Dielectrics and polarization: Using a plot derived from measurements (e.g., total polarization vs. 1/T), can the permanent dipole moment of molecules be obtained from the slope? Consider that for a polyatomic gas the total polarization is P = N(a_e + a_i + μ_p^2 / (3 k T)) * E.

Introduction / Context:
In dielectric materials, the total polarization of a gas or dilute medium can include three contributions: electronic polarization (a_e), ionic polarization (a_i), and orientation polarization caused by permanent molecular dipoles (μ_p). A standard way to extract μ_p from experimental data is to analyze how polarization varies with temperature, because the orientation term depends inversely on absolute temperature T.

Given Data / Assumptions:

• Total polarization of a polyatomic gas: P = N(a_e + a_i + μ_p^2 / (3 k T)) * E.
• N is the number density, k is Boltzmann constant, E is the applied electric field.
• The assertion mentions determining μ_p from a graph (commonly P/E vs. 1/T or dielectric constant vs. 1/T).

Concept / Approach:

The orientation polarization term equals N * (μ_p^2 / (3 k T)) * E, which is proportional to 1/T. Therefore, plotting P/E against 1/T (or equivalently the dielectric susceptibility χ against 1/T) yields a straight line whose slope is proportional to N * μ_p^2 / (3 k). From this slope, the permanent dipole moment μ_p can be calculated. The electronic and ionic terms are temperature independent and contribute to the intercept of the line, not the slope.

Step-by-Step Solution:

Verification / Alternative check:

Equivalently, the Clausius–Mossotti relation can be used to convert measured dielectric constant to molecular polarizability, and the temperature dependence again isolates μ_p via the 1/T behavior.

Why Other Options Are Wrong:

• If R were false, the slope–dipole connection would not hold; but R states the correct formula, which explains A.
• Saying A is false contradicts well-established orientation polarization theory.

Common Pitfalls:

• Not plotting against 1/T; plotting against T will not linearize the orientation term.
• Ignoring density N variations; number density should be known or controlled.

Final Answer:

Both A and R are true and R is correct explanation of A