Thermal Conductivity: Definition, Equation & Calculation

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  • 0:03 Background on Thermal…
  • 1:36 Thermal Conductivity…
  • 2:40 Thermal Conductivity…
  • 4:27 Lesson Summary
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Lesson Transcript
Instructor: Michael Blosser

Michael has a Masters in Physics and a Masters in International Development. He has over 5 years of teaching experience, teaching Physics, Math, and English classes.

This lesson explores and defines thermal conductivity, its equation, and how it differs depending on the material. It also gives examples of how to calculate thermal conductivity.

Background on Thermal Conduction

Have you ever wondered why metals get so hot in the sun, while rubber doesn't feel as hot? Or, why wood in the desert feels cool to the touch in spite of being out under the blazing sun? These examples are due to the different thermal conductivity that each material has and will be explored in this lesson.

Thermal conduction is defined as the transfer of heat within an object or between two objects that are in contact. To put it into more scientific terms, it is the transfer of energy in the form of heat due to a difference in temperature within a material or between materials. Each material (gas or solid) has the capacity to create or conduct heat. This is called the thermal conductivity of a material and it is different depending on the material. For example, the thermal conductivity of iron is vastly different than the thermal conductivity of helium.

Also, scientists have discovered that heat always flows from a higher temperature to a lower temperature. There is an equation that explains this transfer of heat between materials or within a material. This equation is called Fourier's Law for heat conduction, or the thermal conduction equation. This is what it looks like:

Thermal Conduction Equation

  • Q represents the transfer of heat in time t
  • k represents the coefficient of thermal conductivity of the material
  • A is the area through which the heat is flowing
  • ΔT is the difference in temperature between the materials or within the material
  • d is the thickness of the material

Thermal Conductivity Coefficient

A key part of Fourier's heat conduction equation is the coefficient of thermal conductivity, or k, of the material. The coefficient of thermal conductivity of a material is calculated using the same equation, moving variables around until we isolate k on one side. This gives us the coefficient of thermal conductivity equation:

Coefficient of Thermal Conductivity

The same variables represent the same things from the previous equation. Using units of Joules/seconds or Watts for the variables Q/t, the units of meters2 for the variable of A, the units of meters in the variable of d, and the units of Kelvin for the variable ΔT gives us a coefficient of thermal conductivity k of a material in Watts per meter-Kelvin (W/m⋅K).

As mentioned before, each material has a different coefficient of conductivity. Materials that conduct heat well, such as metals and stones, have high coefficients of conductivity, while materials that don't conduct heat well, such as wood and water, have low coefficients of conductivity.

Thermal Conductivity Calculations

Let's use the equations we have learned to work two examples. In one example, we will calculate the transfer of heat flow of an object (thermal conduction) and in the other, we will calculate the coefficient of thermal conductivity of a material.

Example 1

A house wall has an area of 2 m2 and a thickness of 0.5 m with a temperature difference going from 293 Kelvin inside the house to 301 Kelvin outside the house. The wall material has a coefficient of thermal conductivity of 0.5 W per meter-Kelvin (W/m⋅K). What is the thermal conduction (heat transfer) through the wall material per second?

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