Temperature dependence of orientation polarization in polyatomic gases If μp denotes the permanent dipole moment (in coulomb–metre) and T is the absolute temperature, how does the orientation polarization of a dilute polyatomic gas vary with μp and T (qualitative proportionality)?

Introduction / Context:In polar gases, an external electric field tends to align permanent molecular dipoles. Thermal agitation randomizes orientations. The resulting “orientation polarization” is a key contribution to the dielectric constant of gases and many liquids at low frequencies. Understanding its temperature and dipole-moment dependence is fundamental in dielectrics.

Given Data / Assumptions:

• Dilute gas of non-interacting polar molecules with permanent dipole μp.
• Low fields such that linear response (Langevin–Debye approximation) applies.
• Absolute temperature T.

Concept / Approach:

From Debye theory, the mean alignment of dipoles in a weak field gives an orientation polarization term: Porient ≈ N μp^2 E / (3 k T), where N is number density, k is Boltzmann’s constant, and E is field strength. Thus, at fixed E and N, the polarization varies directly with μp^2 and inversely with T. Physically, larger permanent dipoles align more readily; higher temperature increases randomizing thermal energy, reducing net alignment.

Step-by-Step Solution:

Verification / Alternative check:

Measured dielectric constants of polar gases and liquids typically decrease with rising temperature at low frequencies, consistent with the 1/T dependence of the orientation contribution.

Why Other Options Are Wrong:

• μp^2 * T or μp * T: predict increase with T, opposite to physical behavior.
• Independent of temperature: contradicts theory and experiment for polar media.
• 1/(μp^2 T): incorrectly inverts μp dependence.

Common Pitfalls:

Confusing permanent dipole orientation with electronic polarization (which is nearly temperature independent); forgetting that only the orientation term carries the strong 1/T dependence.

Final Answer:

Proportional to μp^2 / T