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Q.

A non-linear triatomic gas is 50% dissociates into individual atoms. Ignoring, the vibrational degree of freedom and any further dissociation , the gas behaves as if the number of degree of freedom is

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a

4.75

b

3.25

c

4.25

d

3.75

answer is B.

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Detailed Solution

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$n_{mix} = n_{1} + n_{2} \to (i)$
Let n_o be the initial number of atoms dissociated $n_{1} = 3 n_{o} / 2$
Not dissociated $n_{2} = n_{o} / 2$
$\begin{array}{l} n_{mix} = n_{1} + n_{2} = 2 n_{o} \\ f_{mix} = \frac{n_{1} f_{1} + {nf}_{2}}{n_{mix}} \\ = 3 .75 \\ f_{mix} = \frac{\frac{3}{2} n_{o} \times 3 + \frac{n_{o}}{2} \times 6}{2 n_{o}} \end{array}$

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