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JEE Main202228 Jul 2022Morning ShiftPhysicsKinetic Theory of GasesActual

Given below are two statements: Statement I : The average momentum of a molecule in a sample of an ideal gas depends on temperature. Statement II : The rms speed of oxygen molecules in a gas is v . If the temperature is doubled and the oxygen molecules dissociate into oxygen atoms, the rms speed will become 2 v . In the light of the above statements, choose the correct answer from the options given below :

Options

  1. ABoth Statement I and Statement II are true
  2. BBoth Statement I and Statement II are false
  3. CStatement I is true but Statement II is false
  4. DStatement I is false but Statement II is true

Correct answer

D. Statement I is false but Statement II is true

Step-by-step solution

Momentum is a vector quantity and average momentum of molecules of a sample is zero due to random motion. P avg   = 0 RMS speed of a molecule is given by v rms = 3 R T M Now the temperature is doubled T new   = 2 T and due to dissociation M new = M 2 . ⇒ v new   v = 2 T M 2 T M ⇒ v new = 2 v

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