is the specific heat ratio of monoatomic gas A having 3 translational degrees of freedom. 
is the specific heat ratio of polyatomic gas B having 3 translational, 3 rotational degrees of freedom and 1 vibrational mode. If 
, then the value of n is ____ .
Text Solution
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(3)
To determine the value of 
, we start by considering the specific heat ratios for gases 
and B.
For gas A, which is monoatomic with 3 translational degrees of freedom:
The degrees of freedom, 
, is 3 .
Therefore, 
.
For gas B , which is polyatomic with 3 translational, 3 rotational degrees of freedom, and 1 vibrational mode:
The total degrees of freedom, 
, is 
(since one vibrational mode contributes 2 degrees of freedom: 1 kinetic +1 potential).
Therefore, 
.
Now, the relation given is:
Substitute the values of 
and 
:
Equating to the given form:
Thus, we have:
Solving for 
:
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