The Weidemann Franz law is one of the most fundamental and elementary laws of physics. It is related to thermal conductivity. This theory was first postulated by two physicists, Rudolph Franz and Gustav Wiedmann.
What is the Wiedmann Franz Law?
Rudolph Franz and Gustav Wiedmann discovered that both, thermal conductivity (k) and electrical conductivity (σ) have the same value at the same temperature for two types of metals.
Here Thermal Conductivity (k) refers to the degree and measures the capacity of the metal to conduct heat.
Electrical conductivity (σ) refers to the degree and measure of the capacity of the material to conduct electricity.
The Wiedman-Franz Law model
This law state that the ratio between the electronic contribution of thermal conductivity and electrical conductivity of a metal is equal to its temperature.
k/σ = LT
Now, where L is the constant of proportionality. It is also known as the Lorenz number.
L=k/σT= 2.44 x 10-8 WΩK-2
The relationship between electrical conductivity and thermal conductivity is majorly based on heat as well as electrical movement. This involves electrons that can move freely in the metal.
This law is based on the important fact that heat, as well as electric transportation majorly, involve the electrons that can move freely in the metal. This law also gives evidence that with the increase the particle velocity, the conductivity of the electricity decreases, and the thermal conductivity increase with that of average particle velocity.
SI unit of thermal conductivity
The SI unit of thermal conductivity is W/m/k.
Wiedemann Franz Law and thermal conductivity
In thermal conductivity, heat transfer mainly happens with the help of conduction. Here the transmission of energy happens in a material without any movement of the material. The amount of the transfer of heat majorly establishes the thermal conductivity as well as the temperature of the material.
When the net energy transfer is from high to low temperature, the direction of the heat transfer will be reversed to the temperature gradient in the interim. The perpendicular surfaces next to a heat source will have the largest value of the heat transmission direction.
Factors Affecting Wiedemann Franz Law
The following are some of the factors that affect the Wiedemann Franz Law:
- Type of Element
The Wiedemann Franz law majorly holds true for metals. So if we analyze it from a periodic table point of view, the Wiedemann Franz law decreases with a decrease in the metallic character.
- Number of Valence Electrons
It is electrons that are majorly the energy carriers. So when thermal as well as electrical conductivity increase, there is an increase in the valence electrons.
- Temperature
Essentially, a temperature rise reduces the electrical conductivity as well as the thermal conductivity. This is not the case with aluminium, where the thermal conductivity essentially increases with the increase in temperature.
Temperature dependence of Wiedemann Franz Law
The value of L is 2.44 x 10-8 WΩK-2 majorly comes from the fact that at very low temperatures, the heat, as well as the charge currents, are essentially carried by electrons.
At a finite temperature, two mechanisms essentially produce the deviation L=k/σT. Now the temperature tends to go to 0K, where the inelastic scattering essentially becomes weak and promotes large scattering values.
For each electron, a thermal change is carried out, and the Lorenz number reaches L0. It is important to note that at a certain finite temperature. Small scattering values are possible. These can be transported without thermal change. Moreover, at a higher temperature, the contribution of the scattering to the thermal transport system becomes important.
Difference between electrical conductivity and thermal conductivity
Essentially electrical conductivity originates from the motion of electrons under the impact of pressure. This is known as voltage. A component’s conductance is determined by multiplying its area by its length and then dividing the result by its conductivity.
The electrons within the material shift from a higher potential to a lower potential when it conducts electricity. The amount of current produced for every unit of voltage difference is another way to describe a component’s conductance. Electrical conductivity is the quality of the material. Conductance is a property of the item.
Thermal conductivity essentially originates from the transmission of kinetic energy. It is majorly termed heat, under the effect of pressure, The most important law behind thermal conductivity is the heat flow equation. This equation states that the rate of heat flow through a given object is proportional to the area of a cross-section of the object and the temperature gradient.
In a mathematical form, this can be written as dH/DT = kA(∆T)/l, where k is the thermal conductivity, A is the cross area, ∆T is the temperature difference between the two ends, and l is the length of the object. ∆T/l can be termed a temperature gradient.
Mathematical examples of Wiedemann Franz Law
The thermal conductivity of a particular material is 4.00 W/m/K, and the electrical conductivity of the material is stated by 6.32 x 107m-1 at a temperature of 200K. Find the Lorentz number of the material.
Given
Thermal Conductivity = 400 W/m/K
Electrical Conductivity = 6.32 x 107m-1
According to the law
k/σ = LT
L= 200 X 6.32 X 107/400
L= 3.16 X 107 WΩK-2
Limitations of Wiedemann Franz Law
The following are some of the limitations of the Wiedemann Franz law:
- The experimentations have shown that the value of L through a constant is not identical for all types of metals.
- The scientist Rosenberg says that the Wiedemann and Franz law states that the law is majorly functional for very high or very low temperatures. It may not hold in-between temperatures.
- It is seen that in the case of high-purity metals, both the thermal as well as electrical conductivities essentially increase as the temperature declines.
- In certain materials like silver as well as aluminium, the value of the constant L may fall with that of temperature.
Summing up
Hopefully, now you have understood everything about the Wiedemann Franz law, its model, derivations as well as limitations.
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