author":1,"featured_media":20921,"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":[98,97,134],"tags":[136],"series":[],"class_list":["post-6557","post","type-post","status-publish","format-standard","has-post-thumbnail","hentry","category-11--ano","category-aplicando","category-derivadas","tag-derivada"],"views":2255,"jetpack_featured_media_url":"https:\/\/www.acasinhadamatematica.pt\/wp-content\/uploads\/2011\/03\/11V2Pag194-36_520x245.png","jetpack_sharing_enabled":true,"jetpack_likes_enabled":true,"_links":{"self":[{"href":"https:\/\/www.acasinhadamatematica.pt\/index.php?rest_route=\/wp\/v2\/posts\/6557","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=6557"}],"version-history":[{"count":0,"href":"https:\/\/www.acasinhadamatematica.pt\/index.php?rest_route=\/wp\/v2\/posts\/6557\/revisions"}],"wp:featuredmedia":[{"embeddable":true,"href":"https:\/\/www.acasinhadamatematica.pt\/index.php?rest_route=\/wp\/v2\/media\/20921"}],"wp:attachment":[{"href":"https:\/\/www.acasinhadamatematica.pt\/index.php?rest_route=%2Fwp%2Fv2%2Fmedia&parent=6557"}],"wp:term":[{"taxonomy":"category","embeddable":true,"href":"https:\/\/www.acasinhadamatematica.pt\/index.php?rest_route=%2Fwp%2Fv2%2Fcategories&post=6557"},{"taxonomy":"post_tag","embeddable":true,"href":"https:\/\/www.acasinhadamatematica.pt\/index.php?rest_route=%2Fwp%2Fv2%2Ftags&post=6557"},{"taxonomy":"series","embeddable":true,"href":"https:\/\/www.acasinhadamatematica.pt\/index.php?rest_route=%2Fwp%2Fv2%2Fseries&post=6557"}],"curies":[{"name":"wp","href":"https:\/\/api.w.org\/{rel}","templated":true}]}}