If a gas has f degrees of freedom, the ratio $C_{p} / C_{v}$ of the gas is

\frac{1 + f}{2}

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1 + \frac{f}{2}

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\frac{1}{2} + f

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1 + \frac{2}{f}

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Solution

The correct option is D $1 + \frac{2}{f}$
We know that $C_{v} = n o . o f d e g r e e s o f f r e e d o m \times m o l a r g a s c o n s t a n t / 2$
$o r C_{v} = f R / 2. A l s o C_{P} - C_{v} = R$
Therefore
$\frac{C_{p}}{C_{v}} = \frac{R}{C_{v}} + 1 = \frac{2 R}{f R} + 1 = \frac{2}{f} + 1$
Hence, the correct choice is (d).

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