{"id":259522,"date":"2022-09-10T12:15:52","date_gmt":"2022-09-10T06:45:52","guid":{"rendered":"https:\/\/infinitylearn.com\/surge\/question\/a-monoatomic-gas-at-a-pressure-p-having-a-volume-v-expands-isothermally-to-a-volume-2v-and-then-adiabatically-to-a-volume-16-v-the-final-pressure-of-the-gas-is-take-%ce%b3-5-3\/"},"modified":"2022-09-10T12:15:52","modified_gmt":"2022-09-10T06:45:52","slug":"a-monoatomic-gas-at-a-pressure-p-having-a-volume-v-expands-isothermally-to-a-volume-2v-and-then-adiabatically-to-a-volume-16-v-the-final-pressure-of-the-gas-is-take-%ce%b3-5-3","status":"publish","type":"questions","link":"https:\/\/infinitylearn.com\/surge\/question\/physics\/a-monoatomic-gas-at-a-pressure-p-having-a-volume-v-expands-i\/","title":{"rendered":"A monoatomic gas at a pressure P having a volume V expands isothermally to a volume\u00a02V and then adiabatically to a volume\u00a016 V. The final pressure of the gas is (Take\u00a0\u03b3\u00a0= 5\/3)"},"content":{"rendered":"","protected":false},"author":1,"template":"","meta":{"_yoast_wpseo_focuskw":"","_yoast_wpseo_title":"","_yoast_wpseo_metadesc":"A monoatomic gas at a pressure P having a volume V expands isothermally to a volume\u00a02V and then adiabatically to a volume\u00a016 V. The final pressure of the gas is (Take\u00a0\u03b3\u00a0= 5\/3)","custom_permalink":"question\/physics\/a-monoatomic-gas-at-a-pressure-p-having-a-volume-v-expands-i\/"},"categories":[],"acf":{"question":"<p>A monoatomic gas at a pressure P having a volume V expands isothermally to a volume&nbsp;2V and then adiabatically to a volume&nbsp;16 V. The final pressure of the gas is (Take&nbsp;<math xmlns=\"http:\/\/www.w3.org\/1998\/Math\/MathML\"><mi>\u03b3<\/mi><\/math>&nbsp;= 5\/3)<\/p>","options":[{"option":"<p>64 P<\/p>","correct":false},{"option":"<p>32 P<\/p>","correct":false},{"option":"<p>P \/ 64<\/p>","correct":true},{"option":"<p>16 P<\/p>","correct":false}],"solution":"<p><math xmlns=\"http:\/\/www.w3.org\/1998\/Math\/MathML\"><mtext>&nbsp;First, isothermal expansion&nbsp;<\/mtext><\/math><\/p><p><math xmlns=\"http:\/\/www.w3.org\/1998\/Math\/MathML\"><mi>P<\/mi><mi>V<\/mi><mo>=<\/mo><msup><mi>P<\/mi><mi mathvariant=\"normal\">\u2032<\/mi><\/msup><mo>(<\/mo><mn>2<\/mn><mi>V<\/mi><mo>)<\/mo><\/math><\/p><p>(For isothermal process,&nbsp;PV = constant)<\/p><p><math xmlns=\"http:\/\/www.w3.org\/1998\/Math\/MathML\"><msup><mi>P<\/mi><mi mathvariant=\"normal\">\u2032<\/mi><\/msup><mo>=<\/mo><mfrac><mi>P<\/mi><mn>2<\/mn><\/mfrac><\/math><\/p><p>Then, adiabatic expansion<\/p><p><math xmlns=\"http:\/\/www.w3.org\/1998\/Math\/MathML\"><msup><mi>P<\/mi><mi mathvariant=\"normal\">\u2032<\/mi><\/msup><mo>(<\/mo><mn>2<\/mn><mi>V<\/mi><msup><mo>)<\/mo><mi>\u03b3<\/mi><\/msup><mo>=<\/mo><msub><mi>P<\/mi><mi>f<\/mi><\/msub><mo>(<\/mo><mn>16<\/mn><mi>V<\/mi><msup><mo>)<\/mo><mi>\u03b3<\/mi><\/msup><\/math><\/p><p><math xmlns=\"http:\/\/www.w3.org\/1998\/Math\/MathML\"><mtext>&nbsp;(For adiabatic process,&nbsp;<\/mtext><mi>P<\/mi><msup><mi>V<\/mi><mi>\u03b3<\/mi><\/msup><mo>=<\/mo><mtext>&nbsp;constant&nbsp;<\/mtext><mo>)<\/mo><\/math><\/p><p><math xmlns=\"http:\/\/www.w3.org\/1998\/Math\/MathML\"><mfrac><mi>P<\/mi><mn>2<\/mn><\/mfrac><mo>(<\/mo><mn>2<\/mn><mi>V<\/mi><msup><mo>)<\/mo><mrow><mn>5<\/mn><mo>\/<\/mo><mn>3<\/mn><\/mrow><\/msup><mo>=<\/mo><msub><mi>P<\/mi><mi>f<\/mi><\/msub><mo>(<\/mo><mn>16<\/mn><mi>V<\/mi><msup><mo>)<\/mo><mrow><mn>5<\/mn><mo>\/<\/mo><mn>3<\/mn><\/mrow><\/msup><\/math><\/p><p><math xmlns=\"http:\/\/www.w3.org\/1998\/Math\/MathML\"><msub><mi>P<\/mi><mi>f<\/mi><\/msub><mo>=<\/mo><mfrac><mi>P<\/mi><mn>2<\/mn><\/mfrac><msup><mfenced separators=\"|\"><mfrac><mrow><mn>2<\/mn><mi>V<\/mi><\/mrow><mrow><mn>16<\/mn><mi>V<\/mi><\/mrow><\/mfrac><\/mfenced><mrow><mn>5<\/mn><mo>\/<\/mo><mn>3<\/mn><\/mrow><\/msup><mo>=<\/mo><mfrac><mi>P<\/mi><mn>2<\/mn><\/mfrac><msup><mfenced separators=\"|\"><mfrac><mn>1<\/mn><mn>8<\/mn><\/mfrac><\/mfenced><mrow><mn>5<\/mn><mo>\/<\/mo><mn>3<\/mn><\/mrow><\/msup><mo>=<\/mo><mfrac><mi>P<\/mi><mn>2<\/mn><\/mfrac><msup><mfenced separators=\"|\"><mfrac><mn>1<\/mn><msup><mn>2<\/mn><mn>3<\/mn><\/msup><\/mfrac><\/mfenced><mrow><mn>5<\/mn><mo>\/<\/mo><mn>3<\/mn><\/mrow><\/msup><mo>=<\/mo><mfrac><mi>P<\/mi><mn>2<\/mn><\/mfrac><mfenced separators=\"|\"><mfrac><mn>1<\/mn><msup><mn>2<\/mn><mn>5<\/mn><\/msup><\/mfrac><\/mfenced><mo>=<\/mo><mfrac><mi>P<\/mi><mn>64<\/mn><\/mfrac><\/math><\/p>","subject":""},"yoast_head":"<!-- This site is optimized with the Yoast SEO plugin v17.9 - https:\/\/yoast.com\/wordpress\/plugins\/seo\/ -->\n<title>A monoatomic gas at a pressure P having a volume V expands isothermally to a volume\u00a02V and then adiabatically to a volume\u00a016 V. 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