{"id":1485,"date":"2018-03-09T05:13:17","date_gmt":"2018-03-08T21:13:17","guid":{"rendered":"https:\/\/gurumuda.net\/physics\/?p=1485"},"modified":"2018-03-09T05:13:17","modified_gmt":"2018-03-08T21:13:17","slug":"kinetic-theory-of-gases-problems-and-solutions","status":"publish","type":"post","link":"https:\/\/gurumuda.net\/physics\/kinetic-theory-of-gases-problems-and-solutions.htm","title":{"rendered":"Kinetic theory of gases &#8211; problems and solutions","gt_translate_keys":[{"key":"rendered","format":"text"}]},"content":{"rendered":"<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\">1. <\/span><span style=\"font-family: Times new roman,serif\">I<\/span><span style=\"font-family: Times new roman,serif\"><span lang=\"en-US\">deal gases in a <\/span><\/span><span style=\"font-family: Times New Roman,serif\"><span lang=\"en-US\">closed container <\/span><\/span><span style=\"font-family: Times new roman,serif\"><span lang=\"en-US\">initially have volume V and <\/span><\/span><a href=\"https:\/\/gurumuda.net\/physics\/pressure-of-fluids-problems-and-solutions.htm\" target=\"_blank\" rel=\"noopener\"><span style=\"font-family: Times new roman,serif\"><span lang=\"en-US\">pressure<\/span><\/span><\/a> <span style=\"font-family: Times new roman,serif\"><span lang=\"en-US\">P<\/span><\/span><span style=\"font-family: Times new roman,serif\"><span lang=\"en-US\">. <\/span><\/span><span style=\"font-family: Times new roman,serif\"><span lang=\"en-US\">If the final pressure is 4P and the volume is kept constant, what is the ra<\/span><\/span><span style=\"font-family: Times new roman,serif\"><span lang=\"en-US\">t<\/span><\/span><span style=\"font-family: Times new roman,serif\"><span lang=\"en-US\">io <\/span><\/span><span style=\"font-family: Times new roman,serif\"><span lang=\"en-US\">of the initial kinetic energy with the final <a href=\"https:\/\/gurumuda.net\/physics\/kinetic-energy-problems-and-solutions.htm\" target=\"_blank\" rel=\"noopener\">kinetic energy<\/a>.<\/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\"><u><span style=\"font-family: Times New Roman,serif\">Known :<\/span><\/u><\/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\">Initial pressure <\/span><span style=\"font-family: Times New Roman,serif\">(P<\/span><sub><span style=\"font-family: Times New Roman,serif\">1<\/span><\/sub><span style=\"font-family: Times New Roman,serif\">) = P<\/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\">Final pressure <\/span><span style=\"font-family: Times New Roman,serif\">(P<\/span><sub><span style=\"font-family: Times New Roman,serif\">2<\/span><\/sub><span style=\"font-family: Times New Roman,serif\">) = 4P<\/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\">Initial volume <\/span><span style=\"font-family: Times New Roman,serif\">(V<\/span><sub><span style=\"font-family: Times New Roman,serif\">1<\/span><\/sub><span style=\"font-family: Times New Roman,serif\">) = V<\/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\">Final volume <\/span><span style=\"font-family: Times New Roman,serif\">(V<\/span><sub><span style=\"font-family: Times New Roman,serif\">2<\/span><\/sub><span style=\"font-family: Times New Roman,serif\">) = V<\/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 ratio of the initial kinetic energy with the final kinetic energy <\/span><span style=\"font-family: Times New Roman,serif\">(K<\/span><span style=\"font-family: Times New Roman,serif\">E<\/span><sub><span style=\"font-family: Times New Roman,serif\">1<\/span><\/sub><span style=\"font-family: Times New Roman,serif\"> : K<\/span><span style=\"font-family: Times New Roman,serif\">E<\/span><sub><span style=\"font-family: Times New Roman,serif\">2<\/span><\/sub><span style=\"font-family: Times New Roman,serif\">)<\/span><\/span><\/span><\/span><\/p>\n<p align=\"justify\"><span style=\"color: #000000\"><span style=\"font-family: Garamond,serif\"><span style=\"font-size: medium\"><u><span style=\"font-family: Times New Roman,serif\">Solution :<\/span><\/u><\/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>The relation between pressure (P), volume (V) and kinetic energy (KE) of <a href=\"https:\/\/gurumuda.net\/physics\/the-ideal-gas-law.htm\" target=\"_blank\" rel=\"noopener\">ideal gases<\/a> :<\/u><\/span><\/span><\/span><\/span><\/p>\n<p align=\"justify\"><img loading=\"lazy\" decoding=\"async\" class=\"aligncenter size-full wp-image-1512\" src=\"https:\/\/gurumuda.net\/physics\/wp-content\/uploads\/2018\/03\/Kinetic-theory-of-gases-problems-and-solutions-18.png\" alt=\"Kinetic theory of gases - problems and solutions 18\" width=\"198\" height=\"196\" \/><\/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>The ratio of the initial kinetic energy with the final kinetic energy :<\/u><\/span><\/span><\/span><\/span><\/p>\n<p align=\"justify\"><img loading=\"lazy\" decoding=\"async\" class=\"aligncenter size-full wp-image-1514\" src=\"https:\/\/gurumuda.net\/physics\/wp-content\/uploads\/2018\/03\/Kinetic-theory-of-gases-problems-and-solutions-19.png\" alt=\"Kinetic theory of gases - problems and solutions 19\" width=\"143\" height=\"161\" \/><\/p>\n<p align=\"justify\"><\/p>\n<p class=\"western\" align=\"justify\"><span style=\"font-size: medium\"><span style=\"font-family: Times New Roman,serif\">2. What is the average translational kinetic energy of molecules in an ideal gas at 57<\/span><sup><span style=\"font-family: Times New Roman,serif\">o<\/span><\/sup><span style=\"font-family: Times New Roman,serif\">C. <\/span><\/span><\/p>\n<p align=\"justify\"><span style=\"color: #000000\"><span style=\"font-family: Garamond,serif\"><span style=\"font-size: medium\"><u><span style=\"font-family: Times New Roman,serif\">Known :<\/span><\/u><\/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\">Temperature of gas <\/span><span style=\"font-family: Times New Roman,serif\">(T) = 57<\/span><sup><span style=\"font-family: Times New Roman,serif\">o<\/span><\/sup><span style=\"font-family: Times New Roman,serif\">C + 273 = 330 Kelvin <\/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\">Boltzmann<\/span><span style=\"font-family: Times New Roman,serif\">&#8216;s constant <\/span><span style=\"font-family: Times New Roman,serif\">(k) = 1.38 x 10<\/span><sup><span style=\"font-family: Times New Roman,serif\">-23<\/span><\/sup><span style=\"font-family: Times New Roman,serif\"> Joule\/Kelvin <\/span><\/span><\/span><\/span><\/p>\n<p align=\"justify\"><span style=\"color: #000000\"><span style=\"font-family: Garamond,serif\"><span style=\"font-size: medium\">Wanted: <span style=\"font-family: Times New Roman,serif\">The average translational kinetic energy<\/span><\/span><\/span><\/span><\/p>\n<p align=\"justify\"><span style=\"color: #000000\"><span style=\"font-family: Garamond,serif\"><span style=\"font-size: medium\"><u><span style=\"font-family: Times New Roman,serif\">Solution :<\/span><\/u><\/span><\/span><\/span><\/p>\n<p class=\"western\" align=\"justify\"><span style=\"font-family: Times new roman,serif\"><span style=\"font-size: medium\">The relation between kinetic energy (KE) and the <a href=\"https:\/\/gurumuda.net\/physics\/thermometers-and-temperature-scales.htm\" target=\"_blank\" rel=\"noopener\">temperature<\/a> of the gas (T) :<\/span><\/span><\/p>\n<p align=\"justify\"><img loading=\"lazy\" decoding=\"async\" class=\"aligncenter size-full wp-image-1488\" src=\"https:\/\/gurumuda.net\/physics\/wp-content\/uploads\/2018\/03\/Kinetic-theory-of-gases-problems-and-solutions-3.png\" alt=\"Kinetic theory of gases - problems and solutions 3\" width=\"120\" height=\"41\" \/><\/p>\n<p class=\"western\" align=\"justify\"><span style=\"font-family: Times new roman,serif\"><span style=\"font-size: medium\">The average translational kinetic energy :<\/span><\/span><\/p>\n<p align=\"justify\"><img loading=\"lazy\" decoding=\"async\" class=\"aligncenter size-full wp-image-1489\" src=\"https:\/\/gurumuda.net\/physics\/wp-content\/uploads\/2018\/03\/Kinetic-theory-of-gases-problems-and-solutions-4.png\" alt=\"Kinetic theory of gases - problems and solutions 4\" width=\"192\" height=\"122\" \/><\/p>\n<p align=\"justify\"><\/p>\n<p class=\"western\" align=\"justify\"><span style=\"font-size: medium\"><span style=\"font-family: Times New Roman,serif\">3. <\/span><span style=\"font-family: Times New Roman,serif\">A gas at <\/span><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 <\/span><span style=\"font-family: Times New Roman,serif\">in a closed container<\/span><span style=\"font-family: Times New Roman,serif\">. <\/span><span style=\"font-family: Times New Roman,serif\">If the kinetic energy of the gas increases 2 times the initial kinetic energy, thus the final temperature of the gas is&#8230;<\/span><\/span><\/p>\n<p align=\"justify\"><span style=\"color: #000000\"><span style=\"font-family: Garamond,serif\"><span style=\"font-size: medium\"><u><span style=\"font-family: Times New Roman,serif\">Known :<\/span><\/u><\/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\">Initial temperature <\/span><span style=\"font-family: Times New Roman,serif\">(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\">Initial kinetic energy <\/span><span style=\"font-family: Times New Roman,serif\">= K<\/span><span style=\"font-family: Times New Roman,serif\">E<\/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\">Final kinetic energy = 4 K<\/span><span style=\"font-family: Times New Roman,serif\">E<\/span><\/span><\/span><\/span><\/p>\n<p align=\"justify\"><span style=\"color: #000000\"><span style=\"font-family: Garamond,serif\"><span style=\"font-size: medium\">Wanted:<u><\/u> <span style=\"font-family: Times New Roman,serif\">The final temperature <\/span><span style=\"font-family: Times New Roman,serif\">(T<\/span><sub><span style=\"font-family: Times New Roman,serif\">2<\/span><\/sub><span style=\"font-family: Times New Roman,serif\">)<\/span><\/span><\/span><\/span><\/p>\n<p align=\"justify\"><span style=\"color: #000000\"><span style=\"font-family: Garamond,serif\"><span style=\"font-size: medium\"><u><span style=\"font-family: Times New Roman,serif\">Solution :<\/span><\/u><\/span><\/span><\/span><\/p>\n<p align=\"justify\"><img loading=\"lazy\" decoding=\"async\" class=\"aligncenter size-medium wp-image-1490\" src=\"https:\/\/gurumuda.net\/physics\/wp-content\/uploads\/2018\/03\/Kinetic-theory-of-gases-problems-and-solutions-5-257x300.png\" alt=\"Kinetic theory of gases - problems and solutions 5\" width=\"257\" height=\"300\" srcset=\"https:\/\/gurumuda.net\/physics\/wp-content\/uploads\/sites\/28\/2018\/03\/Kinetic-theory-of-gases-problems-and-solutions-5-257x300.png 257w, https:\/\/gurumuda.net\/physics\/wp-content\/uploads\/sites\/28\/2018\/03\/Kinetic-theory-of-gases-problems-and-solutions-5.png 266w\" sizes=\"auto, (max-width: 257px) 100vw, 257px\" \/><\/p>\n<p align=\"justify\"><\/p>\n<p class=\"western\" align=\"justify\"><span style=\"font-size: medium\"><span style=\"font-family: Times New Roman,serif\">4. <\/span><span style=\"font-family: Times New Roman,serif\">An ideal gas is in a closed container, is heated so that the final <a href=\"https:\/\/gurumuda.net\/physics\/average-velocity-problems-and-solutions.htm\" target=\"_blank\" rel=\"noopener\">average velocity<\/a> of particles of gas increases by 3 times the initial average velocity. If the initial gas temperature is <\/span><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, <\/span><span style=\"font-family: Times New Roman,serif\">then the final temperature of the ideal gas is&#8230;<\/span><\/span><\/p>\n<p align=\"justify\"><span style=\"color: #000000\"><span style=\"font-family: Garamond,serif\"><span style=\"font-size: medium\"><u><span style=\"font-family: Times New Roman,serif\">Known :<\/span><\/u><\/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\">Initial temperature <\/span><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 Kelvin<\/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\">Initial velocity<\/span><span style=\"font-family: Times New Roman,serif\"> = v<\/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\">Final velocity<\/span><span style=\"font-family: Times New Roman,serif\"> = 2v<\/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\"> : T<\/span><span style=\"font-family: Times New Roman,serif\">he final temperature of ideal gas<\/span><\/span><\/span><\/span><\/p>\n<p class=\"western\" align=\"justify\"><span style=\"font-family: Times new roman,serif\"><span style=\"font-size: medium\"><u>Solution :<\/u><\/span><\/span><\/p>\n<p align=\"justify\"><img loading=\"lazy\" decoding=\"async\" class=\"aligncenter size-medium wp-image-1515\" src=\"https:\/\/gurumuda.net\/physics\/wp-content\/uploads\/2018\/03\/Kinetic-theory-of-gases-problems-and-solutions-20-181x300.png\" alt=\"Kinetic theory of gases - problems and solutions 20\" width=\"181\" height=\"300\" srcset=\"https:\/\/gurumuda.net\/physics\/wp-content\/uploads\/sites\/28\/2018\/03\/Kinetic-theory-of-gases-problems-and-solutions-20-181x300.png 181w, https:\/\/gurumuda.net\/physics\/wp-content\/uploads\/sites\/28\/2018\/03\/Kinetic-theory-of-gases-problems-and-solutions-20.png 194w\" sizes=\"auto, (max-width: 181px) 100vw, 181px\" \/><\/p>\n<p class=\"western\" align=\"justify\"><span style=\"font-size: medium\"><span style=\"font-family: Times New Roman,serif\">The final average velocity<\/span><span style=\"font-family: Times New Roman,serif\"> = 2 x <\/span><span style=\"font-family: Times New Roman,serif\">the initial average velocity<\/span><\/span><\/p>\n<p align=\"justify\"><img loading=\"lazy\" decoding=\"async\" class=\"aligncenter size-medium wp-image-1492\" src=\"https:\/\/gurumuda.net\/physics\/wp-content\/uploads\/2018\/03\/Kinetic-theory-of-gases-problems-and-solutions-7-176x300.png\" alt=\"Kinetic theory of gases - problems and solutions 7\" width=\"176\" height=\"300\" \/><\/p>\n<p align=\"justify\"><\/p>\n<p class=\"western\" align=\"justify\"><span style=\"font-family: Times New Roman,serif\"><span style=\"font-size: medium\">5. <\/span><\/span><span style=\"font-family: Times new roman,serif\"><span style=\"font-size: medium\">Three moles of gas are in a 36 liters volume space. <\/span><\/span><span style=\"font-family: Times new roman,serif\"><span style=\"font-size: medium\"><span lang=\"en-US\">Each gas molecule has a kinetic energy of 5 x 10<\/span><\/span><\/span><sup><span style=\"font-family: Times new roman,serif\"><span style=\"font-size: medium\"><span lang=\"en-US\">-21<\/span><\/span><\/span><\/sup><span style=\"font-family: Times new roman,serif\"><span style=\"font-size: medium\"><span lang=\"en-US\"> Joule.<\/span><\/span><\/span><span style=\"font-family: Times new roman,serif\"><span style=\"font-size: medium\"> Universal gas constant = 8.315 J\/mole.K and Boltzmann&#8217;s constant = 1.38 x 10<\/span><\/span><sup><span style=\"font-family: Times new roman,serif\"><span style=\"font-size: medium\">-23<\/span><\/span><\/sup><span style=\"font-family: Times new roman,serif\"><span style=\"font-size: medium\"> J\/K. What is the gas pressure in the container. <\/span><\/span><\/p>\n<p align=\"justify\"><span style=\"color: #000000\"><span style=\"font-family: Times new roman,serif\"><span style=\"font-size: medium\"><u><span style=\"font-family: Times New Roman,serif\">Known :<\/span><\/u><\/span><\/span><\/span><\/p>\n<p align=\"justify\"><span style=\"color: #000000\"><span style=\"font-family: Times new roman,serif\"><span style=\"font-size: medium\">Number of moles (n) = 3 moles<\/span><\/span><\/span><\/p>\n<p align=\"justify\"><span style=\"color: #000000\"><span style=\"font-family: Times new roman,serif\"><span style=\"font-size: medium\">Volume = 36 liters = 36 dm<sup>3 <\/sup>= 36 x 10<sup>-3<\/sup> m<sup>3<\/sup><\/span><\/span><\/span><\/p>\n<p align=\"justify\"><span style=\"color: #000000\"><span style=\"font-family: Times new roman,serif\"><span style=\"font-size: medium\">Boltzmann&#8217;s constant (k) = 1.38 x 10<sup>-23<\/sup> J\/K<\/span><\/span><\/span><\/p>\n<p align=\"justify\"><span style=\"color: #000000\"><span style=\"font-family: Times new roman,serif\"><span style=\"font-size: medium\">Kinetic energy (KE) = 5 x 10<sup>\u201321<\/sup> Joule<\/span><\/span><\/span><\/p>\n<p align=\"justify\"><span style=\"color: #000000\"><span style=\"font-family: Times new roman,serif\"><span style=\"font-size: medium\">Universal gas constant (R) = 8.315 J\/mole.K<\/span><\/span><\/span><\/p>\n<p align=\"justify\"><span style=\"color: #000000\"><span style=\"font-family: Times new roman,serif\"><span style=\"font-size: medium\"><u>Wanted <\/u>: Gas pressure (P)<\/span><\/span><\/span><\/p>\n<p class=\"western\" align=\"justify\"><span style=\"font-family: Times new roman,serif\"><span style=\"font-size: medium\"><u><span style=\"font-family: Times New Roman,serif\">Solution :<\/span><\/u><\/span><\/span><\/p>\n<p class=\"western\" align=\"justify\"><span style=\"font-family: Times new roman,serif\"><span style=\"font-size: medium\">Calculate the temperature using the equation of kinetic energy of gas. <\/span><\/span><\/p>\n<p align=\"justify\"><img loading=\"lazy\" decoding=\"async\" class=\"aligncenter size-full wp-image-1493\" src=\"https:\/\/gurumuda.net\/physics\/wp-content\/uploads\/2018\/03\/Kinetic-theory-of-gases-problems-and-solutions-8.png\" alt=\"Kinetic theory of gases - problems and solutions 8\" width=\"211\" height=\"205\" \/><\/p>\n<p class=\"western\" align=\"justify\"><span style=\"font-family: Times new roman,serif\"><span style=\"font-size: medium\">Calculate the gas pressure using th equation of ideal gas law (in number of moles, n) : <\/span><\/span><\/p>\n<p class=\"western\" align=\"justify\"><span style=\"font-family: Times new roman,serif\"><span style=\"font-size: medium\">P V = n R T<\/span><\/span><\/p>\n<p class=\"western\" align=\"justify\"><span style=\"font-family: Times new roman,serif\"><span style=\"font-size: medium\">P (36 x 10<sup>-3<\/sup>) = (3)(8.315)(241.5)<\/span><\/span><\/p>\n<p class=\"western\" align=\"justify\"><span style=\"font-family: Times new roman,serif\"><span style=\"font-size: medium\">P (36 x 10<sup>-3<\/sup>) = 6024.22<\/span><\/span><\/p>\n<p align=\"justify\"><img loading=\"lazy\" decoding=\"async\" class=\"aligncenter size-full wp-image-1494\" src=\"https:\/\/gurumuda.net\/physics\/wp-content\/uploads\/2018\/03\/Kinetic-theory-of-gases-problems-and-solutions-9.png\" alt=\"Kinetic theory of gases - problems and solutions 9\" width=\"221\" height=\"178\" \/><\/p>\n<p class=\"western\" align=\"justify\"><span style=\"font-family: Times new roman,serif\"><span style=\"font-size: medium\">The gas pressure is 1.67 x 10<sup>5<\/sup> Pascal or 1.67 atmospheres.<\/span><\/span><!--more--><\/p>\n","protected":false,"gt_translate_keys":[{"key":"rendered","format":"html"}]},"excerpt":{"rendered":"<p>1. Ideal gases in a closed container initially have volume V and pressure P. If the final pressure is 4P and the volume is kept constant, what is the ratio of the initial kinetic energy with the final kinetic energy. Known : Initial pressure (P1) = P Final pressure (P2) = 4P Initial volume (V1) &#8230; <a title=\"Kinetic theory of gases &#8211; problems and solutions\" class=\"read-more\" href=\"https:\/\/gurumuda.net\/physics\/kinetic-theory-of-gases-problems-and-solutions.htm\" aria-label=\"Read more about Kinetic theory of gases &#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":"Kinetic theory of gases - 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-1485","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\/1485","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=1485"}],"version-history":[{"count":0,"href":"https:\/\/gurumuda.net\/physics\/wp-json\/wp\/v2\/posts\/1485\/revisions"}],"wp:attachment":[{"href":"https:\/\/gurumuda.net\/physics\/wp-json\/wp\/v2\/media?parent=1485"}],"wp:term":[{"taxonomy":"category","embeddable":true,"href":"https:\/\/gurumuda.net\/physics\/wp-json\/wp\/v2\/categories?post=1485"},{"taxonomy":"post_tag","embeddable":true,"href":"https:\/\/gurumuda.net\/physics\/wp-json\/wp\/v2\/tags?post=1485"}],"curies":[{"name":"wp","href":"https:\/\/api.w.org\/{rel}","templated":true}]}}