The specific heats,
Question:

The specific heats, $\mathrm{C}_{p}$ and $\mathrm{C}_{v}$ of a gas of diatomic molecules, $\mathrm{A}$, are given (in units of $\mathrm{J} \mathrm{mol}^{-1} \mathrm{k}^{-1}$ ) 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:

  1. (1) A is rigid but B has a vibrational mode.

  2. (2) A has a vibrational mode but B has none.

  3. (3) A has one vibrational mode and B has two.

  4. (4) Both A and B have a vibrational mode each.


Correct Option: , 2

Solution:

(2) $\gamma_{A}=\frac{C_{P}}{C_{v}}=\frac{29}{22}=1.32<1.4$ (diatomic)

and $\gamma_{B}=\frac{30}{21}=\frac{10}{7}=1.43>1.4$

Gas A has more than 5 -degrees of freedom.

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