JEE MainPhysicsKinetic Theory of Gases
Two separate vessels contain Helium (molar mass 4 g mol ⁻¹ ) and Neon (molar mass 20 g mol ⁻¹ ) respectively. The first vessel contains a mass m of Helium at pressure P and volume V . The second vessel contains a mass 2m of Neon at pressure 2P and volume V 2 . The ratio of the average translational kinetic energy per molecule of Helium to that of Neon is:
Options
- A2:5
- B1:1
- C2:1
- D5:2
Correct answer
A. 2:5
Step-by-step solution
The average translational kinetic energy per molecule of a gas is directly proportional to its absolute temperature T , since K = 3 2 k_BT . From the ideal gas equation, PV = nRT = m M RT , the temperature can be expressed as T = PVM mR . For Helium in the first vessel: T₁ = P V 4 m R = 4PV mR For Neon in the second vessel: T₂ = (2P) ( V 2 ) 20 (2m) R = PV 20 2mR = 10PV mR The ratio of the average translational kinetic energy per molecule of Helium to that of Neon is equal to the ratio of their temperatures: K₁ K₂