First slide

Specific heat and degrees of freedom

Question

Consider two ideal diatomic gases A and B at some temperature T. Molecules of the gas A are rigid, and have a mass m. Molecular of the gas B has an additional vibrational mode, and have a mass $\frac{m}{4}$ . The ratio of the specific heats ( $C_{V}^{A}$ and $C_{V}^{B}$ ) of gas A and B , respectively is :

Moderate

A

5:9
B

5:7
C

3:5
D

7:9

Solution

For Gas A (diatomic), degree of freedom (f) = 3+2 = 5
For Gas B (diatomic + vibration), degree of freedom (f) = 3+2 +2= 7
$I n g e n e r a l, f o r a n y g a s S p e c i f i c h e a t a t c o n s \tan t v o l u m e C_{V} = \frac{f R}{2}$
Specific heat at constant volume of $A = \frac{5}{2} R T$
Specific heat at constant volume of $B = \frac{7}{2} R T$
$∴ R a t i o = \frac{5}{7}$

Get Instant Solutions

When in doubt download our app. Now available Google Play Store- Doubts App

Recieve an sms with download link

Doubts App

OR

SCAN ME

Doubts App

Doubts App