JEE Main 2023 · 30 January · evening · Single correct · +4 / −1
A flask contains hydrogen and oxygen in the ratio of 2: 1 by mass at temperature 27° C. The ratio of average kinetic energy per molecule of hydrogen and oxygen respectively is:
- (a) 1 : 1
- (b) 4 : 1
- (c) 1 : 4
- (d) 2 : 1
Answer and solution
Answer (a) 1 : 1
Solution
Physics sir · 4 steps
Energy per molecule depends only on temperature and degrees of freedom, so the masses do not matter here.
- Equipartition. Each degree of freedom carries 1/2kT of energy on average. So the average kinetic energy of one molecule is f/2kT.
E̅_(molecule) = f/2kT
- Compare the gases. H₂ and O₂ are both diatomic, so f = 5 for each. Both are in the same flask at T = 300 K, so each molecule has 5/2kT.
- Ignore the masses. The 2 : 1 mass ratio changes how many molecules of each gas there are. It does not change the energy of a single molecule, because neither m nor M appears in f/2kT.
- So. The ratio is 5/2kT : 5/2kT, which is 1 : 1, option (a).
The idea to keep. Same temperature and same type of molecule means the same average kinetic energy per molecule, whatever the mass. Mass only changes the speed and the number of molecules.
Answer from the NTA final answer key. Solution by PrepWiser.