Four cylinders contain equal number of moles of argon, hydrogen, nitrogen and carbon dioxide at the same temperature. The energy is minimum in

According to the law of equipartition of energy, the Kinetic energy associated with each degree of freedom of a molecule is kT/2,

KE=

where k is Boltzmann constant,

T is absolute temperature.

f is the number of degrees of freedom

The number of degrees of freedom of a system is the minimum number of coordinates required to completely describe its position and orientation.

Now argon,

which is a monoatomic gas, can only translate along the x, y and z axes.

Hence, it has 3 degrees of freedom. Now, for a system,

total associated energy is:

Total energy of all the degrees of freedom,

Where

E = total energy,

f = number of degrees of freedom

k = Boltzmann constant = 1.38 x 10^{-23}m^{2} kg s^{-2} K^{-1}

T = absolute temperature (Kelvin)

For argon, f = 3. Therefore, which is minimum.

Options (b) and (c) are incorrect since they are diatomic and

have more than 3 degrees of freedom(translational and rotational degrees of freedom of 2 molecules).

Option (d) is incorrect since carbon dioxide is triatomic and has

more than 3 degrees of freedom(translational and rotational degrees of freedom of 3 molecules).

Hence, the correct answer is option (a).

1