question_answer

The degrees of freedom of a molecule of a tridiatomic gas are:                     [AIPMT 1999]

A)  2   

B)                               4        

C)  6        

D)                   None of these

Correct Answer: D

Solution :

Key Idea: A diatomic molecule can rotate about any of three co-ordinate axes.

The molecule of a triatomic gas has a tendency of rotating about any of three co-ordinate axes. So it has 6 degrees of freedom, 3 translational and 3 rotational. At high enough temperature a triatomic molecule has 2 vibrational degrees of freedom.

But as temperature requirement is not given, so we answer simply by assuming triatomic gas molecule at room temperature.

Thus,    \[f=6\]

(3 translational + 3 rotational) at room temperature.

Alternative:

For non linear triatomic gas, \[N=3\] and restrictions k are also 3.

\[\therefore \]    \[f=3N-k\]

\[=3\times 3-3=6\]

For linear triatomic gas \[k=2\]

\[\therefore \]    \[f=3\times 3-2=7\]