Question
A non-linear triatomic gas is filled inside a vessel. If $$'\alpha '$$ fraction of moles dissociate into individual atoms, then average degree of freedom for the mixture is : (neglect vibrational degrees of freedom)
A.
$$\frac{{3\alpha + 6}}{{\alpha + 1}}$$
B.
$$\frac{{\alpha + 6}}{{2\alpha + 1}}$$
C.
$$\frac{{3\alpha + 6}}{{\alpha + 2}}$$
D.
$$\frac{{3\alpha + 6}}{{2\alpha + 1}}$$
Answer :
$$\frac{{3\alpha + 6}}{{2\alpha + 1}}$$
Solution :
$${f_{\max }} = \frac{{\left( {n\alpha } \right)\left( 3 \right)\left( 3 \right) + \left( {n - n\alpha } \right)\left( 6 \right)}}{{\left( {n\alpha } \right)\left( 3 \right) + \left( {n - n\alpha } \right)}} = \frac{{3\alpha + 6}}{{2\alpha + 1}}$$