Thermal Conductivity - Learn

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