{"id":154,"date":"2015-08-07T21:26:45","date_gmt":"2015-08-07T21:26:45","guid":{"rendered":"http:\/\/digitalobby.spu.edu\/energy\/?page_id=154"},"modified":"2019-10-25T18:41:39","modified_gmt":"2019-10-25T18:41:39","slug":"quantitative-energy-analysis","status":"publish","type":"page","link":"https:\/\/scholars.spu.edu\/seeley\/lane-seeley\/physics-learning-resources\/home\/quantitative-energy-analysis\/","title":{"rendered":"Quantifying Energy Conservation"},"content":{"rendered":"<p>Like many\u00a0topics in physics, energy can seem like an endless stream of equations to memorize and choose between. \u00a0Actually there is one essential equation for energy with two categories of supporting equations. \u00a0The essential energy equation is the conservation equation:<\/p>\n<p>\\(\\Delta \u00a0E_{sys}= \u00a0\\sum \u00a0E_{inputs} &#8211; \\sum \u00a0E_{outputs}\\)\u00a0 \u00a0 \u00a0 <a href=\"https:\/\/scholars.spu.edu\/seeley\/wp-content\/uploads\/sites\/13\/2015\/08\/Inputs-Outputs.jpg\"><img loading=\"lazy\" decoding=\"async\" class=\"alignnone wp-image-159\" src=\"https:\/\/scholars.spu.edu\/seeley\/wp-content\/uploads\/sites\/13\/2015\/08\/Inputs-Outputs-277x300.jpg\" alt=\"Inputs &amp; Outputs\" width=\"66\" height=\"71\" srcset=\"https:\/\/scholars.spu.edu\/seeley\/wp-content\/uploads\/sites\/13\/2015\/08\/Inputs-Outputs-277x300.jpg 277w, https:\/\/scholars.spu.edu\/seeley\/wp-content\/uploads\/sites\/13\/2015\/08\/Inputs-Outputs.jpg 303w\" sizes=\"auto, (max-width: 66px) 100vw, 66px\" \/><\/a><\/p>\n<p>This equation is often called the first law of thermodynamics and simply says that the change in the total energy of any <a href=\"https:\/\/scholars.spu.edu\/seeley\/lane-seeley\/physics-learning-resources\/home\/systems\/\">system<\/a> is always equal to the total inputs minus the total outputs from that system. \u00a0You will see many versions of this equation for special cases (work-kinetic energy theorem, etc&#8230;) and\u00a0it&#8217;s helpful\u00a0to remember that they all come from the same equation (<a href=\"http:\/\/citeseerx.ist.psu.edu\/viewdoc\/download?doi=10.1.1.460.3984&amp;rep=rep1&amp;type=pdf\">Energy and the Confused Student IV: A Global Approach to Energy, Jewitt 2008<\/a>). \u00a0This equation can be expanded to show all of the different ways in which energy can change along with the different mechanisms for energy input and output:<\/p>\n\\(\\Delta \u00a0E_{k,tran}+ \\Delta \u00a0E_{k,rot}+ \\Delta \u00a0E_{th}+ \\Delta \u00a0E_{grav}+&#8230; = W+Q+ T_{MT}+&#8230;\\)\n<p>On the left side of this equation are changes in energy in all of the various <a href=\"https:\/\/scholars.spu.edu\/seeley\/lane-seeley\/physics-learning-resources\/home\/table-of-energy-forms\/\">forms<\/a> it can take. \u00a0On the right side are all of the various ways in which energy can <a href=\"https:\/\/scholars.spu.edu\/seeley\/lane-seeley\/physics-learning-resources\/home\/transfer\/\">transferred<\/a> to or\u00a0from a system.<\/p>\n","protected":false},"excerpt":{"rendered":"<p>Like many\u00a0topics in physics, energy can seem like an endless stream of equations to memorize and choose between. \u00a0Actually there is one [&hellip;]<\/p>\n","protected":false},"author":12,"featured_media":0,"parent":6,"menu_order":0,"comment_status":"open","ping_status":"closed","template":"page-templates\/page_fullwidth.php","meta":{"_exactmetrics_skip_tracking":false,"_exactmetrics_sitenote_active":false,"_exactmetrics_sitenote_note":"","_exactmetrics_sitenote_category":0,"footnotes":""},"class_list":["post-154","page","type-page","status-publish","hentry"],"_links":{"self":[{"href":"https:\/\/scholars.spu.edu\/seeley\/wp-json\/wp\/v2\/pages\/154","targetHints":{"allow":["GET"]}}],"collection":[{"href":"https:\/\/scholars.spu.edu\/seeley\/wp-json\/wp\/v2\/pages"}],"about":[{"href":"https:\/\/scholars.spu.edu\/seeley\/wp-json\/wp\/v2\/types\/page"}],"author":[{"embeddable":true,"href":"https:\/\/scholars.spu.edu\/seeley\/wp-json\/wp\/v2\/users\/12"}],"replies":[{"embeddable":true,"href":"https:\/\/scholars.spu.edu\/seeley\/wp-json\/wp\/v2\/comments?post=154"}],"version-history":[{"count":3,"href":"https:\/\/scholars.spu.edu\/seeley\/wp-json\/wp\/v2\/pages\/154\/revisions"}],"predecessor-version":[{"id":658,"href":"https:\/\/scholars.spu.edu\/seeley\/wp-json\/wp\/v2\/pages\/154\/revisions\/658"}],"up":[{"embeddable":true,"href":"https:\/\/scholars.spu.edu\/seeley\/wp-json\/wp\/v2\/pages\/6"}],"wp:attachment":[{"href":"https:\/\/scholars.spu.edu\/seeley\/wp-json\/wp\/v2\/media?parent=154"}],"curies":[{"name":"wp","href":"https:\/\/api.w.org\/{rel}","templated":true}]}}