Thermal Conductivity


Different materials have different conducting properties. Thermal conductivity measures the rate at which thermal energy can flow through a substance. It is dependent on the type of substance, the cross-sectional area and the thickness of the substance as well as the temperature difference across the object/s.  The unit of thermal conductivity is Wm-1K-1.

Calculations involving thermal conductivity:

\cfrac { Q }{ t } =\cfrac { kA\Delta T }{ d }

where:

\cfrac { Q }{ t } is the rate of heat energy transferred (Js-1) and (W)

k is the thermal conductivity of the material (Wm-1K-1)

A is the surface area perpendicular to the heat flow (m2)

\Delta T is the temperature difference across the material (°C or K)

d is the thickness of the material through which the heat is being transferred (m)


Thermal conductivities of some common materials:

  • silver = 420 Wm-1K-1
  • copper = 386 Wm-1K-1
  • gold = 315Wm-1K-1
  • aluminium = 204 Wm-1K-1
  • concrete = 1 Wm-1K-1
  • water = 0.6 Wm-1K-1
  • wood = 0.15 Wm-1K-1
  • air = 0.025 Wm-1K-1

Example 1:

a) What is the rate that energy is transferred through a 70cm long piece of copper with a cross-sectional area of 0.15m2 with one end at 20°C and the other end at 55°C?

b) how much energy is transferred in 250 seconds?

Answer:

a) k = 386Wm-1K-1

A = 0.15m2

\Delta T = 55 − 20 = 35°C

d = 70cm = 0.7m

using: \cfrac { Q }{ t } =\cfrac { kA\Delta T }{ d }

\cfrac { Q }{ t } =\cfrac { 386\times 0.15\times 35 }{ 0.7 }

\cfrac { Q }{ t } =\;2895 Js-1

b) Q=\; 2895\times 250

Q=\; 723750 J

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