AIPMT PRELIMS 2000 Physics Degrees of Freedom MCQ Question

In thermodynamics, the degree of freedom (f) of a gas is related to its specific heat ratio (γ). The correct expression for the degree of freedom is given by the formula: $f = \frac{2}{\gamma - 1}$. This formula arises from the relationship between the specific heat at constant volume (C_v) and the specific heat at constant pressure (C_p), where γ is defined as $\gamma = \frac{C_p}{C_v}$.

Let's analyze the other options:

• Option B: $f = \frac{\gamma + 1}{2}$ is incorrect because it does not align with the established relationship between f and γ.
• Option C: $f = \frac{2}{\gamma + 1}$ is also incorrect for the same reason.
• Option D: $f = \frac{1}{\gamma + 1}$ is not a correct representation of the degree of freedom either.

Thus, the correct answer is A, which accurately describes the relationship between degree of freedom and the specific heat ratio.