Thermal Conductivity

Have you ever wondered why a teaspoon dipped in a hot drink is instantaneously warm to the touch while a burning match can be held in your fingers until it almost burns out completely? While playing with fire is never a good idea, it seems counterintuitive for your afternoon tea to burn you before the actual fire would. Turns out, the ability of the spoon and the matchstick to transfer heat from their source is the main reason behind this. This property is known as the thermal conductivity of a material. As you can imagine, quantifying this property for different materials allows us to control heat transfer on varying occasions, ensuring that handles of hot things like pots and spoons remain cold while metal radiators stay as hot as possible. In this article, we'll look at thermal conductivity, its properties, and applications.

Get started

Millions of flashcards designed to help you ace your studies

Sign up for free
  • + Add tag
  • Immunology
  • Cell Biology
  • Mo

Why are metals such good thermal conductors?

Show Answer
  • + Add tag
  • Immunology
  • Cell Biology
  • Mo

What are the best heat conductors?

Show Answer
  • + Add tag
  • Immunology
  • Cell Biology
  • Mo

Which of the following scenarios involves heat transfer with high thermal conductivity? 

Show Answer
  • + Add tag
  • Immunology
  • Cell Biology
  • Mo

One end of an insulated metal rod is held at \(100\,\mathrm{C^{\circ}}\), while the other end is placed in an ice bath keeping its temperature \(0\,\mathrm{C^{\circ}}\). It takes \(15\,\mathrm{min}\) for \(6880 \, \mathrm{J}\) of energy to get transferred from one end of the rod to the other. Determine the type of metal this rod is made of, if it's \(50 \, \mathrm{cm}\) long, and has a cross-sectional area equal to \(0.5 \, \mathrm{cm}\).

Show Answer
  • + Add tag
  • Immunology
  • Cell Biology
  • Mo

When does heat conduction occur?

Show Answer
  • + Add tag
  • Immunology
  • Cell Biology
  • Mo

Which state of matter usually has the lowest thermal conductivity? 

Show Answer
  • + Add tag
  • Immunology
  • Cell Biology
  • Mo

What is the equation used to calculate thermal conductivity? 

Show Answer
  • + Add tag
  • Immunology
  • Cell Biology
  • Mo

Thermal conductivity is is the transfer of heat from an object with a higher temperature to that with a lower temperature, through direct contact. 

Show Answer
  • + Add tag
  • Immunology
  • Cell Biology
  • Mo

What happens to thermal conductivity if the cross-sectional area of the bodies increases four times?

Show Answer
  • + Add tag
  • Immunology
  • Cell Biology
  • Mo

What happens to thermal conductivity if thermal conduction increases twice?

Show Answer
  • + Add tag
  • Immunology
  • Cell Biology
  • Mo

Thermal conductivity is usually determined experimentally. 

Show Answer
  • + Add tag
  • Immunology
  • Cell Biology
  • Mo

Why are metals such good thermal conductors?

Show Answer
  • + Add tag
  • Immunology
  • Cell Biology
  • Mo

What are the best heat conductors?

Show Answer
  • + Add tag
  • Immunology
  • Cell Biology
  • Mo

Which of the following scenarios involves heat transfer with high thermal conductivity? 

Show Answer
  • + Add tag
  • Immunology
  • Cell Biology
  • Mo

One end of an insulated metal rod is held at \(100\,\mathrm{C^{\circ}}\), while the other end is placed in an ice bath keeping its temperature \(0\,\mathrm{C^{\circ}}\). It takes \(15\,\mathrm{min}\) for \(6880 \, \mathrm{J}\) of energy to get transferred from one end of the rod to the other. Determine the type of metal this rod is made of, if it's \(50 \, \mathrm{cm}\) long, and has a cross-sectional area equal to \(0.5 \, \mathrm{cm}\).

Show Answer
  • + Add tag
  • Immunology
  • Cell Biology
  • Mo

When does heat conduction occur?

Show Answer
  • + Add tag
  • Immunology
  • Cell Biology
  • Mo

Which state of matter usually has the lowest thermal conductivity? 

Show Answer
  • + Add tag
  • Immunology
  • Cell Biology
  • Mo

What is the equation used to calculate thermal conductivity? 

Show Answer
  • + Add tag
  • Immunology
  • Cell Biology
  • Mo

Thermal conductivity is is the transfer of heat from an object with a higher temperature to that with a lower temperature, through direct contact. 

Show Answer
  • + Add tag
  • Immunology
  • Cell Biology
  • Mo

What happens to thermal conductivity if the cross-sectional area of the bodies increases four times?

Show Answer
  • + Add tag
  • Immunology
  • Cell Biology
  • Mo

What happens to thermal conductivity if thermal conduction increases twice?

Show Answer
  • + Add tag
  • Immunology
  • Cell Biology
  • Mo

Thermal conductivity is usually determined experimentally. 

Show Answer

Review generated flashcards

Sign up for free
You have reached the daily AI limit

Start learning or create your own AI flashcards

Contents
Contents

Jump to a key chapter

    Thermal Conductivity Definition

    Heat transfer occurs when heat moves from a hotter object to a colder one. Depending on the material these objects are made of, the rate of heat transfer will vary. This rate can be described using thermal conductivity.

    Thermal conductivity is the measure of a material’s ability to transfer thermal energy.

    It's a property of matter on an atomic scale. Not to be confused with thermal conduction, which is one of the three ways in which heat can be transferred.

    Thermal conduction is the transfer of heat from an object with a higher temperature to that with a lower temperature through direct contact.

    Thermal conduction and conductivity are intertwined concepts, as one relies on the other. If thermal conductivity is increased, the rate of heat transfer (conduction) will also increase, meaning they are directly proportional.

    Thermal Conductivity Formula

    Thermal conductivity is one of the parameters used to calculate the rate at which heat is transferred between two objects with different temperatures, as visualized in Figure 1 below.

    Mathematically, that can be expressed using the thermal conduction equation

    $$ \frac{Q}{\Delta t} = k\frac{A\Delta T}{L}$$

    where \(\frac{Q}{\Delta t}\) is the rate of heat transfer, \(A\) is the cross-sectional area, \(\Delta T\) is the temperature difference, \(L\) is the plane thickness, and \(k\) is the thermal conductivity of the material. By simply rearranging this equation, we can obtain the formula for thermal conductivity

    $$ k=\frac{Q}{\Delta t}\frac{L}{\Delta T A}$$

    which has the units of \(\frac{\mathrm{W}}{\mathrm{m} \, \mathrm{K}}\). In other words, thermal conductivity is the heat capacity that a material with a cross-sectional area of \(1\,\mathrm{m}^2\) can transmit at a distance of \(1 \, \mathrm{m}\), if a temperature difference of \(1\, \mathrm{K}\) has occurred in the material. The thermal conductivity of a specific material will vary with temperature and is usually determined experimentally.

    Thermal Conductivity Example Values

    Some commonly used materials and their thermal conductivity values, \(k,\) are compiled in the table below.

    Table 1 - Thermal conductivity values for metals, solids, and gases.

    Material\(k\) \( \left(\frac{\mathrm{W}}{\mathrm{m} \, \mathrm{K}}\right) \)
    Aluminum205.0
    Brass109.0
    Copper385.0
    Lead34.7
    Mercury8.3
    Silver406.0
    Steel50.2
    Concrete0.8
    Cork0.04
    Felt0.04
    Fiberglass0.04
    Glass0.8
    Ice1.6
    Rock wool0.04
    Styrofoam0.027
    Wood0.12 - 0.04
    Air0.024
    Argon0.016
    Helium0.14
    Hydrogen0.14
    Oxygen0.023

    High Thermal Conductivity Materials

    Being aware of the thermal conductivity of various materials is important in everyday life and construction. For instance, heat should be conducted well by the surfaces of heating radiators, which are usually made of steel or aluminum. Those are examples of high thermal conductivity materials.

    High thermal conductivity materials allow for heat to pass through them easily.

    The best heat conductors, just like electric current conductors, are metals. That is due to their atomic structure consisting of free electrons. As heat is supplied to a metal, the electrons vibrate more intensely and therefore energy gets passed through the material quickly.

    Despite diamonds having the highest thermal conductivity among all solid materials, they are great insulators.

    Heat pipes are devices that transfer heat at a very high efficiency. They are closed evaporator condenser systems, where a working fluid gets vacuum sealed in a metal shell. The fluid is the key component determining the thermal conductivity of a specific heat pipe. Depending on its purpose, the pipe can be filled with various liquids like water, ammonia, or sodium.

    Thermal Conductivity Heat pipes in a laptop StudySmarterFig. 2 - Heat pipes are used in laptops to divert the heat from the processing units and prevent the device from overheating.

    To put it in perspective, copper is a great thermal conductor with \( k=385 \, \frac{\mathrm{W}}{\mathrm{m} \, \mathrm{K}}\). Heat pipes, however, take it to the next level with thermal conductivity ranging from \(10 \,000 \) to \(100 \,000\, \frac{\mathrm{W}}{\mathrm{m} \, \mathrm{K}} \). They are commonly used in spacecraft, computers, and nuclear power cells as cooling systems.

    Low Thermal Conductivity Materials

    The opposite of high thermal conductivity materials is those with low thermal conductivity.

    Low thermal conductivity materials don't allow for heat to pass through them easily.

    These are especially important when we need thermal control and energy efficiency in manufacturing. For instance, during the winter, the walls, roof, and windows of a building must retain the heat in the rooms as much as possible and therefore conduct the heat as poorly as possible. That's why special microporous insulating materials and double-glazed windows are made because air (and all other gases) are poor heat conductors. Non-metals and many organic substances conduct heat much worse. The case of a burning match that we mentioned in the beginning, is a great example of a poor thermal conductor.

    Thermal Conductivity A burning match held by a hand StudySmarterFig. 3 - When a match is ignited, the person holding it won't burn their fingers from touching the wood, as it's a material with low thermal conductivity.

    Materials that have low thermal conductivity are great insulators. Wood, for instance, has many air pockets within its structure containing the heat rather than passing it on. Plastic, on the other hand, has low thermal conductivity due to the lack of free electrons, which are responsible for passing the heat in the case of metals. Other examples of low thermal conductivity materials are visible in Table 1, including concrete, glass, and gasses.

    Aerogel is the material with the lowest thermal conductivities among all solids \( \left (0.013 \, \frac{\mathrm{W}}{\mathrm{m} \, \mathrm{K}}\right ) \), which is even less than that of argon gas. It's a very fragile solid, mostly made up of air, and is used in laser experiments, thermal insulation, and even managing waste.

    Thermal Conductivity A hand holding a transparent gaseous block of aerogel StudySmarter Fig. 4 - Aerogel is the most effective thermal insulator ever made, with the lowest thermal conductivity among solids.

    Thermal Conductivity Examples

    Let's look at some examples of problems utilizing the concept of thermal conductivity.

    One end of an insulated metal rod is held at \(120\,\mathrm{C^{\circ}}\), while the other end is placed in an ice bath keeping its temperature \(0\,\mathrm{C^{\circ}}\). It takes half an hour for \(6810 \, \mathrm{J}\) of energy to get transferred from one end of the rod to the other, melting half the ice in the bath. Determine the type of metal this rod is made of, if it's \(80 \, \mathrm{cm}\) long, and has a diameter equal to \(0.5 \, \mathrm{cm}\).

    Solution

    We can use the heat transfer equation

    $$ \frac{Q}{\Delta t} = k\frac{A\Delta T}{L}$$

    to calculate the thermal conductivity \(k\) of the rod and therefore determine the material.

    A rod is shaped like a long cylinder, so its cross-sectional area will be a circle. Considering we are given the diameter \(D\), in SI units the area will then be

    \begin{align} A&=\pi r^2 \\ A&=\pi \left (\frac{D}{2} \right )^2 \\A&=\pi \left (\frac{0.005 \, \mathrm{m}}{2} \right )^2 \\ A&=2\times10^{-5} \, \mathrm{m}^2. \end{align}

    One end of the rod has a temperature of \(0\,\mathrm{C^{\circ}}\), so the temperature difference is simply equal to \(120\,\mathrm{C^{\circ}}\), which in kelvins is equal to

    $$ \Delta T = 120\,\mathrm{C^{\circ}} + 273 = 393 \, \mathrm{K}. $$

    Finally, we are told that the heat transfer occurs for \(30 \, \mathrm{min}\) which can be expressed in seconds as

    $$ \Delta t = 30 \, \cancel{\mathrm{min}} \cdot \frac{60 \, \mathrm{s}}{1 \, \cancel{\mathrm{min}}}= 1800\, \mathrm{s}.$$

    Now we simply plug in all the values into the rearranged heat transfer equation

    \begin{align} k&=\frac{Q}{\Delta t}\frac{L}{\Delta T A} \\ k&=\frac{(6810 \, \mathrm{J})}{(1800 \, \mathrm{s})}\frac{(0.8 \, \cancel{\mathrm{m}})}{(393 \, \mathrm{K})(2\times10^{-5} \, \mathrm{m}^\cancel{2})} \\ k&=385 \, \frac{\mathrm{W}}{\mathrm{m} \, \mathrm{K}}. \end{align}

    We can compare this result to the thermal conductivity values compiled in Table 1 above and conclude that this rod is likely made from copper.

    Thermal Conductivity - Key takeaways

    • Conduction is the transfer of heat from an object with a higher temperature to that with a lower temperature, through direct contact.
    • Thermal conductivity is the measure of a material’s ability to transfer thermal energy.
    • Mathematically, thermal conductivity can be found using the thermal conduction equation \[k=\frac{Q}{\Delta t}\frac{L}{\Delta T A}.\].
    • High thermal conductivity materials allow for heat to pass through them easily, metals being a common example.
    • Low thermal conductivity materials don't allow for heat to pass through them easily, for example, wood and plastic.


    References

    1. Fig. 1 - Thermal conduction diagram, StudySmarter Originals.
    2. Table 1 - Thermal conductivities, Young, Hugh D., University Physics with Modern Physics, 14th Ed., Addison-Wesley, Boston, 2015.
    3. Fig. 2 - Copper heat pipes (https://unsplash.com/photos/4D9PHPZ5U_c) by Vishnu Mohanan (https://unsplash.com/@vishnumaiea) on Unsplash is licensed by Unsplash License (https://unsplash.com/license).
    4. Fig. 3 - Burning match (https://commons.wikimedia.org/wiki/File:Burning_match.jpg) by Осадчая Екатерина licensed by CC BY-SA 4.0 (https://creativecommons.org/licenses/by-sa/4.0/deed.en).
    5. Fig. 4 - Aerogel hand (https://commons.wikimedia.org/wiki/File:Aerogel_hand.jpg) by Courtesy NASA/JPL-Caltech licensed by Public Domain.
    Frequently Asked Questions about Thermal Conductivity

    What is thermal conductivity?

    Thermal conductivity is the ability of a material to transfer heat.

    What are the types of materials that we can distinguish when studying thermal conductivity?

    When studying the thermal conductivity of materials, we can split them into three types: metals, non-metallic solids, and gases. 

    What is an example of a thermal conductor?

    Some examples of thermal conductors include metals which have high thermal conductivity, while gasses, wood, and plastic are examples of materials with low thermal conductivity. 

    What is the formula for calculating thermal conductivity?

    The formula for calculating thermal conductivity, k, of a material is k=(QL)/(ΔtΔTA). Where Q is the heat, L is the material thickness, A is its cross-sectional area, Δt the time period for the heat transfer, and ΔT the temperature difference.

    What is the importance of thermal conductivity?

    Thermal conductivity is important when considering factors like thermal control and energy efficiency in manufacturing and heating. 

    Save Article

    Test your knowledge with multiple choice flashcards

    Why are metals such good thermal conductors?

    What are the best heat conductors?

    Which of the following scenarios involves heat transfer with high thermal conductivity? 

    Next

    Discover learning materials with the free StudySmarter app

    Sign up for free
    1
    About StudySmarter

    StudySmarter is a globally recognized educational technology company, offering a holistic learning platform designed for students of all ages and educational levels. Our platform provides learning support for a wide range of subjects, including STEM, Social Sciences, and Languages and also helps students to successfully master various tests and exams worldwide, such as GCSE, A Level, SAT, ACT, Abitur, and more. We offer an extensive library of learning materials, including interactive flashcards, comprehensive textbook solutions, and detailed explanations. The cutting-edge technology and tools we provide help students create their own learning materials. StudySmarter’s content is not only expert-verified but also regularly updated to ensure accuracy and relevance.

    Learn more
    StudySmarter Editorial Team

    Team Physics Teachers

    • 9 minutes reading time
    • Checked by StudySmarter Editorial Team
    Save Explanation Save Explanation

    Study anywhere. Anytime.Across all devices.

    Sign-up for free

    Sign up to highlight and take notes. It’s 100% free.

    Join over 22 million students in learning with our StudySmarter App

    The first learning app that truly has everything you need to ace your exams in one place

    • Flashcards & Quizzes
    • AI Study Assistant
    • Study Planner
    • Mock-Exams
    • Smart Note-Taking
    Join over 22 million students in learning with our StudySmarter App
    Sign up with Email