Relaxation time versus viscosity in polar liquids As the viscosity of a liquid increases, how does the dielectric relaxation time (characteristic time constant for dipole reorientation) change?

Introduction / Context:Dielectric relaxation time characterizes how fast dipoles in a polar liquid reorient to follow a changing electric field. Understanding its dependence on viscosity connects molecular kinetics to macroscopic dielectric behavior (Debye relaxation).

Given Data / Assumptions:

• Polar molecules experiencing rotational diffusion in a viscous medium.
• Low to moderate fields so that linear response applies.
• Temperature and molecular size held fixed while viscosity varies.

Concept / Approach:According to the Debye model, rotational relaxation time τ is proportional to the product of viscosity η and effective molecular volume V divided by thermal energy. A common form is τ ∝ η * a^3 / (k_B * T), where a is an effective molecular radius. As viscosity increases, rotational motion is hindered, so the time to reorient increases.

Step-by-Step Solution:Relate torque balance and rotational drag: higher η → larger rotational friction.Debye relation: τ = (4π * η * a^3) / (k_B * T) (proportionality shown).Thus, when η increases while T and a remain constant, τ increases proportionally.

Verification / Alternative check:Empirical dielectric spectroscopy shows that cooling (which raises viscosity) lengthens relaxation times dramatically, consistent with the theoretical dependence.

Why Other Options Are Wrong:“Remains constant” contradicts the friction dependence. “Decreases” is opposite to observed behavior. “First decreases then increases” lacks physical basis here. “Becomes zero” is impossible; higher viscosity slows dynamics but does not eliminate them entirely.

Common Pitfalls:

• Confusing translational diffusion with rotational reorientation; both slow with viscosity.
• Ignoring temperature effects which can mask the sole effect of viscosity in real systems.

Final Answer:Increases