Question

A vessel contains a mixture of hydrogen and helium at same temperature in the ratio 1 : 5. The ratio of the average translational kinetic energies of hydrogen and helium molecules will be :
1. 1 : 5
2. 5 : 1
3. 1 : 1
4. 1 : 10

Answer 1

Correct Answer - Option 3 : 1 : 1

The correct answer is option 3) i.e. 1 : 1

CONCEPT:

• The kinetic energy of gas: There are no attractive forces between the gas molecules of an ideal gas, and there is no rotation or vibration within these molecules.
  • The kinetic energy due to the translational motion of an ideal gas is dependent on its temperature. 

The average kinetic energy per molecule of a gas is given by:

\(KE = \frac{3}{2}k_B T\)

​Where T is the temperature of the gas in Kelvin and kB is the Boltzmann's constant (1.38 × 10-23 J/K)

EXPLANATION:

We know, \(KE = \frac{3}{2}k_B T\)

• Therefore, the kinetic energy of a gas is independent of the mass and is dependent only on the temperature.

Hence, Hydrogen and Helium will have the same translational kinetic energy at the same temperature with a ratio 1: 1