question_answer

The specific heats, \[{{C}_{P}}\] and \[{{C}_{V}}\] of a gas of diatomic molecules, A, are given (in units of \[J\,mo{{l}^{-1}}{{K}^{-1}}\]) by 29 and 22, respectively. Another gas of diatomic molecules, B, has the corresponding values 30 and 21. If they are treated as ideal gases, then :- [JEE Main 9-4-2019 Afternoon]

A) A has one vibrational mode and B has two

B) Both A and B have a vibrational mode each

C) A is rigid but B has a vibrational mode

D) A has a vibrational mode but B has none

Correct Answer: D

Solution :

For A \[R={{C}_{p}}-{{C}_{\text{v}}}=7\] \[{{C}_{\text{v}}}=\frac{fR}{2}=22\Rightarrow f=\frac{44}{7}=6.3\] For B \[R={{C}_{p}}-{{C}_{\text{v}}}=9\] \[{{C}_{\text{v}}}=\frac{fR}{2}=21\Rightarrow f=\frac{42}{9}\]