JEE MainPhysicsKinetic Theory of Gases
A closed container holds a mixture of Helium (a monatomic gas) and Oxygen (a diatomic gas) in thermal equilibrium. Which of the following statements is correct regarding the properties of the two gases?
Options
- AThe average total kinetic energy per molecule is the same for both gases.
- BThe root mean square speed of the molecules is the same for both gases.
- CThe average translational kinetic energy per unit mass is the same for both gases.
- DThe average translational kinetic energy per molecule is the same for both gases.
Correct answer
D. The average translational kinetic energy per molecule is the same for both gases.
Step-by-step solution
In thermal equilibrium, both gases in the mixture are at the same temperature T . The average translational kinetic energy per molecule for any gas depends only on its absolute temperature and is given by 3 2 k_BT . Since both gases are at the same temperature, their average translational kinetic energies per molecule are identical. The average total kinetic energy per molecule depends on the degrees of freedom ( f ), given by f 2 k_BT . Helium is monatomic ( f=3 ) and Oxygen is diatomic ( f=5 ), so their total kin