Metals as thermal conductors — assessing the explanation Assertion (A): Metals are better heat conductors than electrical insulators. Reason (R): If dT/dx is the temperature gradient, Q is heat-flux density, and K is thermal conductivity, then Q = − K (dT/dx).

Introduction / Context:
Metals typically have higher thermal conductivity than insulating solids. The assertion addresses this empirical fact, while the reason quotes Fourier’s law of heat conduction, a constitutive relation linking heat flux to temperature gradient. The key is whether stating Fourier’s law explains why metals conduct heat better than insulators.

Given Data / Assumptions:

• Fourier’s law holds in steady, linear conduction regimes: Q = −K dT/dx.
• Metals have mobile conduction electrons; insulators transport heat mainly via phonons.
• K is a material property that depends on carriers and scattering.

Concept / Approach:
The assertion is true because free electrons in metals carry heat efficiently, and electron contribution substantially increases K. The reason, Fourier’s law, is also true—but it does not explain the difference in K between metals and insulators; it merely defines how heat flux relates to gradient once K is known. The explanation of “why” resides in microscopic transport theory (electron vs phonon contributions), not in Fourier’s macroscopic law itself.

Step-by-Step Solution:
Accept A: metals generally exhibit higher K due to electron heat transport.Accept R: Q = −K dT/dx is valid for linear conduction.Assess explanatory power: the equation alone does not justify “metals are better”; it does not state why K is larger for metals.Therefore, both statements are true, but R does not correctly explain A.

Verification / Alternative check:
The Wiedemann–Franz law links electrical and thermal conductivity in metals, reinforcing that electron transport underlies high K in metals, an explanation absent from Fourier’s law.

Why Other Options Are Wrong:
Claiming R explains A confuses definition with mechanism; claiming either statement false contradicts well-established physics.

Common Pitfalls:
Mixing up constitutive relations with microscopic causes; overlooking that K varies widely across materials.

Final Answer:
Both A and R are true but R is not correct explanation of A