{"id":4715,"date":"2015-10-08T16:52:26","date_gmt":"2015-10-08T14:52:26","guid":{"rendered":"http:\/\/pimedios.es\/?p=4715"},"modified":"2015-10-08T17:10:18","modified_gmt":"2015-10-08T15:10:18","slug":"enfriamiento-newtoniano","status":"publish","type":"post","link":"https:\/\/pimedios.jesussoto.es\/?p=4715","title":{"rendered":"Enfriamiento newtoniano"},"content":{"rendered":"<p><iframe loading=\"lazy\" width=\"560\" height=\"315\" src=\"https:\/\/www.youtube.com\/embed\/imqUZvaafrI\" frameborder=\"0\" allowfullscreen><\/iframe><\/p>\n<p>La Ley nos dice que $$\\frac{dT}{dt}=-k(T-T_a)$$<br \/>\ndonde $T_a$ es la temperatura ambiente y $k$ una constante de proporcionalidad. Esta ecuaci\u00f3n aparece entre los primeros ejemplos de ecuaciones diferenciales, pues su soluci\u00f3n es muy sencilla.<\/p>\n<p>Observando vemos que resulta una ecuaci\u00f3n diferencial de variables separadas:<br \/>\n$$\\frac{dT}{T-T_a}=-kdt,$$ que integrando dar\u00e1<br \/>\n$$\\log|T(t)-T_a|=-kt+c&#8217;$$<br \/>\ndonde $c&#8217;$ es una constante de integraci\u00f3n. Esto nos dice que<br \/>\n$$T(t)-T_a=e^{-kt+c&#8217;}=ce^{-kt},$$<br \/>\ny, por tanto, $$T(t)=ce^{-kt}+T_a.$$<br \/>\nConociendo alg\u00fan valor inicial y la $T_a$ obtenemos la soluci\u00f3n particular de cada problema.<\/p>\n","protected":false},"excerpt":{"rendered":"<p>La Ley de enfriamiento de Newton<\/p>\n","protected":false},"author":2,"featured_media":0,"comment_status":"open","ping_status":"open","sticky":false,"template":"","format":"standard","meta":{"footnotes":""},"categories":[6,9],"tags":[609],"class_list":["post-4715","post","type-post","status-publish","format-standard","hentry","category-historia","category-personajes","tag-isaac-newton","entry"],"_links":{"self":[{"href":"https:\/\/pimedios.jesussoto.es\/index.php?rest_route=\/wp\/v2\/posts\/4715","targetHints":{"allow":["GET"]}}],"collection":[{"href":"https:\/\/pimedios.jesussoto.es\/index.php?rest_route=\/wp\/v2\/posts"}],"about":[{"href":"https:\/\/pimedios.jesussoto.es\/index.php?rest_route=\/wp\/v2\/types\/post"}],"author":[{"embeddable":true,"href":"https:\/\/pimedios.jesussoto.es\/index.php?rest_route=\/wp\/v2\/users\/2"}],"replies":[{"embeddable":true,"href":"https:\/\/pimedios.jesussoto.es\/index.php?rest_route=%2Fwp%2Fv2%2Fcomments&post=4715"}],"version-history":[{"count":4,"href":"https:\/\/pimedios.jesussoto.es\/index.php?rest_route=\/wp\/v2\/posts\/4715\/revisions"}],"predecessor-version":[{"id":4719,"href":"https:\/\/pimedios.jesussoto.es\/index.php?rest_route=\/wp\/v2\/posts\/4715\/revisions\/4719"}],"wp:attachment":[{"href":"https:\/\/pimedios.jesussoto.es\/index.php?rest_route=%2Fwp%2Fv2%2Fmedia&parent=4715"}],"wp:term":[{"taxonomy":"category","embeddable":true,"href":"https:\/\/pimedios.jesussoto.es\/index.php?rest_route=%2Fwp%2Fv2%2Fcategories&post=4715"},{"taxonomy":"post_tag","embeddable":true,"href":"https:\/\/pimedios.jesussoto.es\/index.php?rest_route=%2Fwp%2Fv2%2Ftags&post=4715"}],"curies":[{"name":"wp","href":"https:\/\/api.w.org\/{rel}","templated":true}]}}