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