The specific heats, `C_(P)` and `C_(V)` of a gas of diatomic molecules, A are given (in units of `Jmol^(-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 :

Options

A. A has one vibrational degree of freedom and B has two vibrational degrees of freedom
B. A has one vibrational degree of freedom and B has zero vibrational degree of freedom
C. A and B both have one vibrational degree of freedom
D. A and B both have two vibrational degrees of freedom

Answer

B

Explanation

If f is the degree of freedom of a gas molecule, then
`(C _(P))/( C _(V)) = ((f +2 )/(f))`
`(( C _(P))/( C _(V)) ) _(A) = (29)/(22) = (( f _(A)+ 2)/( f _(A)))`
`implies f _(A) = 6`
`((C _(P))/( C _(V))) = (30)/(21) = ((f _(A) + 2)/( f _(A)))`
`implies f _(B) = 5 `
So A has one vibrational degree of freedom and B has none