The specific heats, $C_{P}$ and $C_{V}$ of a gas of diatomic molecules, A, are given (in units of J $\mathrm{mol}^{-1} \mathrm{~K}^{-1}$) 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:-

(D) A has a vibrational mode but B has none

(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

JEE Main · 2019 · 09 Apr 2019 · Shift 2 · Heat & Thermodynamics

The specific heats,

C_{P}

and

C_{V}

of a gas of diatomic molecules, A, are given (in units of J

mol^{- 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:-

Answer: (D)

For an ideal gas the degrees of freedom follow from

C_{v} = \frac{f}{2} R

with

R \approx 8.3

J/mol K, and a rigid diatomic molecule has

f = 5

, giving

C_{v} \approx 20.8

. Gas A has

C_{v} = 22

, a little above the rigid value, which signals an additional vibrational mode beginning to contribute. Gas B has

C_{v} = 21

, essentially the rigid-diatomic figure, so no vibrational mode is active in it. Hence A carries a vibrational mode while B has none.

JEE Main · 2019 · 09 Apr 2019 · Shift 2 · Single correct option