{"id":259708,"date":"2022-09-10T12:18:04","date_gmt":"2022-09-10T06:48:04","guid":{"rendered":"https:\/\/infinitylearn.com\/surge\/question\/the-molecules-of-a-given-mass-of-a-gas-have-rms-velocity-of-200-ms-1-at-27c-and-10-x-105-nm-2-pressure-when-the-temperature-and-pressure-of-the-gas\/"},"modified":"2022-09-10T12:18:04","modified_gmt":"2022-09-10T06:48:04","slug":"the-molecules-of-a-given-mass-of-a-gas-have-rms-velocity-of-200-ms-1-at-27c-and-10-x-105-nm-2-pressure-when-the-temperature-and-pressure-of-the-gas","status":"publish","type":"questions","link":"https:\/\/infinitylearn.com\/surge\/question\/physics\/the-molecules-of-a-given-mass-of-a-gas-have-rms-velocity-of\/","title":{"rendered":"The molecules of a given mass of a gas have rms velocity of\u00a0200\u00a0ms-1\u00a0at 27\u00b0C and\u00a010\u00a0\u00d7\u00a0105\u00a0Nm-2\u00a0pressure. When the temperature and pressure of the gas are respectively, 127\u00b0C and\u00a00.05\u00a0\u00d7\u00a0105\u00a0Nm-2, the rms velocity of its molecules (in\u00a0ms-1) is\u00a0"},"content":{"rendered":"","protected":false},"author":1,"template":"","meta":{"_yoast_wpseo_focuskw":"","_yoast_wpseo_title":"","_yoast_wpseo_metadesc":"The molecules of a given mass of a gas have rms velocity of\u00a0200\u00a0ms-1\u00a0at 27\u00b0C and\u00a010\u00a0\u00d7\u00a0105\u00a0Nm-2\u00a0pressure. When the temperature and pressure of the gas are respectively, 127\u00b0C and\u00a00.05\u00a0\u00d7\u00a0105\u00a0Nm-2, the rms velocity of its molecules (in\u00a0ms-1) is\u00a0","custom_permalink":"question\/physics\/the-molecules-of-a-given-mass-of-a-gas-have-rms-velocity-of\/"},"categories":[],"acf":{"question":"

The molecules of a given mass of a gas have rms velocity of 200<\/mn> <\/mo>ms<\/mi>-<\/mo>1<\/mn><\/mrow><\/msup><\/math> at 27\u00b0C and 10<\/mn> <\/mo>\u00d7<\/mo> <\/mo>10<\/mn>5<\/mn><\/msup> <\/mo>Nm<\/mi>-<\/mo>2<\/mn><\/mrow><\/msup><\/math> pressure. When the temperature and pressure of the gas are respectively, 127\u00b0C and 0<\/mn>.<\/mo>05<\/mn> <\/mo>\u00d7<\/mo> <\/mo>10<\/mn>5<\/mn><\/msup> <\/mo>Nm<\/mi>-<\/mo>2<\/mn><\/mrow><\/msup><\/math>, the rms velocity of its molecules (in ms<\/mi>-<\/mo>1<\/mn><\/mrow><\/msup><\/math>) is <\/p>","options":[{"option":"

400<\/mn>3<\/mn><\/msqrt><\/mfrac><\/math><\/p>","correct":true},{"option":"

100<\/mn>2<\/mn><\/msqrt><\/mrow>3<\/mn><\/mfrac><\/math><\/p>","correct":false},{"option":"

100<\/mn>3<\/mn><\/mfrac><\/math><\/p>","correct":false},{"option":"

100<\/mn>2<\/mn><\/msqrt><\/math><\/p>","correct":false}],"solution":"

It is given that,<\/p>

     v<\/mi>rms<\/mi><\/msub><\/mfenced>1<\/mn><\/msub>=<\/mo>200<\/mn> <\/mo>ms<\/mi><\/mrow>-<\/mo>1<\/mn><\/mrow><\/msup>,<\/mo>T<\/mi>1<\/mn><\/msub>=<\/mo>300<\/mn> <\/mo>K<\/mi>,<\/mo>p<\/mi>1<\/mn><\/msub>=<\/mo>10<\/mn>5<\/mn><\/msup>Nm<\/mi>-<\/mo>2<\/mn><\/mrow><\/msup><\/math><\/p>

           T<\/mi>2<\/mn><\/msub>=<\/mo>400<\/mn> <\/mo>K<\/mi>,<\/mo>p<\/mi>2<\/mn><\/msub>=<\/mo>0<\/mn>.<\/mo>05<\/mn>\u00d7<\/mo>10<\/mn>5<\/mn><\/msup>Nm<\/mi>-<\/mo>2<\/mn><\/mrow><\/msup>,<\/mo>v<\/mi>rms<\/mi><\/msub><\/mfenced>2<\/mn><\/msub>=<\/mo>?<\/mo><\/math><\/p>

As, rms velocity of gas molecules,<\/p>

                         v<\/mi>r<\/mi>m<\/mi>s<\/mi><\/mrow><\/msub> <\/mo>\u221d<\/mo> <\/mo>T<\/mi><\/msqrt><\/math>                            \u2235<\/mo>v<\/mi>rms<\/mi><\/msub>=<\/mo>3<\/mn>R<\/mi>T<\/mi><\/mrow>M<\/mi><\/mfrac><\/msqrt><\/mrow><\/mfenced><\/math><\/p>

For two different cases,<\/p>

\u21d2<\/mo><\/math>             v<\/mi>rms<\/mi><\/msub><\/mfenced>1<\/mn><\/msub>v<\/mi>rms<\/mi><\/msub><\/mfenced>2<\/mn><\/msub><\/mfrac>=<\/mo>T<\/mi>1<\/mn><\/msub>T<\/mi>2<\/mn><\/msub><\/mfrac><\/msqrt>\u21d2<\/mo>200<\/mn>v<\/mi>rms<\/mi><\/msub><\/mfenced>2<\/mn><\/msub><\/mfrac>=<\/mo>300<\/mn>400<\/mn><\/mfrac><\/msqrt>=<\/mo>3<\/mn>4<\/mn><\/mfrac><\/msqrt><\/math><\/p>

\u21d2<\/mo><\/math>             v<\/mi>rms <\/mtext><\/msub><\/mfenced>2<\/mn><\/msub>=<\/mo>2<\/mn>3<\/mn><\/msqrt><\/mfrac>\u00d7<\/mo>200<\/mn>=<\/mo>400<\/mn>3<\/mn><\/msqrt><\/mfrac> <\/mo>ms<\/mi><\/mrow>-<\/mo>1<\/mn><\/mrow><\/msup><\/math><\/p>","subject":""},"yoast_head":"\nThe molecules of a given mass of a gas have rms velocity of\u00a0200\u00a0ms-1\u00a0at 27\u00b0C and\u00a010\u00a0\u00d7\u00a0105\u00a0Nm-2\u00a0pressure. When the temperature and pressure of the gas are respectively, 127\u00b0C and\u00a00.05\u00a0\u00d7\u00a0105\u00a0Nm-2, the rms velocity of its molecules (in\u00a0ms-1) is\u00a0 - Infinity Learn by Sri Chaitanya<\/title>\n<meta name=\"description\" content=\"The molecules of a given mass of a gas have rms velocity of\u00a0200\u00a0ms-1\u00a0at 27\u00b0C and\u00a010\u00a0\u00d7\u00a0105\u00a0Nm-2\u00a0pressure. When the temperature and pressure of the gas are respectively, 127\u00b0C and\u00a00.05\u00a0\u00d7\u00a0105\u00a0Nm-2, the rms velocity of its molecules (in\u00a0ms-1) is\u00a0\" \/>\n<meta name=\"robots\" content=\"index, follow, max-snippet:-1, max-image-preview:large, max-video-preview:-1\" \/>\n<link rel=\"canonical\" href=\"https:\/\/infinitylearn.com\/surge\/question\/physics\/the-molecules-of-a-given-mass-of-a-gas-have-rms-velocity-of\/\" \/>\n<meta property=\"og:locale\" content=\"en_US\" \/>\n<meta property=\"og:type\" content=\"article\" \/>\n<meta property=\"og:title\" content=\"The molecules of a given mass of a gas have rms velocity of\u00a0200\u00a0ms-1\u00a0at 27\u00b0C and\u00a010\u00a0\u00d7\u00a0105\u00a0Nm-2\u00a0pressure. 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