question_answer

                The degrees of freedom of a molecule of a diatomic gas are:                                                     

A)                 2      

B)                 4                             

C)                 6             

D)                 8

Correct Answer: C

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