The specific heats , C_{p} and  C_{v} of a gas of diatomic molecules ,A, are given ( in units of J\:mol^{-1} ) by 29 and 22 , respectively . Another gas of diatomic molecules , B , has the corresponding value 30 and 21 . If they are treated as ideal gases , then :

  • Option 1)

    A is rigid but B has a vibrational mode.

  • Option 2)

    a has a vibrational mode but B has none.

  • Option 3)

    A has one vibrational mode and B has two.

  • Option 4)

    Both A and B have a vibrational mode each.

 

Answers (1)

\frac{C_{p}}{C_{v}}=1+\frac{2}{f}

For gas A ,

\frac{29}{22}=1+\frac{2}{f}\Rightarrow\frac{2}{f}=\frac{7}{22}

\Rightarrow f=\frac{44}{7}\simeq 6

\frac{C_{p}}{C_{v}}=\frac{30}{21}=1+\frac{2}{f} \Rightarrow \frac{2}{f}=\frac{9}{21}

\Rightarrow f=\frac{42}{9} \simeq 5


Option 1)

A is rigid but B has a vibrational mode.

Option 2)

a has a vibrational mode but B has none.

Option 3)

A has one vibrational mode and B has two.

Option 4)

Both A and B have a vibrational mode each.

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