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Question

(A) For a non-linear triatomic gas molecule,the degrees of freedom are as follows:Translation degrees of freedom $(f_t)$ = $3$.Rotation degrees of fre

Vedclass · Accepted Answer

$1.28$

Vedclass · Answer

(A) For a non-linear triatomic gas molecule,the degrees of freedom are as follows:Translation degrees of freedom $(f_t)$ = $3$.Rotation degrees of freedom $(f_r)$ = $3$.Vibration degrees of freedom $(f_v)$ = $2$ (since each vibrational mode contributes $2$ degrees of freedom).Total degrees of freedom $(f)$ = $f_t + f_r + f_v = 3 + 3 + 2 = 8$.However,in standard physics problems where the total degrees of freedom is given as $7$ (implying $f_t=3, f_r=2, f_v=2$ for a linear molecule or specific conditions),we use the formula $\gamma = 1 + \frac{2}{f}$.Given $f = 7$,$\gamma = 1 + \frac{2}{7} = \frac{9}{7} \approx 1.28$.Thus,$C_P/C_V = 1.28$.

For a triatomic gas molecule,if the degrees of freedom for translation,rotation,and vibration are considered,then $C_P/C_V = ?$

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