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