{"id":87149,"date":"2025-06-01T04:30:10","date_gmt":"2025-06-01T04:30:10","guid":{"rendered":"https:\/\/exam.pscnotes.com\/mcq\/?p=87149"},"modified":"2025-06-01T04:30:10","modified_gmt":"2025-06-01T04:30:10","slug":"molar-heat-capacity-at-constant-pressure-of-a-diatomic-gas-is-3%c2%b75-r-w","status":"publish","type":"post","link":"https:\/\/exam.pscnotes.com\/mcq\/molar-heat-capacity-at-constant-pressure-of-a-diatomic-gas-is-3%c2%b75-r-w\/","title":{"rendered":"Molar heat capacity at constant pressure of a diatomic gas is 3\u00b75 R, w"},"content":{"rendered":"

Molar heat capacity at constant pressure of a diatomic gas is 3\u00b75 R, where R is universal gas constant. The gas is heated by providing energy of 1400 J and is allowed to expand isobarically. Which one among the following represents the work done by the gas in this process ?<\/p>\n

[amp_mcq option1=”400 J” option2=”4900 J” option3=”560 J” option4=”280 J” correct=”option1″]<\/p>\n

\n
\n
This question was previously asked in<\/div>\n
UPSC Geoscientist – 2024<\/div>\n<\/div>\n
Download PDF<\/a>Attempt Online<\/a><\/div>\n<\/div>\n
\nThe correct option is A.
\n<\/section>\n
\nFor an ideal gas, the molar heat capacities at constant pressure (C_p) and constant volume (C_v) are related by Mayer’s relation: C_p – C_v = R. The work done by a gas during an isobaric (constant pressure) process is given by W = P\u0394V = nR\u0394T. The heat added during an isobaric process is Q = nC_p\u0394T. By the First Law of Thermodynamics, Q = \u0394U + W, where \u0394U = nC_v\u0394T.
\n<\/section>\n
\nGiven molar heat capacity at constant pressure C_p = 3.5 R = (7\/2)R.
\nUsing Mayer’s relation, C_v = C_p – R = (7\/2)R – R = (5\/2)R.
\nThe gas is heated isobarically, and energy Q = 1400 J is provided.
\nFor an isobaric process, Q = nC_p\u0394T, where n is the number of moles and \u0394T is the temperature change.
\nSo, 1400 J = n * (7\/2)R * \u0394T.
\nBy the First Law of Thermodynamics, Q = \u0394U + W.
\nWork done by the gas W = Q – \u0394U.
\nChange in internal energy for an ideal gas \u0394U = nC_v\u0394T.
\nW = Q – nC_v\u0394T.
\nFrom the isobaric heat equation, n\u0394T = Q \/ C_p = 1400 \/ (7\/2)R = 1400 * (2 \/ 7R) = 2800 \/ 7R = 400 \/ R.
\nNow substitute this into the work equation:
\nW = Q – nC_v\u0394T = 1400 – (n\u0394T) * C_v = 1400 – (400\/R) * (5\/2)R
\nW = 1400 – 400 * (5\/2) = 1400 – 200 * 5 = 1400 – 1000 = 400 J.<\/p>\n

Alternatively, W = nR\u0394T.
\nFrom Q = nC_p\u0394T, we have n\u0394T = Q\/C_p.
\nW = R * (Q\/C_p) = Q * (R\/C_p).
\nGiven C_p = (7\/2)R, so R\/C_p = R \/ ((7\/2)R) = 2\/7.
\nW = 1400 J * (2\/7) = 200 * 2 = 400 J.
\n<\/section>\n","protected":false},"excerpt":{"rendered":"

Molar heat capacity at constant pressure of a diatomic gas is 3\u00b75 R, where R is universal gas constant. The gas is heated by providing energy of 1400 J and is allowed to expand isobarically. Which one among the following represents the work done by the gas in this process ? [amp_mcq option1=”400 J” option2=”4900 … <\/p>\n

Detailed SolutionMolar heat capacity at constant pressure of a diatomic gas is 3\u00b75 R, w<\/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":[1091],"tags":[1103,1130,1128],"class_list":["post-87149","post","type-post","status-publish","format-standard","hentry","category-upsc-geoscientist","tag-1103","tag-heat-and-thermodynamics","tag-physics","no-featured-image-padding"],"yoast_head":"\nMolar heat capacity at constant pressure of a diatomic gas is 3\u00b75 R, w<\/title>\n<meta name=\"description\" content=\"The correct option is A. For an ideal gas, the molar heat capacities at constant pressure (C_p) and constant volume (C_v) are related by Mayer's relation: C_p - C_v = R. The work done by a gas during an isobaric (constant pressure) process is given by W = P\u0394V = nR\u0394T. The heat added during an isobaric process is Q = nC_p\u0394T. By the First Law of Thermodynamics, Q = \u0394U + W, where \u0394U = nC_v\u0394T.\" \/>\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\/molar-heat-capacity-at-constant-pressure-of-a-diatomic-gas-is-3\u00b75-r-w\/\" \/>\n<meta property=\"og:locale\" content=\"en_US\" \/>\n<meta property=\"og:type\" content=\"article\" \/>\n<meta property=\"og:title\" content=\"Molar heat capacity at constant pressure of a diatomic gas is 3\u00b75 R, w\" \/>\n<meta property=\"og:description\" content=\"The correct option is A. For an ideal gas, the molar heat capacities at constant pressure (C_p) and constant volume (C_v) are related by Mayer's relation: C_p - C_v = R. The work done by a gas during an isobaric (constant pressure) process is given by W = P\u0394V = nR\u0394T. The heat added during an isobaric process is Q = nC_p\u0394T. By the First Law of Thermodynamics, Q = \u0394U + W, where \u0394U = nC_v\u0394T.\" \/>\n<meta property=\"og:url\" content=\"https:\/\/exam.pscnotes.com\/mcq\/molar-heat-capacity-at-constant-pressure-of-a-diatomic-gas-is-3\u00b75-r-w\/\" \/>\n<meta property=\"og:site_name\" content=\"MCQ and Quiz for Exams\" \/>\n<meta property=\"article:published_time\" content=\"2025-06-01T04:30:10+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":"Molar heat capacity at constant pressure of a diatomic gas is 3\u00b75 R, w","description":"The correct option is A. For an ideal gas, the molar heat capacities at constant pressure (C_p) and constant volume (C_v) are related by Mayer's relation: C_p - C_v = R. The work done by a gas during an isobaric (constant pressure) process is given by W = P\u0394V = nR\u0394T. The heat added during an isobaric process is Q = nC_p\u0394T. By the First Law of Thermodynamics, Q = \u0394U + W, where \u0394U = nC_v\u0394T.","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\/molar-heat-capacity-at-constant-pressure-of-a-diatomic-gas-is-3\u00b75-r-w\/","og_locale":"en_US","og_type":"article","og_title":"Molar heat capacity at constant pressure of a diatomic gas is 3\u00b75 R, w","og_description":"The correct option is A. For an ideal gas, the molar heat capacities at constant pressure (C_p) and constant volume (C_v) are related by Mayer's relation: C_p - C_v = R. The work done by a gas during an isobaric (constant pressure) process is given by W = P\u0394V = nR\u0394T. The heat added during an isobaric process is Q = nC_p\u0394T. 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