Question

Rotational degrees
of freedom
​

Answer 1

degree of freedom is defined as the number of independent ways through which a system can exchange energy.

Degree of freedom are of three types

1) translational

2) rotational

3)vibrational

note :- vibrational DOF is not considered to be active at low temperatures.

1) for monoatomic gas example:- He

-> translational degree of freedom is = 3

(note:- translational motion means straight line motion)

becoz the monoatomic gas contains one atom that can move in the three axis x , y, z independently

-> rotational degree of freedom is zero becoz see rotation is always performed about an external axis

for example the Earth rotates around the sun and it spins about its own axis .

In case of monoatomic gas the atom can't perform rotation about an axis becoz if it performs then the rotation will depend on the other axis

if the atom rotates about the y axis then it's co-ordinates through which it will pass during the rotation will depend on the x- coordinate and z-coordinate

2) for diatomic gas example:- CO

-> translational degree of freedom is 3

-> rotational degree of freedom is 2

total degree of freedom is 5

3) triatomic gas linear gas example:- CO2

-> translational degree of freedom is 3

-> rotational degree of freedom is 2

4) triatomic non linear gas example:- SO2

-> translational degree of freedom is 3

-> rotational degree of freedom is 3

5) polyatomic gas example:- CH4

-> translational degree of freedom= 3

-> rotational degree of freedom is 3

now to calculate vibrational degree of freedom the formula used is

vibrational degree of freedom = 3N - (translational degree of freedom + rotational degree of freedom)

N = atomicity i.e. no of atoms present in the gas