Degrees Of Freedom

Counting degrees of freedom draws on the framework in NCERT Class 11, Chapter 13 (Kinetic Theory), where a degree of freedom is an independent way a molecule can store energy. A diatomic molecule, modelled as two atoms joined by a rigid bond, has three translational degrees of freedom corresponding to motion along the x, y and z axes. It additionally has two rotational degrees of freedom about the two axes perpendicular to the bond line, while rotation about the bond axis itself contributes negligibly. At ordinary room temperature vibrational modes are not excited, so they are excluded, giving a total of $3+2=5$ degrees of freedom. The option of three counts only translation, forgetting rotation. The option of six wrongly adds a third rotational mode about the bond axis. The option of seven adds vibrational modes that are frozen out at room temperature. The distinction matters because the total internal energy of the gas is built by giving each active degree of freedom its equal share of thermal energy under equipartition. A consistency check aligns with measured heat capacities: a diatomic gas has $C_V=\frac{5}{2}R$, exactly matching five degrees of freedom through the equipartition rule of $\frac{1}{2}R$ per degree per mole.