{"id":88447,"date":"2025-06-01T07:11:24","date_gmt":"2025-06-01T07:11:24","guid":{"rendered":"https:\/\/exam.pscnotes.com\/mcq\/?p=88447"},"modified":"2025-06-01T07:11:24","modified_gmt":"2025-06-01T07:11:24","slug":"a-stainless-steel-chamber-contains-ar-gas-at-a-temperature-t-and-press","status":"publish","type":"post","link":"https:\/\/exam.pscnotes.com\/mcq\/a-stainless-steel-chamber-contains-ar-gas-at-a-temperature-t-and-press\/","title":{"rendered":"A stainless steel chamber contains Ar gas at a temperature T and press"},"content":{"rendered":"

A stainless steel chamber contains Ar gas at a temperature T and pressure P. The total number of Ar atoms in the chamber is n. Now Ar gas in the chamber is replaced by CO\u2082 gas and the total number of CO\u2082 molecules in the chamber is n\/2 at the same temperature T. The pressure in the chamber now is P’. Which one of the following relations holds true? (Both the gases behave as ideal gases)<\/p>\n

[amp_mcq option1=”P’ = P” option2=”P’ = 2P” option3=”P’ = P\/2″ option4=”P’ = P\/4″ correct=”option3″]<\/p>\n

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This question was previously asked in<\/div>\n
UPSC NDA-2 – 2018<\/div>\n<\/div>\n
Download PDF<\/a>Attempt Online<\/a><\/div>\n<\/div>\n
\nThe ideal gas law states that PV = nRT, where P is pressure, V is volume, n is the number of moles, R is the ideal gas constant, and T is temperature. For the first scenario with Ar gas, we have PV = n_Ar RT. Since the number of atoms is n, and assuming R is taken such that n represents the total number of particles, the equation can be written as PV = nRT. For the second scenario with CO\u2082 gas, the number of molecules is n\/2, and the temperature T and volume V (of the chamber) are the same. So, P’V = (n\/2)RT. Dividing the second equation by the first gives (P’V)\/(PV) = ((n\/2)RT)\/(nRT), which simplifies to P’\/P = (n\/2)\/n = 1\/2. Therefore, P’ = P\/2.
\n<\/section>\n
\nThe key principle is the ideal gas law (PV = nRT or PV = NkT, where N is the number of particles and k is Boltzmann’s constant). The pressure of an ideal gas depends only on the number of particles, volume, and temperature, not on the type of gas (as long as it behaves ideally). Since the number of particles is halved while temperature and volume are kept constant, the pressure must also be halved.
\n<\/section>\n
\nAvogadro’s hypothesis states that equal volumes of all ideal gases, at the same temperature and pressure, contain the same number of molecules. This question applies the ideal gas law inversely, showing that for a fixed volume and temperature, pressure is directly proportional to the number of moles or molecules.
\n<\/section>\n","protected":false},"excerpt":{"rendered":"

A stainless steel chamber contains Ar gas at a temperature T and pressure P. The total number of Ar atoms in the chamber is n. Now Ar gas in the chamber is replaced by CO\u2082 gas and the total number of CO\u2082 molecules in the chamber is n\/2 at the same temperature T. The pressure … <\/p>\n

Detailed SolutionA stainless steel chamber contains Ar gas at a temperature T and press<\/span><\/a><\/p>\n","protected":false},"author":1,"featured_media":0,"comment_status":"closed","ping_status":"open","sticky":false,"template":"","format":"standard","meta":{"footnotes":""},"categories":[1094],"tags":[1114,1130,1128],"class_list":["post-88447","post","type-post","status-publish","format-standard","hentry","category-upsc-nda-2","tag-1114","tag-heat-and-thermodynamics","tag-physics","no-featured-image-padding"],"yoast_head":"\nA stainless steel chamber contains Ar gas at a temperature T and press<\/title>\n<meta name=\"description\" content=\"The ideal gas law states that PV = nRT, where P is pressure, V is volume, n is the number of moles, R is the ideal gas constant, and T is temperature. For the first scenario with Ar gas, we have PV = n_Ar RT. Since the number of atoms is n, and assuming R is taken such that n represents the total number of particles, the equation can be written as PV = nRT. For the second scenario with CO\u2082 gas, the number of molecules is n\/2, and the temperature T and volume V (of the chamber) are the same. So, P'V = (n\/2)RT. Dividing the second equation by the first gives (P'V)\/(PV) = ((n\/2)RT)\/(nRT), which simplifies to P'\/P = (n\/2)\/n = 1\/2. Therefore, P' = P\/2. The key principle is the ideal gas law (PV = nRT or PV = NkT, where N is the number of particles and k is Boltzmann's constant). The pressure of an ideal gas depends only on the number of particles, volume, and temperature, not on the type of gas (as long as it behaves ideally). Since the number of particles is halved while temperature and volume are kept constant, the pressure must also be halved.\" \/>\n<meta name=\"robots\" content=\"index, follow, max-snippet:-1, max-image-preview:large, max-video-preview:-1\" \/>\n<link rel=\"canonical\" href=\"https:\/\/exam.pscnotes.com\/mcq\/a-stainless-steel-chamber-contains-ar-gas-at-a-temperature-t-and-press\/\" \/>\n<meta property=\"og:locale\" content=\"en_US\" \/>\n<meta property=\"og:type\" content=\"article\" \/>\n<meta property=\"og:title\" content=\"A stainless steel chamber contains Ar gas at a temperature T and press\" \/>\n<meta property=\"og:description\" content=\"The ideal gas law states that PV = nRT, where P is pressure, V is volume, n is the number of moles, R is the ideal gas constant, and T is temperature. For the first scenario with Ar gas, we have PV = n_Ar RT. Since the number of atoms is n, and assuming R is taken such that n represents the total number of particles, the equation can be written as PV = nRT. For the second scenario with CO\u2082 gas, the number of molecules is n\/2, and the temperature T and volume V (of the chamber) are the same. So, P'V = (n\/2)RT. Dividing the second equation by the first gives (P'V)\/(PV) = ((n\/2)RT)\/(nRT), which simplifies to P'\/P = (n\/2)\/n = 1\/2. Therefore, P' = P\/2. The key principle is the ideal gas law (PV = nRT or PV = NkT, where N is the number of particles and k is Boltzmann's constant). The pressure of an ideal gas depends only on the number of particles, volume, and temperature, not on the type of gas (as long as it behaves ideally). Since the number of particles is halved while temperature and volume are kept constant, the pressure must also be halved.\" \/>\n<meta property=\"og:url\" content=\"https:\/\/exam.pscnotes.com\/mcq\/a-stainless-steel-chamber-contains-ar-gas-at-a-temperature-t-and-press\/\" \/>\n<meta property=\"og:site_name\" content=\"MCQ and Quiz for Exams\" \/>\n<meta property=\"article:published_time\" content=\"2025-06-01T07:11:24+00:00\" \/>\n<meta name=\"author\" content=\"rawan239\" \/>\n<meta name=\"twitter:card\" content=\"summary_large_image\" \/>\n<meta name=\"twitter:label1\" content=\"Written by\" \/>\n\t<meta name=\"twitter:data1\" content=\"rawan239\" \/>\n\t<meta name=\"twitter:label2\" content=\"Est. reading time\" \/>\n\t<meta name=\"twitter:data2\" content=\"2 minutes\" \/>\n<!-- \/ Yoast SEO Premium plugin. -->","yoast_head_json":{"title":"A stainless steel chamber contains Ar gas at a temperature T and press","description":"The ideal gas law states that PV = nRT, where P is pressure, V is volume, n is the number of moles, R is the ideal gas constant, and T is temperature. For the first scenario with Ar gas, we have PV = n_Ar RT. Since the number of atoms is n, and assuming R is taken such that n represents the total number of particles, the equation can be written as PV = nRT. For the second scenario with CO\u2082 gas, the number of molecules is n\/2, and the temperature T and volume V (of the chamber) are the same. So, P'V = (n\/2)RT. Dividing the second equation by the first gives (P'V)\/(PV) = ((n\/2)RT)\/(nRT), which simplifies to P'\/P = (n\/2)\/n = 1\/2. Therefore, P' = P\/2. The key principle is the ideal gas law (PV = nRT or PV = NkT, where N is the number of particles and k is Boltzmann's constant). The pressure of an ideal gas depends only on the number of particles, volume, and temperature, not on the type of gas (as long as it behaves ideally). Since the number of particles is halved while temperature and volume are kept constant, the pressure must also be halved.","robots":{"index":"index","follow":"follow","max-snippet":"max-snippet:-1","max-image-preview":"max-image-preview:large","max-video-preview":"max-video-preview:-1"},"canonical":"https:\/\/exam.pscnotes.com\/mcq\/a-stainless-steel-chamber-contains-ar-gas-at-a-temperature-t-and-press\/","og_locale":"en_US","og_type":"article","og_title":"A stainless steel chamber contains Ar gas at a temperature T and press","og_description":"The ideal gas law states that PV = nRT, where P is pressure, V is volume, n is the number of moles, R is the ideal gas constant, and T is temperature. For the first scenario with Ar gas, we have PV = n_Ar RT. Since the number of atoms is n, and assuming R is taken such that n represents the total number of particles, the equation can be written as PV = nRT. For the second scenario with CO\u2082 gas, the number of molecules is n\/2, and the temperature T and volume V (of the chamber) are the same. So, P'V = (n\/2)RT. Dividing the second equation by the first gives (P'V)\/(PV) = ((n\/2)RT)\/(nRT), which simplifies to P'\/P = (n\/2)\/n = 1\/2. Therefore, P' = P\/2. The key principle is the ideal gas law (PV = nRT or PV = NkT, where N is the number of particles and k is Boltzmann's constant). The pressure of an ideal gas depends only on the number of particles, volume, and temperature, not on the type of gas (as long as it behaves ideally). Since the number of particles is halved while temperature and volume are kept constant, the pressure must also be halved.","og_url":"https:\/\/exam.pscnotes.com\/mcq\/a-stainless-steel-chamber-contains-ar-gas-at-a-temperature-t-and-press\/","og_site_name":"MCQ and Quiz for Exams","article_published_time":"2025-06-01T07:11:24+00:00","author":"rawan239","twitter_card":"summary_large_image","twitter_misc":{"Written by":"rawan239","Est. reading time":"2 minutes"},"schema":{"@context":"https:\/\/schema.org","@graph":[{"@type":"WebPage","@id":"https:\/\/exam.pscnotes.com\/mcq\/a-stainless-steel-chamber-contains-ar-gas-at-a-temperature-t-and-press\/","url":"https:\/\/exam.pscnotes.com\/mcq\/a-stainless-steel-chamber-contains-ar-gas-at-a-temperature-t-and-press\/","name":"A stainless steel chamber contains Ar gas at a temperature T and press","isPartOf":{"@id":"https:\/\/exam.pscnotes.com\/mcq\/#website"},"datePublished":"2025-06-01T07:11:24+00:00","dateModified":"2025-06-01T07:11:24+00:00","author":{"@id":"https:\/\/exam.pscnotes.com\/mcq\/#\/schema\/person\/5807dafeb27d2ec82344d6cbd6c3d209"},"description":"The ideal gas law states that PV = nRT, where P is pressure, V is volume, n is the number of moles, R is the ideal gas constant, and T is temperature. For the first scenario with Ar gas, we have PV = n_Ar RT. Since the number of atoms is n, and assuming R is taken such that n represents the total number of particles, the equation can be written as PV = nRT. For the second scenario with CO\u2082 gas, the number of molecules is n\/2, and the temperature T and volume V (of the chamber) are the same. So, P'V = (n\/2)RT. Dividing the second equation by the first gives (P'V)\/(PV) = ((n\/2)RT)\/(nRT), which simplifies to P'\/P = (n\/2)\/n = 1\/2. Therefore, P' = P\/2. The key principle is the ideal gas law (PV = nRT or PV = NkT, where N is the number of particles and k is Boltzmann's constant). The pressure of an ideal gas depends only on the number of particles, volume, and temperature, not on the type of gas (as long as it behaves ideally). Since the number of particles is halved while temperature and volume are kept constant, the pressure must also be halved.","breadcrumb":{"@id":"https:\/\/exam.pscnotes.com\/mcq\/a-stainless-steel-chamber-contains-ar-gas-at-a-temperature-t-and-press\/#breadcrumb"},"inLanguage":"en-US","potentialAction":[{"@type":"ReadAction","target":["https:\/\/exam.pscnotes.com\/mcq\/a-stainless-steel-chamber-contains-ar-gas-at-a-temperature-t-and-press\/"]}]},{"@type":"BreadcrumbList","@id":"https:\/\/exam.pscnotes.com\/mcq\/a-stainless-steel-chamber-contains-ar-gas-at-a-temperature-t-and-press\/#breadcrumb","itemListElement":[{"@type":"ListItem","position":1,"name":"Home","item":"https:\/\/exam.pscnotes.com\/mcq\/"},{"@type":"ListItem","position":2,"name":"UPSC NDA-2","item":"https:\/\/exam.pscnotes.com\/mcq\/category\/upsc-nda-2\/"},{"@type":"ListItem","position":3,"name":"A stainless steel chamber contains Ar gas at a temperature T and press"}]},{"@type":"WebSite","@id":"https:\/\/exam.pscnotes.com\/mcq\/#website","url":"https:\/\/exam.pscnotes.com\/mcq\/","name":"MCQ and Quiz for Exams","description":"","potentialAction":[{"@type":"SearchAction","target":{"@type":"EntryPoint","urlTemplate":"https:\/\/exam.pscnotes.com\/mcq\/?s={search_term_string}"},"query-input":"required name=search_term_string"}],"inLanguage":"en-US"},{"@type":"Person","@id":"https:\/\/exam.pscnotes.com\/mcq\/#\/schema\/person\/5807dafeb27d2ec82344d6cbd6c3d209","name":"rawan239","image":{"@type":"ImageObject","inLanguage":"en-US","@id":"https:\/\/exam.pscnotes.com\/mcq\/#\/schema\/person\/image\/","url":"https:\/\/secure.gravatar.com\/avatar\/761a7274f9cce048fa5b921221e7934820d74514df93ef195a9d22af0c1c9001?s=96&d=mm&r=g","contentUrl":"https:\/\/secure.gravatar.com\/avatar\/761a7274f9cce048fa5b921221e7934820d74514df93ef195a9d22af0c1c9001?s=96&d=mm&r=g","caption":"rawan239"},"sameAs":["https:\/\/exam.pscnotes.com"],"url":"https:\/\/exam.pscnotes.com\/mcq\/author\/rawan239\/"}]}},"amp_enabled":true,"_links":{"self":[{"href":"https:\/\/exam.pscnotes.com\/mcq\/wp-json\/wp\/v2\/posts\/88447","targetHints":{"allow":["GET"]}}],"collection":[{"href":"https:\/\/exam.pscnotes.com\/mcq\/wp-json\/wp\/v2\/posts"}],"about":[{"href":"https:\/\/exam.pscnotes.com\/mcq\/wp-json\/wp\/v2\/types\/post"}],"author":[{"embeddable":true,"href":"https:\/\/exam.pscnotes.com\/mcq\/wp-json\/wp\/v2\/users\/1"}],"replies":[{"embeddable":true,"href":"https:\/\/exam.pscnotes.com\/mcq\/wp-json\/wp\/v2\/comments?post=88447"}],"version-history":[{"count":0,"href":"https:\/\/exam.pscnotes.com\/mcq\/wp-json\/wp\/v2\/posts\/88447\/revisions"}],"wp:attachment":[{"href":"https:\/\/exam.pscnotes.com\/mcq\/wp-json\/wp\/v2\/media?parent=88447"}],"wp:term":[{"taxonomy":"category","embeddable":true,"href":"https:\/\/exam.pscnotes.com\/mcq\/wp-json\/wp\/v2\/categories?post=88447"},{"taxonomy":"post_tag","embeddable":true,"href":"https:\/\/exam.pscnotes.com\/mcq\/wp-json\/wp\/v2\/tags?post=88447"}],"curies":[{"name":"wp","href":"https:\/\/api.w.org\/{rel}","templated":true}]}}