Quantrex Quantrex AcademyJEE · NEET · NDA PYQs with solutions Open app
JEE MainPhysicsKinetic Theory of Gases

Two different ideal gases, A and B , are kept in separate containers. The most probable speed of the molecules in gas A is equal to the root mean square speed of the molecules in gas B . If the average translational kinetic energy per molecule of gas A is twice that of gas B , then the ratio of the molar mass of gas A to that of gas B ( M_A M_B ) is

Options

  1. A3 4
  2. B4 3
  3. C2 3
  4. D2

Correct answer

B. 4 3

Step-by-step solution

The average translational kinetic energy per molecule of an ideal gas depends only on its absolute temperature T and is given by E = 3 2 kT . Given that E_A = 2E_B , we have: 3 2 kT_A = 2 ( 3 2 kT_B ) T_A = 2T_B The most probable speed of molecules in gas A is v_ mp,A = 2RT_A M_A . The root mean square speed of molecules in gas B is v_ rms,B = 3RT_B M_B . According to the given condition, v_ mp,A = v_ rms,B : 2RT_A M_A = 3RT_B M_B Squaring both sides: 2T_A M_A = 3T_B M_B Substitute T_A = 2T_B into the equation: 2(2

Practice Kinetic Theory of Gases on Quantrex Academy →

More from Kinetic Theory of Gases

If 2 mole of an ideal monoatomic gas at temperature T , is mixed with 6 mole of another ideal monoatomic gas at temperature 2T then the temperature of mixture is : 2026Given below are two statements: one is labelled as Assertion A and the other is labelled as Reason R Statement I: Change in internal energy of a system containing n mole of ideal g 2026Given below are two statements: one is labelled as Assertion A and the other is labelled as Reason R Assertion A: If the average kinetic energy of H₂ and O₂ molecules, kept in two 2026One gas of n₁ mole of molecules at temperature T₁ , volume V₁ , and pressure P₁ , and another gas of n₂ mole of molecules at temperature T₂ , volume V₂ , and pressure P₂ , are mixe 2026A mixture of carbon dioxide and oxygen has volume 8310 cm ^3 , temperature 300 K, pressure 100 kPa and mass 13.2 g. The number of moles of carbon dioxide and oxygen gases in the mi 2026The mean free path of a molecule of diameter 5 10⁻¹⁰ ~m at the temperature 41^ C and pressure 1.38 10⁵ ~Pa , is given as _ _ _ _ m. (Given k_ B =1.38 10⁻²³ ~J / K ). 2026A gas of certain mass filled in a closed cylinder at a pressure of 3.23 kPa has temperature 50^ C . The gas is now heated to double its temperature. The modified pressure is _ _ _ 2026Consider two boxes containing ideal gases A and B such that their temperatures, pressures and number densities are same. The molecular size of A is half of that of B and mass of mo 2026 Full Kinetic Theory of Gases list All JEE Main PYQs