A mixture of two gasses A and B is kept in a vessel which is maintained at a temperature T . In the vessel there are N molecules each of mass m , of the gas A and 2 N molecules each of mass 2 m of the gas B . The mean square velocity of the

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A mixture of two gasses A and B is kept in a vessel which is maintained at a temperature T . In the vessel there are N molecules each of mass m , of the gas A and 2 N molecules each of mass 2 m of the gas B . The mean square velocity of the molecules of the gas B is v 2 and the mean square velocity of the molecules of the gas A along the x direction is w 2 . The value of w 2 v 2 is

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Correct answer: D. 2 3

Mean kinetic energy of the two types of molecules should be equal. The mean square velocity of A type molecules = ω 2 + ω 2 + ω 2 = 3 ω 2 Therefore, 1 2 m 3 ω 2 = 1 2 2 m v 2 This gives ω 2 v 2 = 2 3

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