{"id":1458,"date":"2018-03-08T03:12:42","date_gmt":"2018-03-07T19:12:42","guid":{"rendered":"https:\/\/gurumuda.net\/physics\/?p=1458"},"modified":"2018-03-08T03:12:42","modified_gmt":"2018-03-07T19:12:42","slug":"gay-lussacs-law-constant-volume-problems-and-solutions","status":"publish","type":"post","link":"https:\/\/gurumuda.net\/physics\/gay-lussacs-law-constant-volume-problems-and-solutions.htm","title":{"rendered":"Gay-Lussac&#8217;s law (constant volume) &#8211; problems and solutions","gt_translate_keys":[{"key":"rendered","format":"text"}]},"content":{"rendered":"<p class=\"western\" align=\"justify\"><span style=\"font-family: Times New Roman,serif\"><span style=\"font-size: medium\">1. <\/span><\/span><span style=\"font-family: Times new roman,serif\"><span style=\"font-size: medium\">I<\/span><\/span><span style=\"font-family: Times new roman,serif\"><span style=\"font-size: medium\"><span lang=\"en-US\">deal gases initially have <a href=\"https:\/\/gurumuda.net\/physics\/pressure-of-fluids-problems-and-solutions.htm\" target=\"_blank\" rel=\"noopener\">pressure<\/a> P and <a href=\"https:\/\/gurumuda.net\/physics\/thermometers-and-temperature-scales.htm\" target=\"_blank\" rel=\"noopener\">temperature<\/a> T. The gas undergoes the <a href=\"https:\/\/gurumuda.net\/physics\/isochoric-thermodynamics-processes-problems-and-solutions.htm\" target=\"_blank\" rel=\"noopener\">isochoric process<\/a> so that the final pressure becomes 4 times the initial pressure. What is the final temperature of the gas? <\/span><\/span><\/span><\/p>\n<p class=\"western\"><span style=\"font-family: Times New Roman,serif\"><span style=\"font-size: medium\"><u>Known :<\/u><\/span><\/span><\/p>\n<p class=\"western\"><span style=\"font-family: Times New Roman,serif\"><span style=\"font-size: medium\">Initial pressure (P<\/span><\/span><sub><span style=\"font-family: Times New Roman,serif\">1<\/span><\/sub><span style=\"font-family: Times New Roman,serif\"><span style=\"font-size: medium\">) = P<\/span><\/span><\/p>\n<p class=\"western\"><span style=\"font-family: Times New Roman,serif\"><span style=\"font-size: medium\">Final pressure (P<\/span><\/span><sub><span style=\"font-family: Times New Roman,serif\">2<\/span><\/sub><span style=\"font-family: Times New Roman,serif\"><span style=\"font-size: medium\">) = 4P<\/span><\/span><\/p>\n<p class=\"western\"><span style=\"font-family: Times New Roman,serif\"><span style=\"font-size: medium\">Initial temperature (T<\/span><\/span><sub><span style=\"font-family: Times New Roman,serif\">1<\/span><\/sub><span style=\"font-family: Times New Roman,serif\"><span style=\"font-size: medium\">) = T<\/span><\/span><\/p>\n<p class=\"western\">Wanted:<span style=\"font-family: Times New Roman,serif\"><span style=\"font-size: medium\"> Final temperature (T<\/span><\/span><sub><span style=\"font-family: Times New Roman,serif\">2<\/span><\/sub><span style=\"font-family: Times New Roman,serif\"><span style=\"font-size: medium\">)<\/span><\/span><\/p>\n<p class=\"western\"><span style=\"font-family: Times New Roman,serif\"><span style=\"font-size: medium\"><u>Solution :<\/u><\/span><\/span><\/p>\n<p class=\"western\" align=\"justify\"><span style=\"font-family: Times New Roman,serif\"><span style=\"font-size: medium\"><u>The formula of <\/u><\/span><\/span><span style=\"font-family: Times New Roman,serif\"><span style=\"font-size: medium\"><u><a href=\"https:\/\/gurumuda.net\/physics\/gay-lussacs-law-constant-volume-problems-and-solutions.htm\" target=\"_blank\" rel=\"noopener\">Gay-Lussac&#8217;s law<\/a> :<\/u><\/span><\/span><\/p>\n<p align=\"justify\"><img loading=\"lazy\" decoding=\"async\" class=\"aligncenter size-full wp-image-1459\" src=\"https:\/\/gurumuda.net\/physics\/wp-content\/uploads\/2018\/03\/Gay-Lussacs-law-constant-volume-problems-and-solutions-1.png\" alt=\"Gay-Lussac's law (constant volume) - problems and solutions 1\" width=\"151\" height=\"186\" \/><\/p>\n<p class=\"western\" align=\"justify\"><span style=\"font-family: Times new roman,serif\"><span style=\"font-size: medium\"><span lang=\"en-US\">The final temperature becomes 4 times the initial temperature.<\/span><\/span><\/span><\/p>\n<p align=\"justify\"><\/p>\n<p align=\"justify\"><span style=\"color: #000000\"><span style=\"font-family: Garamond,serif\"><span style=\"font-size: medium\"><span style=\"font-family: Times New Roman,serif\">2. In a closed container, ideal gases initially have a temperature of 27<\/span><sup><span style=\"font-family: Times New Roman,serif\">o<\/span><\/sup><span style=\"font-family: Times New Roman,serif\">C. If <\/span><span style=\"font-family: Times new roman,serif\"><span lang=\"en-US\">the final pressure becomes 2 times the initial pressure, what is the final temperature?<\/span><\/span><\/span><\/span><\/span><\/p>\n<p align=\"justify\"><span style=\"color: #000000\"><span style=\"font-family: Garamond,serif\"><span style=\"font-size: medium\"><span style=\"font-family: Times New Roman,serif\"><u>Known :<\/u><\/span><\/span><\/span><\/span><\/p>\n<p class=\"western\"><span style=\"font-family: Times New Roman,serif\"><span style=\"font-size: medium\">Initial pressure (P<\/span><\/span><sub><span style=\"font-family: Times New Roman,serif\">1<\/span><\/sub><span style=\"font-family: Times New Roman,serif\"><span style=\"font-size: medium\">) = P<\/span><\/span><\/p>\n<p class=\"western\"><span style=\"font-family: Times New Roman,serif\"><span style=\"font-size: medium\">Final pressure (P<\/span><\/span><sub><span style=\"font-family: Times New Roman,serif\">2<\/span><\/sub><span style=\"font-family: Times New Roman,serif\"><span style=\"font-size: medium\">) = 2P<\/span><\/span><\/p>\n<p class=\"western\"><span style=\"font-family: Times New Roman,serif\"><span style=\"font-size: medium\">Initial temperature (T<\/span><\/span><sub><span style=\"font-family: Times New Roman,serif\">1<\/span><\/sub><span style=\"font-family: Times New Roman,serif\"><span style=\"font-size: medium\">) = 27<\/span><\/span><sup><span style=\"font-family: Times New Roman,serif\"><span style=\"font-size: medium\">o<\/span><\/span><\/sup><span style=\"font-family: Times New Roman,serif\"><span style=\"font-size: medium\">C + 273 = 300 K<\/span><\/span><\/p>\n<p class=\"western\">Wanted:<span style=\"font-family: Times New Roman,serif\"><span style=\"font-size: medium\"> Final temperature (T<\/span><\/span><sub><span style=\"font-family: Times New Roman,serif\">2<\/span><\/sub><span style=\"font-family: Times New Roman,serif\"><span style=\"font-size: medium\">) <\/span><\/span><\/p>\n<p class=\"western\"><span style=\"font-family: Times New Roman,serif\"><span style=\"font-size: medium\"><u>Solution :<\/u><\/span><\/span><\/p>\n<p><img loading=\"lazy\" decoding=\"async\" class=\"aligncenter size-full wp-image-1460\" src=\"https:\/\/gurumuda.net\/physics\/wp-content\/uploads\/2018\/03\/Gay-Lussacs-law-constant-volume-problems-and-solutions-2.png\" alt=\"Gay-Lussac's law (constant volume) - problems and solutions 2\" width=\"161\" height=\"200\" \/><\/p>\n\n<p align=\"justify\"><span style=\"color: #000000\"><span style=\"font-family: Garamond,serif\"><span style=\"font-size: medium\"><span style=\"font-family: Times New Roman,serif\">3. A tire is filled to a gauge pressure of 2 atm at 27\u00b0C. After a drive, the temperature within the tire rises to 47\u00b0C. What is the pressure within the tire now?<\/span><\/span><\/span><\/span><\/p>\n<p align=\"justify\"><span style=\"color: #000000\"><span style=\"font-family: Garamond,serif\"><span style=\"font-size: medium\"><span style=\"font-family: Times New Roman,serif\"><u>Known :<\/u><\/span><\/span><\/span><\/span><\/p>\n<p align=\"justify\"><span style=\"color: #000000\"><span style=\"font-family: Garamond,serif\"><span style=\"font-size: medium\"><span style=\"font-family: Times New Roman,serif\">The atmospheric pressure = 1 atm = 1 x 10<\/span><sup><span style=\"font-family: Times New Roman,serif\">5<\/span><\/sup><span style=\"font-family: Times New Roman,serif\"> Pa<\/span><\/span><\/span><\/span><\/p>\n<p align=\"justify\"><span style=\"color: #000000\"><span style=\"font-family: Garamond,serif\"><span style=\"font-size: medium\"><span style=\"font-family: Times New Roman,serif\">The initial gauge pressure = 2 atm = 2 x 10<\/span><sup><span style=\"font-family: Times New Roman,serif\">5<\/span><\/sup><span style=\"font-family: Times New Roman,serif\"> Pa<\/span><\/span><\/span><\/span><\/p>\n<p align=\"justify\"><span style=\"color: #000000\"><span style=\"font-family: Garamond,serif\"><span style=\"font-size: medium\"><span style=\"font-family: Times New Roman,serif\">The initial absolute pressure (P<\/span><sub><span style=\"font-family: Times New Roman,serif\">1<\/span><\/sub><span style=\"font-family: Times New Roman,serif\">) = 1 atm + 2 atm = 3 atm = 3 x 10<\/span><sup><span style=\"font-family: Times New Roman,serif\">5<\/span><\/sup><span style=\"font-family: Times New Roman,serif\"> Pa<\/span><\/span><\/span><\/span><\/p>\n<p align=\"justify\"><span style=\"color: #000000\"><span style=\"font-family: Garamond,serif\"><span style=\"font-size: medium\"><span style=\"font-family: Times New Roman,serif\">The initial temperature (T<\/span><sub><span style=\"font-family: Times New Roman,serif\">1<\/span><\/sub><span style=\"font-family: Times New Roman,serif\">) = 27<\/span><sup><span style=\"font-family: Times New Roman,serif\">o<\/span><\/sup><span style=\"font-family: Times New Roman,serif\">C + 273 = 300 K<\/span><\/span><\/span><\/span><\/p>\n<p align=\"justify\"><span style=\"color: #000000\"><span style=\"font-family: Garamond,serif\"><span style=\"font-size: medium\"><span style=\"font-family: Times New Roman,serif\">The final temperature (T<\/span><sub><span style=\"font-family: Times New Roman,serif\">1<\/span><\/sub><span style=\"font-family: Times New Roman,serif\">) = 47<\/span><sup><span style=\"font-family: Times New Roman,serif\">o<\/span><\/sup><span style=\"font-family: Times New Roman,serif\">C + 273 = 320 K<\/span><\/span><\/span><\/span><\/p>\n<p align=\"justify\"><span style=\"color: #000000\"><span style=\"font-family: Garamond,serif\"><span style=\"font-size: medium\"><span style=\"font-family: Times New Roman,serif\"><u>Wanted :<\/u><\/span><span style=\"font-family: Times New Roman,serif\"> The final gauge temperature<\/span><\/span><\/span><\/span><\/p>\n<p align=\"justify\"><span style=\"color: #000000\"><span style=\"font-family: Garamond,serif\"><span style=\"font-size: medium\"><span style=\"font-family: Times New Roman,serif\"><u>Solution :<\/u><\/span><\/span><\/span><\/span><\/p>\n<p align=\"justify\"><img loading=\"lazy\" decoding=\"async\" class=\"aligncenter size-full wp-image-1461\" src=\"https:\/\/gurumuda.net\/physics\/wp-content\/uploads\/2018\/03\/Gay-Lussacs-law-constant-volume-problems-and-solutions-3.png\" alt=\"Gay-Lussac's law (constant volume) - problems and solutions 3\" width=\"220\" height=\"174\" \/><\/p>\n<p align=\"justify\"><span style=\"color: #000000\"><span style=\"font-family: Garamond,serif\"><span style=\"font-size: medium\"><span style=\"font-family: Times New Roman,serif\">The final gauge pressure = final absolute pressure \u2013 atmospheric pressure<\/span><\/span><\/span><\/span><\/p>\n<p align=\"justify\"><span style=\"color: #000000\"><span style=\"font-family: Garamond,serif\"><span style=\"font-size: medium\"><span style=\"font-family: Times New Roman,serif\">The final gauge pressure = 3.2 atm \u2013 1 atm <\/span><\/span><\/span><\/span><\/p>\n<p align=\"justify\"><span style=\"color: #000000\"><span style=\"font-family: Garamond,serif\"><span style=\"font-size: medium\"><span style=\"font-family: Times New Roman,serif\">The final gauge pressure = 2.2 atm<\/span><\/span><\/span><\/span><!--more--><\/p>\n","protected":false,"gt_translate_keys":[{"key":"rendered","format":"html"}]},"excerpt":{"rendered":"<p>1. Ideal gases initially have pressure P and temperature T. The gas undergoes the isochoric process so that the final pressure becomes 4 times the initial pressure. What is the final temperature of the gas? Known : Initial pressure (P1) = P Final pressure (P2) = 4P Initial temperature (T1) = T Wanted: Final temperature &#8230; <a title=\"Gay-Lussac&#8217;s law (constant volume) &#8211; problems and solutions\" class=\"read-more\" href=\"https:\/\/gurumuda.net\/physics\/gay-lussacs-law-constant-volume-problems-and-solutions.htm\" aria-label=\"Read more about Gay-Lussac&#8217;s law (constant volume) &#8211; problems and solutions\">Read more<\/a><\/p>\n","protected":false,"gt_translate_keys":[{"key":"rendered","format":"html"}]},"author":1,"featured_media":0,"comment_status":"open","ping_status":"closed","sticky":false,"template":"","format":"standard","meta":{"_seopress_titles_title":"","_seopress_titles_desc":"","_seopress_robots_index":"","_seopress_robots_follow":"","_seopress_robots_imageindex":"","_seopress_robots_snippet":"","_seopress_robots_primary_cat":"","_seopress_robots_breadcrumbs":"","_seopress_robots_freeze_modified_date":"","_seopress_robots_custom_modified_date":"","_seopress_robots_canonical":"","_seopress_social_fb_title":"","_seopress_social_fb_desc":"","_seopress_social_fb_img":"","_seopress_social_fb_img_attachment_id":0,"_seopress_social_fb_img_width":0,"_seopress_social_fb_img_height":0,"_seopress_social_twitter_title":"","_seopress_social_twitter_desc":"","_seopress_social_twitter_img":"","_seopress_social_twitter_img_attachment_id":0,"_seopress_social_twitter_img_width":0,"_seopress_social_twitter_img_height":0,"_seopress_redirections_value":"","_seopress_redirections_enabled":"","_seopress_redirections_enabled_regex":"","_seopress_redirections_logged_status":"","_seopress_redirections_param":"","_seopress_redirections_type":0,"_seopress_analysis_target_kw":"Gay-Lussac&#039;s law (constant volume) - problems and solutions","_seopress_news_disabled":"","_seopress_video_disabled":"","_seopress_video":[],"_seopress_pro_schemas_manual":[],"_seopress_pro_rich_snippets_disable_all":"","_seopress_pro_rich_snippets_disable":[],"_seopress_pro_schemas":[],"footnotes":""},"categories":[3],"tags":[],"class_list":["post-1458","post","type-post","status-publish","format-standard","hentry","category-solved-problems-in-basic-physics"],"gt_translate_keys":[{"key":"link","format":"url"}],"_links":{"self":[{"href":"https:\/\/gurumuda.net\/physics\/wp-json\/wp\/v2\/posts\/1458","targetHints":{"allow":["GET"]}}],"collection":[{"href":"https:\/\/gurumuda.net\/physics\/wp-json\/wp\/v2\/posts"}],"about":[{"href":"https:\/\/gurumuda.net\/physics\/wp-json\/wp\/v2\/types\/post"}],"author":[{"embeddable":true,"href":"https:\/\/gurumuda.net\/physics\/wp-json\/wp\/v2\/users\/1"}],"replies":[{"embeddable":true,"href":"https:\/\/gurumuda.net\/physics\/wp-json\/wp\/v2\/comments?post=1458"}],"version-history":[{"count":0,"href":"https:\/\/gurumuda.net\/physics\/wp-json\/wp\/v2\/posts\/1458\/revisions"}],"wp:attachment":[{"href":"https:\/\/gurumuda.net\/physics\/wp-json\/wp\/v2\/media?parent=1458"}],"wp:term":[{"taxonomy":"category","embeddable":true,"href":"https:\/\/gurumuda.net\/physics\/wp-json\/wp\/v2\/categories?post=1458"},{"taxonomy":"post_tag","embeddable":true,"href":"https:\/\/gurumuda.net\/physics\/wp-json\/wp\/v2\/tags?post=1458"}],"curies":[{"name":"wp","href":"https:\/\/api.w.org\/{rel}","templated":true}]}}