Coefficient of thermal conductivity measures the ability of a substance to transport heat. Wood and plastic are low conductivity materials that insulate and prevent heat movement, whereas metals and other high conductivity materials swiftly absorb and spread heat. Materials with high thermal conductivity transfer heat efficiently and are good conductors of heat, while materials with low thermal conductivity transfer heat slowly and are considered poor conductors or insulators. This helps in choosing materials for various purposes.
In this article, we will learn in detail about the coefficient of thermal conductivity, its units, factors affecting it, and other facts related to it.
What is Coefficient of Thermal Conductivity?
Coefficient of thermal conductivity is the measurement of a the ability of a substance to conduct heat. It represents the rate at which heat flows through a unit area of a material with a unit temperature gradient. Materials with a high coefficient of thermal conductivity are conductors, while those with a low coefficient of thermal conductivity are insulators or poor conductors of heat.
Thermal Conductivity
The capacity of a substance to transport heat is referred to as thermal conductivity. For example, wood conducts heat less effectively than metals because of its less structured atomic structure, while metals transmit heat well because of their densely packed atoms and free electrons. On a stove, a plastic container takes longer to heat than a metal pot. Choosing materials for specialized uses, such as insulation or cooking, is made easier with an understanding of heat conductivity.
Unit of Coefficient of Thermal Conductivity
The SI unit of measurement for thermal conductivity is watts per meter-kelvin (W/mK), i.e., Wm-1K-1. It is represented by the symbol k.
This unit indicates the quantity of heat energy (measured in watts) that may per unit temperature differential (measured in kelvin) over a material having a thickness of one meter
The other unit of measurement for coefficient of thermal conductivity is watts per meter per degree Celsius (W/m°C)
- The unit of measurement for heat energy is "watts". It is comparable to calculating the power output of a heater.
- Like a ruler, a "meter" is a unit of length. Here, it's employed to determine a material's thickness.
- The temperature is measured in "degree Celsius". It indicates the difference in temperature between the two sides of the substance.
The below table consists of metals and their respective thermal conductivity.
Metal | Thermal Conductivity(W/moC) |
|---|
Copper | 401 |
|---|
Aluminum | 237 |
|---|
Silver | 429 |
|---|
Gold | 317 |
|---|
Iron | 80 |
|---|
Fourier's Law of Heat Conduction
Fourier's Law of Heat Conduction is a formula that is essential to comprehending the flow of heat through materials according to their temperature gradient and thermal conductivity.
When a material has a known thermal conductivity (k), temperature differential (ΔT), and surface area (A) and thickness (d), the formula to determine the rate of heat transfer (Q) through it is:
Q = -\frac{k \cdot A \cdot \Delta T}{d}
Where:
- Q is the rate of heat transfer (in watts),
- k is the thermal conductivity of the material (in watts per meter-kelvin, W/mK),
- A is the cross-sectional area through which heat flows (in square meters),
- ΔT is the temperature difference across the material (in kelvin),
- d is the thickness of the material (in meters).
NOTE: The negative sign indicates that heat flows from regions of higher temperature to regions of lower temperature.
We know that coefficient of thermal conductivity quantifies the ability to conduct heat from one point other. The formula of coefficient of thermal conductivity is given as
k = \frac{Q}{A \cdot \Delta T \cdot t}
where,
- Q is the amount of heat transferred through the material (in watts),
- A is the cross-sectional area through which the heat flows (in square meters),
- ?T is the temperature difference across the material (in degrees Celsius or Kelvin), and
- t is the time over which the heat transfer occurs (in seconds).
Factors Affecting Thermal Conductivity
Following factors affect the thermal conductivity of a material:
Material Composition
Different materials have varying heat-conduction properties. Heat energy may be easily transferred and carried by electrons in metals such as aluminum and copper, which makes them good heat conductors. Plastics and ceramics, on the other hand, have a lower heat conductivity because they contain less free electrons.
Crystal Structure
Thermal conductivity is dependent on the configuration of atoms in a material's crystal lattice. Better in conducting heat than materials with more disordered structures are those with highly ordered structures, like graphite or diamond.
Density
Thermal conductivity is influenced by a material's density, or how closely its atoms are packed. Denser materials are often more thermally conductive because they have more atoms accessible for heat transmission.
Temperature
Different materials respond differently to temperature in terms of thermal conductivity. Some people experience a gain in thermal conductivity with temperature, whereas others experience a fall. These differences might be caused by modifications in the crystal structure or atomic vibrations.
Pressure
When pressure is applied, a material's electrical or crystal structure may change, which may have an impact on the material's thermal conductivity. Pressure has the ability to either enhance or reduce heat conductivity, depending on the substance.
Moisture Content
A material's heat conductivity can be affected by impurities or moisture. Adding water to a material can enhance its total thermal conductivity because, in comparison to other liquids, water has a comparatively high thermal conductivity.
Applications of Coefficient of Thermal Conductivity
There are many uses for the coefficient of thermal conductivity in a variety of sectors and domains, such as:
Electronics: To avoid overheating and guarantee peak performance, effective thermal management is crucial in electronic devices like computer processors and integrated circuits. When creating heat sinks, thermal interface materials, and other cooling solutions to disperse heat produced by electronic components, coefficient of thermal conductivity is essential.
Construction: Thermal conductivity is an important factor to consider when selecting building materials and insulation systems. Low thermal conductivity materials are used to insulate floors, walls, and roofs, which lowers the amount of energy needed to heat and cool buildings. Examples of these materials include fiberglass, foam boards, and aerogels.
Automotive: Thermal conductivity is important for exhaust systems, thermal barriers, and engine cooling systems in the automotive industry. To maximize engine performance and fuel efficiency, heat exchangers, radiators, and thermal insulators are made to resist or transfer heat effectively.
Manufacturing: A number of manufacturing processes, including heat treatment, welding, and metalworking, depend on thermal conductivity. A thorough understanding of a material's thermal characteristics aids in process parameter optimization, heat distribution control, and the avoidance of thermal distortion or damage to manufactured components.
Energy Systems: Heat exchanger, boiler, and pipeline performance and efficiency are all impacted by thermal conductivity in energy generation and distribution systems. Heat transfer equipment uses materials with high thermal conductivity, like copper and aluminum, to improve energy transfer rates.
Medical Equipment: Thermal conductivity is important for medical equipment, such as systems for diagnostic imaging, thermal ablation, and cryotherapy. Medical treatments and procedures can be controlled by the use of materials with particular thermal properties.
Practice Problems on Coefficient of Thermal Conductivity
Try out the following practice problems on coefficient of thermal conductivity:
Q1. A 0.5-meter-long copper rod with a 400 W/mK thermal conductivity conduct heat from a source at 100°C to a sink at 50°C. Determine the heat transfer rate via the rod.
Q2. A wall has a 0.2 W/mK thermal conductivity and is 0.3 meters thick. Determine the rate of heat transmission through the wall if there is a 20°C temperature differential across it.
Q3. An insulated pipe with an outside diameter of 10 cm and an inner diameter of 8 cm is used to transmit hot water at 80°C across a room at 20°C. The insulation around the pipe is 2 centimeters thick and has a thermal conductivity of 0.05 W/mK. Calculate the rate at which heat escapes through the insulation.
Q4. A ceramic plate measuring 0.4 meters by 0.4 meters and having a thermal conductivity of 1.5 W/mK is heated to 200°C on one side and held at 50°C on the other. Determine the heat transmission rate via the plate.
Q5. In a room that is 25°C, there is a refrigerator that has an internal temperature of -5°C. The refrigerator's walls are 5 cm thick and have a thermal conductivity of 0.5 W/mK. Find out how quickly heat moves through the refrigerator's walls.