{"id":332163,"date":"2023-01-06T02:06:56","date_gmt":"2023-01-05T20:36:56","guid":{"rendered":"https:\/\/infinitylearn.com\/surge\/question\/an-ideal-gas-%ce%b3-1-5-is-expanded-adiabatically-how-many-times-has-the-gas-to-be-expanded-to-reduce-the-root-mean-square-velocity-of-molecules-2-0-times\/"},"modified":"2025-06-26T18:03:27","modified_gmt":"2025-06-26T12:33:27","slug":"an-ideal-gas-%ce%b3-1-5-is-expanded-adiabatically-how-many-times-has-the-gas-to-be-expanded-to-reduce-the-root-mean-square-velocity-of-molecules-2-0-times","status":"publish","type":"questions","link":"https:\/\/infinitylearn.com\/surge\/question\/physics\/an-ideal-gas--15-is-expanded-adiabatically-how-many-t\/","title":{"rendered":"An ideal gas (\u03b3\u00a0= 1.5) is expanded adiabatically. How many times has the gas to be expanded to reduce the root mean square velocity of molecules 2.0 times\u00a0"},"content":{"rendered":"","protected":false},"author":1,"template":"","meta":{"_yoast_wpseo_focuskw":"","_yoast_wpseo_title":"","_yoast_wpseo_metadesc":"An ideal gas (\u03b3\u00a0= 1.5) is expanded adiabatically. How many times has the gas to be expanded to reduce the root mean square velocity of molecules 2.0 times\u00a0","custom_permalink":"question\/physics\/an-ideal-gas--15-is-expanded-adiabatically-how-many-t\/"},"categories":[],"acf":{"question":"<p>An ideal gas (<math xmlns=\"http:\/\/www.w3.org\/1998\/Math\/MathML\"><mi mathvariant=\"normal\">\u03b3<\/mi><\/math>&nbsp;= 1.5) is expanded adiabatically. How many times has the gas to be expanded to reduce the root mean square velocity of molecules 2.0 times&nbsp;<\/p>","options":[{"option":"<p>4 times<\/p>","correct":false},{"option":"<p>16 times<\/p>","correct":true},{"option":"<p>8 times<\/p>","correct":false},{"option":"<p>2 times<\/p>","correct":false}],"solution":"<p><math xmlns=\"http:\/\/www.w3.org\/1998\/Math\/MathML\"><msub><mi mathvariant=\"normal\">v<\/mi><mi>rms<\/mi><\/msub><mo>=<\/mo><msqrt><mfrac><mrow><mn>3<\/mn><mi>RT<\/mi><\/mrow><mi mathvariant=\"normal\">M<\/mi><\/mfrac><\/msqrt><mo stretchy=\"false\">\u21d2<\/mo><msub><mi mathvariant=\"normal\">v<\/mi><mi>rms<\/mi><\/msub><mo>\u221d<\/mo><msqrt><mi mathvariant=\"normal\">T<\/mi><\/msqrt><\/math><br>v<sub>rms<\/sub> is to reduce two times i.e. temperature of the gas will have to reduce four times or&nbsp;<math xmlns=\"http:\/\/www.w3.org\/1998\/Math\/MathML\"><mfrac><msup><mi mathvariant=\"normal\">T<\/mi><mi mathvariant=\"normal\">\u2032<\/mi><\/msup><mi mathvariant=\"normal\">T<\/mi><\/mfrac><mo>=<\/mo><mfrac><mn>1<\/mn><mn>4<\/mn><\/mfrac><\/math><br>During adiabatic process<br><math xmlns=\"http:\/\/www.w3.org\/1998\/Math\/MathML\"><mtable columnalign=\"left\" columnspacing=\"0em 2em 0em 2em 0em 2em 0em 2em 0em 2em 0em\"><mtr><mtd><msup><mi>TV<\/mi><mrow><mi mathvariant=\"normal\">\u03b3<\/mi><mo>\u2212<\/mo><mn>1<\/mn><\/mrow><\/msup><mo>=<\/mo><msup><mi mathvariant=\"normal\">T<\/mi><mi mathvariant=\"normal\">\u2032<\/mi><\/msup><msup><mi mathvariant=\"normal\">V<\/mi><mrow><mi mathvariant=\"normal\">\u2032<\/mi><mi mathvariant=\"normal\">\u03b3<\/mi><mo>\u2212<\/mo><mn>1<\/mn><\/mrow><\/msup><\/mtd><\/mtr><mtr><mtd><mo stretchy=\"false\">\u21d2<\/mo><mfrac><msup><mi mathvariant=\"normal\">V<\/mi><mi mathvariant=\"normal\">\u2032<\/mi><\/msup><mi mathvariant=\"normal\">V<\/mi><\/mfrac><mo>=<\/mo><msup><mfenced separators=\"|\"><mfrac><mi mathvariant=\"normal\">T<\/mi><msup><mi mathvariant=\"normal\">T<\/mi><mi mathvariant=\"normal\">\u2032<\/mi><\/msup><\/mfrac><\/mfenced><mfrac><mn>1<\/mn><mrow><mi mathvariant=\"normal\">\u03b3<\/mi><mo>\u2212<\/mo><mn>1<\/mn><\/mrow><\/mfrac><\/msup><mo>=<\/mo><mo>(<\/mo><mn>4<\/mn><msup><mo>)<\/mo><mfrac><mn>1<\/mn><mrow><mn>1<\/mn><mo>.5<\/mo><mo>\u2212<\/mo><mn>1<\/mn><\/mrow><\/mfrac><\/msup><mo>=<\/mo><mo>(<\/mo><mn>4<\/mn><msup><mo>)<\/mo><mn>2<\/mn><\/msup><mo>=<\/mo><mn>16<\/mn><\/mtd><\/mtr><mtr><mtd><mo stretchy=\"false\">\u21d2<\/mo><msup><mi mathvariant=\"normal\">V<\/mi><mi mathvariant=\"normal\">\u2032<\/mi><\/msup><mo>=<\/mo><mn>16<\/mn><mi mathvariant=\"normal\">V<\/mi><\/mtd><\/mtr><\/mtable><\/math><\/p>","subject":""},"yoast_head":"<!-- This site is optimized with the Yoast SEO plugin v17.9 - https:\/\/yoast.com\/wordpress\/plugins\/seo\/ -->\n<title>An ideal gas (\u03b3\u00a0= 1.5) is expanded adiabatically. 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