The specific heats, Cp and Cv 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 :-

Question

The specific heats, Cp and Cv 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 :- (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

Tardigrade Admin · Accepted Answer

For A R=Cp-Cv=7 Cv=(f R/2)=22 ⇒ f=(44/7)=6.3

For B R=Cp-Cv=9 Cv=(f R/2)=21 ⇒ f=(42/9)

Q. The specific heats, $C_{p}$ and $C_{v}$ of a gas of diatomic molecules, A are given (in units of $J m o l^{- 1} K^{- 1}$ ) 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 :-

A has one vibrational mode and B has two

Both A and B have a vibrational mode each

A is rigid but B has a vibrational mode

A has a vibrational mode but B has none

For $A$
$R = C_{p} - C_{v} = 7$
$C_{v} = \frac{f R}{2} = 22$
$\Rightarrow f = \frac{44}{7} = 6.3$

For $B$
$R = C_{p} - C_{v} = 9$
$C_{v} = \frac{f R}{2} = 21$
$\Rightarrow f = \frac{42}{9}$ $

Q. The specific heats, Cp​ and Cv​ of a gas of diatomic molecules, A are given (in units of Jmol−1K−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 :-