{"id":3258,"date":"2022-05-08T19:30:39","date_gmt":"2022-05-08T19:30:39","guid":{"rendered":"https:\/\/mdr.foobrdigital.com\/?p=3258"},"modified":"2022-05-08T19:30:39","modified_gmt":"2022-05-08T19:30:39","slug":"kinetic-gas-equation-derivation","status":"publish","type":"post","link":"https:\/\/mudassirbackup.infinitycodestudio.com\/index.php\/2022\/05\/08\/kinetic-gas-equation-derivation\/","title":{"rendered":"Kinetic Gas Equation Derivation"},"content":{"rendered":"\n<figure class=\"wp-block-image size-full\"><img decoding=\"async\" src=\"https:\/\/mdr.foobrdigital.com\/wp-content\/uploads\/2022\/05\/kinetic-gas-equation-derivation.png\" alt=\"\" class=\"wp-image-3259\" title=\"Kinetic Gas Equation Derivation\"\/><\/figure>\n\n\n\n<h2 class=\"wp-block-heading\">What Is Kinetic Theory Of Gases?<\/h2>\n\n\n\n<p>The kinetic theory of gases describes gas as a large number of submicroscopic particles such as atoms and molecules, all of which are in random and constant motion. The randomness arises from the particles collisions with each other and with the walls of the container.<\/p>\n\n\n\n<h2 class=\"wp-block-heading\">Derivation Of Kinetic Gas Equation<\/h2>\n\n\n\n<figure class=\"wp-block-image size-full\"><img decoding=\"async\" src=\"https:\/\/mdr.foobrdigital.com\/wp-content\/uploads\/2022\/05\/derivation-of-kinetic-gas-equation.png\" alt=\"\" class=\"wp-image-3260\" title=\"Derivation Of Kinetic Gas Equation\"\/><\/figure>\n\n\n\n<p>Consider a cubical container of length \u2018<em>l&nbsp;<\/em>\u2019 filled with gas molecules each having mass \u2018<em>m<\/em>\u2019 and let&nbsp;<em>N<\/em>&nbsp;be the total number of gas molecules in the container. Due to the influence of temperature, the gas molecules move in random directions with a velocity \u2018v.\u2019<\/p>\n\n\n\n<p>The pressure of the gas molecules is the force exerted by the gas molecule per unit area of the wall of the container and is given by the equation<\/p>\n\n\n\n<p>P = F A<\/p>\n\n\n\n<p>Let us consider a gas molecule moving in the x-direction towards face A. The molecule hits the wall with a velocity V<sub>x<\/sub>\u00a0and rebounds back with the same velocity V<sub>x<\/sub>, and will experience a change of momentum which is equal to<\/p>\n\n\n\n<p>\u0394 p = \u2212 2 m V x<\/p>\n\n\n\n<p>For a total of N number of gas molecules in the container, all such change in momentum is given by<\/p>\n\n\n\n<p>\u0394 p = \u2212 2 N m V x<\/p>\n\n\n\n<p>The force is given by the equation<\/p>\n\n\n\n<p>F = \u0394 p t<\/p>\n\n\n\n<p>Therefore,<\/p>\n\n\n\n<p>F = \u2212 2 N m V x \/t<\/p>\n\n\n\n<p>Gas molecules will hit the wall A and will travel back across the box, collide with the opposite face and hit face A again after a time t which is given by the equation<\/p>\n\n\n\n<p>t = 2 l \/ V x<\/p>\n\n\n\n<p>Substituting the value of t in the force equation, we get the force on the molecules as<\/p>\n\n\n\n<p>F = \u2212 2 N m V x 2 l V x<\/p>\n\n\n\n<p>Therefore, the force exerted on the wall is.<\/p>\n\n\n\n<p>F w a l l = N m V x 2 l<\/p>\n\n\n\n<p>Now, the pressure P is given by the equation<\/p>\n\n\n\n<p>This equation above is known as the kinetic theory equation.<\/p>\n\n\n\n<p>The velocity V in the kinetic gas equation is known as the root-mean-square velocity and is given by the equation<\/p>\n\n\n\n<p>V r m s = V 1 2 + V 2 2 + V 3 2 \u2026 \u2026 . . + V n 2 N<\/p>\n\n\n\n<p>We use this equation to calculate the root-mean-square velocity of gas molecules at any given temperature and pressure<\/p>\n","protected":false},"excerpt":{"rendered":"<p>What Is Kinetic Theory Of Gases? The kinetic theory of gases describes gas as a large number of submicroscopic particles such as atoms and molecules, all of which are in random and constant motion. The randomness arises from the particles collisions with each other and with the walls of the container. Derivation Of Kinetic Gas [&hellip;]<\/p>\n","protected":false},"author":1,"featured_media":0,"comment_status":"open","ping_status":"open","sticky":false,"template":"","format":"standard","meta":{"footnotes":""},"categories":[665],"tags":[],"_links":{"self":[{"href":"https:\/\/mudassirbackup.infinitycodestudio.com\/index.php\/wp-json\/wp\/v2\/posts\/3258"}],"collection":[{"href":"https:\/\/mudassirbackup.infinitycodestudio.com\/index.php\/wp-json\/wp\/v2\/posts"}],"about":[{"href":"https:\/\/mudassirbackup.infinitycodestudio.com\/index.php\/wp-json\/wp\/v2\/types\/post"}],"author":[{"embeddable":true,"href":"https:\/\/mudassirbackup.infinitycodestudio.com\/index.php\/wp-json\/wp\/v2\/users\/1"}],"replies":[{"embeddable":true,"href":"https:\/\/mudassirbackup.infinitycodestudio.com\/index.php\/wp-json\/wp\/v2\/comments?post=3258"}],"version-history":[{"count":0,"href":"https:\/\/mudassirbackup.infinitycodestudio.com\/index.php\/wp-json\/wp\/v2\/posts\/3258\/revisions"}],"wp:attachment":[{"href":"https:\/\/mudassirbackup.infinitycodestudio.com\/index.php\/wp-json\/wp\/v2\/media?parent=3258"}],"wp:term":[{"taxonomy":"category","embeddable":true,"href":"https:\/\/mudassirbackup.infinitycodestudio.com\/index.php\/wp-json\/wp\/v2\/categories?post=3258"},{"taxonomy":"post_tag","embeddable":true,"href":"https:\/\/mudassirbackup.infinitycodestudio.com\/index.php\/wp-json\/wp\/v2\/tags?post=3258"}],"curies":[{"name":"wp","href":"https:\/\/api.w.org\/{rel}","templated":true}]}}