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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,
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.
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,
E = total energy,
f = number of degrees of freedom
k = Boltzmann constant = 1.38 x 10-23m2 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).