The Physics
Hypertextbook
Opus in profectus

# Conduction

## Discussion

Heat conduction (as opposed to electrical conduction) is the flow of internal energy from a region of higher temperature to one of lower temperature by the interaction of the adjacent particles (atoms, molecules, ions, electrons, etc.) in the intervening space.

Note: it's the rate (P or Φ) at which heat is transferred, not the amount (Q) of heat transferred.

 P = ∆Q ∆t

 P = dQ dt

 ⎡⎢⎣ W = J ⎤⎥⎦ s

Factors affecting the rate of heat transfer by conduction.

1. temperature difference
2. length
3. cross-sectional area
4. material
 P = kA∆T ℓ

Fourier's law (compare to Ohm's law).

 φ = P = ∆Q = − k ∇T A A ∆t

Conductivities vary for material being greatest for metallic solids, lower for nonmetallic solids, very low for liquids, and extremely low for gases. The best ordinary metallic conductors are (in decreasing order) silver, copper, gold, aluminum, beryllium, and tungsten. Diamond beats them all, and graphite beats diamond only if the heat can be forced to conduct in a direction parallel to the crystal layers. The material with the greatest thermal conductivity is a superfluid form of liquid helium called helium II, which only exists at temperatures below 2.17 K. Since it's highly unlikely you will encounter this substance, it's not worth thinking about except in the fact that it is an exceptional material.

Thermal conductivity for selected materials (~300 K except where otherwise indicated)
material k (W/m K) material k (W/m K)
air, sea level 0.025   neoprene 0.15–0.45
air, 10,000 m 0.020   nickel 90.7
aluminum 237   particle board 0.15
asbestos 0.05–0.15   paper 0.04–0.09
asphalt 0.15–0.52   plaster 0.15–0.27
brass (273 K) 120   platinum 71.6
brick 0.18   plutonium 6.74
bronze (273 K) 110   plywood 0.11
carbon, diamond 895   polyester 0.05
carbon, graphite (∥) 1950   polystyrene foam 0.03–0.05
carbon, graphite (⊥) 5.7   polyurethane foam 0.02–0.03
carpet 0.03–0.08   sand 0.27
chromium 93.7   silica aerogel 0.026
concrete 0.05–1.50   silver 429
copper 401   soap powder 0.11
cotton 0.04   snow (< 273 K) 0.16
feathers 0.034   steel, plain (273 K) 45–65
fiberglas 0.035   steel, stainless (273 K) 14
freon 12, liquid 0.0743   straw 0.05
freon 12, vapor 0.00958   teflon 0.25
felt 0.06   tin 66.6
glass 1.1–1.2   titanium 21.9
gold 317   tungsten 174
granite 2.2   uranium 27.6
helium gas 0.152   vacuum 0
helium I (< 4.2 K) 0.0307   water, ice (223 K) 2.8
helium II (< 2.2 K) ~100,000?   water, ice (273 K) 2.2
ice cream powder 0.05   water, liquid (273 K) 0.561
iron 80.2   water, liquid (373 K) 0.679
lead 35.3   water, vapor (273 K) 0.016
limestone 1   water, vapor (373 K) 0.025
marble 1.75   wood 0.09–0.14
mercury 8.34   wool 0.03–0.04
mica 0.26   zinc 116
mylar 0.0001?   zirconia 0.056?

Thoughts on conductivity…

• The preferred utensil for candy making is the wooden spoon. Metal utensils conduct heat away and interfere with controlled crystallization.
• Why are toilet seats cold even if the air in the bathroom isn't?
• Why do some Inuit peoples build shelters (igloos) out of snow? Isn't snow cold?

Related quantities: r value.

 P = kA∆T ℓ
 ∆Q = kA ∆T ∆t ℓ

Comparison.

 I = 1 V R
 R = ℓ kA

The clo. Studies of clothing have lead to the definition of the unit of clothing, which corresponds to the insulating value of clothing needed to maintain a subject in comfort sitting at rest in a room at 21 °C (70 °F) with air movement of 0.1 m/s and humidity less than 50%. One clo of insulation is equivalent to a lightweight business suit. Half of the planet would probably disagree with the relevance of this unit.

Newton's law of cooling Q/t ∝ ∆T. Heat leaks faster from a cool house than a warm house. Thus, it's more cost effective to turn your air conditioner off when you're away, than to leave it on hoping to keep your house cool.