Question

The thermal conductivity is minimum for

• A. Copper
• B. Water
• C. Silver
• D. Air

Hint:

Thermal Conductivity Phases Rule: - General trend: \(k_{\text{solids}} \gt k_{\text{liquids}} \gt k_{\text{gases}}\). - Silver holds the highest thermal conductivity among common metals. - Gases (like air) have minimal thermal conductivity and are often used for insulation.

Answer 1

The Correct Option is D

Concept: Thermal conductivity (\(k\)) is an intrinsic physical property of a material that measures its ability to conduct heat. The rate of heat transfer via conduction is governed by Fourier's Law: \[ q = -k \cdot A \cdot \frac{dT}{dx} \] The mechanism of thermal conduction depends heavily on the physical state of matter:

• Solids (Metals): Conduction is highly efficient, driven by the movement of free electrons and lattice vibrations (phonons).

• Liquids: Conduction occurs via continuous collisions between closely packed molecules, providing moderate heat transfer efficiency.

• Gases: Molecules are spaced far apart. Conduction relies entirely on random molecular collisions, making gases poor conductors of heat.

Step 1: Comparing the thermal conductivity values of the given options.
Let us look at typical thermal conductivity values (\(k\)) at standard temperature and pressure (\(25^\circ\text{C}\), \(1\,\text{atm}\)) to compare the materials:

• Silver (\(k \approx 429\,\text{W/m}\cdot\text{K}\)): A noble metal with excellent electrical and thermal conductivity due to its high density of free electrons.

• Copper (\(k \approx 401\,\text{W/m}\cdot\text{K}\)): A metal with very high thermal conductivity, widely used in industrial heat exchangers and electrical wiring.

• Water (\(k \approx 0.6\,\text{W/m}\cdot\text{K}\)): A non-metallic liquid with moderate thermal conductivity compared to metals.

• Air (\(k \approx 0.026\,\text{W/m}\cdot\text{K}\)): A gas with widely spaced molecules, resulting in very low thermal conductivity.

Step 2: Identifying the minimum value.
Comparing these values shows that air has a thermal conductivity that is orders of magnitude lower than the liquid and metallic solid options: \[ k_{\text{air}} \lt k_{\text{water}} \ll k_{\text{copper}} \lt k_{\text{silver}} \] Because of its exceptionally low thermal conductivity, stagnant air acts as an effective thermal insulator. This confirms Option (D) as the correct choice.