Question

Which of the following statement is correct?

• A. Thermal conductivity of gases decreases with temperature
• B. In good conductors, thermal conductivity increases with temperature
• C. In insulators, thermal conductivity decreases with temperature
• D. Liquids (water) have higher thermal conductivity than metals and alloys

Hint:

Metals conduct heat mainly via electrons, so their thermal behavior differs strongly from gases and insulators.

Answer 1

The Correct Option is B

Concept: Thermal conductivity ($k$) depends on the mechanism of heat transfer in a material: - In metals: heat is mainly conducted by free electrons - In gases: heat is transferred by molecular collisions - In insulators: heat transfer is mainly by lattice vibrations (phonons) Thus, temperature dependence of thermal conductivity differs for each class of materials.

Step 1: Analyze gases (Option A).
For gases, as temperature increases: - Molecular velocity increases - Collision frequency increases Hence thermal conductivity: \[ k \propto \sqrt{T} \] So it actually increases, not decreases. Thus (A) is incorrect.

Step 2: Analyze metals (Option B).
In metals: - Heat conduction is dominated by free electrons - As temperature increases, electron energy increases - Overall thermal conductivity shows increasing trend in many engineering materials (especially good conductors at moderate range) Hence (B) is considered correct in standard engineering approximation.

Step 3: Analyze insulators (Option C).
In insulators: - Heat transfer is by lattice vibrations - With increasing temperature, scattering increases - So thermal conductivity generally decreases after a point Thus (C) is partially true but not the best universal statement here.

Step 4: Analyze liquids (Option D).
Metals have: \[ k \approx 50 - 400 \, W/mK \] Water has: \[ k \approx 0.6 \, W/mK \] So metals $\gg$ liquids. Hence (D) is false. Final Answer: \[ \boxed{\text{(B)}} \]