Key Factors Affecting Thermal Conductivity in Metals
Conductivity of Metals
Conduction is an important concept in Physics. It is one of the three concepts by which heat and energy can be transferred from one place to the other within a material or from one material to another. Conduction occurs by direct contact whereas Convection occurs by movement or flow of heat. Radiation on the other hand occurs with the help of electromagnetic waves. Conduction mostly occurs in metals and the conductivity of metals is different from one another. When it comes to the best metal for thermal conductivity, ideally it is Silver but Copper is used instead. The reason for it is that Silver is too expensive and is infeasible to use. Copper, on the other hand, is available in abundance, is affordable, and can be used in any application.
Law of Conduction
A list containing the conductivity of various metals is used to compare and accordingly use metal for a specific purpose. Calculating the thermal conductivity of the metal rod was one of the initial and important experiments that were carried out to measure the conductivity of metals.
The law of conduction or the Fourier’s law states that the time required for heat transfer through metal is proportional to the negative gradient in the area and temperature. This law is applicable in two forms; differential form and integral form.
Various calculations can be made to measure the transfer of heat. Heat flux for instance is the amount of heat flow that occurs per unit area. Similarly, the opposite of thermal conductivity, which is thermal resistivity, can also be calculated.
Thermal resistivity is the ability of a material to not conduct heat. This property is present in materials that do not conduct heat. They are used as insulators. Some of them are rubber, fabric, cork, ceramic, styrofoam, etc.
Heat transfer is bound to occur when two materials of different temperatures come in contact with each other. Thermal insulation is done to minimize the heat that is transferred from one material to the other. This process also depends on the product density and the specific heat capacity of the insulating material used.
Thermal Conductivity of Metals: Uses
Based on their rate of conduction, metals are classified and used for particular applications. If a metal has high thermal conductivity, then it is used in heat sink applications. On the other hand, if the metal has low thermal conductivity, then it is used in thermal insulation applications.
Insulation acts against heat transfer whereas heat sink favors it. If you consider some metals like steel and copper then, the thermal conductivity of steel and copper is 45 W/m-K i.e. 45 Watts per meter-Kelvin and 385 W/m-K i.e. 385 Watts per meter-Kelvin respectively.
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Solved Example
Question 1: Consider a window of width 1.3m and height 1.7m, having a thickness of 6.3mm and a thermal conductivity value of 0.28 W/m/degree C. The temperature inside the house is 22 degrees Celsius and that outside the house -5 degrees Celsius. Calculate the rate of heat transfer.
Answer: Surface Area of the window = length x breadth
= (1.3 x 1.7) meter square
= 2.21 meter square
The thickness of the window = 6.3 mm
= 0.0063 m
Rate of heat transfer = (Thermal conductivity) x (Surface area) x (Difference of the temperatures) / (Thickness of the window)
= (0.28 W/m/degree C) x (2.21 meter square) x (22-(-5) degrees C) / (0.0063 m)
~ 2652 W
The rate of heat transfer for the given example is 2652 W.
Fun Fact
Did you know that besides metals, gases can be conductors of heat too? Yes, that’s right. In the entire periodic table, metals and gases are the two categories of elements that can conduct heat. Most of the metals and some other elements are conductors of electricity as well. Gases, however, do not conduct electricity.
Even though they can conduct heat, their rate of conductivity is much less than the rate of conductivity of metals. Due to this, gases are instead used as insulators. Thermal insulation or resistivity is the property of not being able to conduct heat.
Materials such as rubber, wood, plastic, glass, etc. are used as insulators. They work opposite to the thermal conductivity of metals.
FAQs on Thermal Conductivity of Metals Explained
1. What is meant by the thermal conductivity of a metal?
The thermal conductivity of a metal is an intrinsic property that measures its ability to conduct or transfer heat. It is formally defined as the quantity of heat that flows per unit time through a unit area of the metal with a unit temperature gradient perpendicular to that area. In simple terms, it indicates how quickly heat can travel through a material. Metals like silver and copper have high thermal conductivity, meaning they are excellent heat conductors.
2. Why are metals generally good thermal conductors?
Metals are excellent thermal conductors primarily due to the presence of free-moving (delocalised) electrons. When a metal is heated, these electrons gain kinetic energy and move rapidly through the metallic lattice structure. They collide with other electrons and ions, efficiently transferring thermal energy from the hotter part to the colder part. This electron-based heat transfer is much faster than the vibrational (phonon) transfer found in non-metals, giving metals their characteristic high conductivity.
3. What formula is used to calculate heat transfer through a metal conductor?
The rate of heat transfer (H) through a metal conductor is calculated using Fourier's Law of Heat Conduction. The formula is: H = -kA(dT/dx), where:
- H is the rate of heat flow (in Watts).
- k is the coefficient of thermal conductivity of the metal.
- A is the cross-sectional area through which heat is flowing.
- dT/dx is the temperature gradient, which is the change in temperature over the change in distance.
4. Which metals have the highest thermal conductivity and why are they used?
Silver has the highest thermal conductivity among all metals (approx. 429 W/mK), followed closely by copper (approx. 401 W/mK) and gold (approx. 317 W/mK). While silver is the best conductor, its high cost limits its use. Therefore, copper is widely used in applications requiring excellent heat transfer, such as:
- Electrical wiring (to dissipate heat generated by resistance)
- Heat sinks for electronic components like CPUs
- Cooking utensils and cookware
- Automobile radiators
5. How does an increase in temperature affect the thermal conductivity of metals?
For pure metals, the thermal conductivity generally decreases as temperature increases. This might seem counterintuitive. The reason is that at higher temperatures, the metal ions (the lattice) vibrate more vigorously. These increased vibrations cause more frequent collisions with the free electrons that carry the heat, effectively scattering them and impeding their flow. This increased resistance to electron movement leads to a reduction in the overall thermal conductivity.
6. What are some practical applications of metals with high thermal conductivity?
The high thermal conductivity of metals is exploited in numerous applications where efficient heat transfer is crucial. Key examples include:
- Cooking Pans: Metals like aluminium and copper are used to ensure heat from the stove is spread quickly and evenly across the bottom of the pan for uniform cooking.
- Heat Sinks: In computers and other electronics, heat sinks made of aluminium or copper are attached to processors to draw away waste heat and prevent overheating.
- Car Radiators: These use metal fins to quickly transfer heat from the hot engine coolant to the surrounding air.
- Heat Exchangers: Used in industrial processes and HVAC systems to efficiently transfer heat from one fluid to another.
7. What is the difference between thermal conductivity and electrical conductivity in metals?
Both thermal and electrical conductivity in metals are high because they both rely on the movement of free electrons. However, they measure different phenomena:
- Thermal Conductivity measures the ability to transfer heat energy. It involves the transfer of kinetic energy by electrons and lattice vibrations (phonons).
- Electrical Conductivity measures the ability to transport electric charge. It involves the flow of electrons under the influence of an electric field.
8. What is the SI unit and dimensional formula for the coefficient of thermal conductivity (k)?
The coefficient of thermal conductivity (k) is a key parameter in thermal physics. Its units and dimensions are:
- SI Unit: The standard SI unit for thermal conductivity is Watts per meter-Kelvin, written as W/(m·K) or Wm-1K-1.
- Dimensional Formula: The dimensional formula for 'k' is derived from the heat conduction formula. It is [MLT-3θ-1], where M represents Mass, L represents Length, T represents Time, and θ represents Temperature.
