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JEE Main20205 Sep 2020Evening ShiftPhysicsKinetic Theory of GasesActual

Nitrogen gas is at 300 ° C temperature. The temperature (in K ) at which the rms speed of a H 2 molecule would be equal to the rms speed of a nitrogen molecule, is … … … . (Molar mass of N 2 gas 28 g ).

Correct answer

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Step-by-step solution

Given, Temperature of Nitrogen gas is T 1 = 300   ° C = 300 + 273 = 573   K Molar mass of H 2 gas is M H 2 = 2   g Molar mass of N 2 gas is M N 2 = 28   g The rms speed of gas is given by V rms = 3 RT M Now rms speed of hydrogen gas is equal to rms speed of nitrogen gas, i.e.; V r m s H 2 = V r m s N 2 ⇒ T H 2 T N 2 = M H 2 M N 2 Substitute the given values i above equation, we get, T H 2 = 2 28 × 573 T H 2 = 41   K

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