Question 7

The ratio of specific heats $$\frac{C_p}{C_v}$$ in terms of degree of freedom $$f$$ is given by :

For an ideal gas, the molar specific heats are related to the degree of freedom $$f$$ as follows:

$$C_v = \frac{f}{2}R$$

$$C_p = C_v + R = \frac{f}{2}R + R = \left(\frac{f}{2} + 1\right)R$$

The ratio of specific heats is:

$$\gamma = \frac{C_p}{C_v} = \frac{\frac{f}{2}R + R}{\frac{f}{2}R} = \frac{\frac{f}{2} + 1}{\frac{f}{2}} = 1 + \frac{2}{f}$$

Hence, the correct answer is Option B.

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