Where K and σ are thermal and electrical conductivities in a solid, according to Wiedemann-Franz law
Understanding the Wiedemann-Franz Law
The Wiedemann-Franz law describes the relationship between the thermal conductivity and electrical conductivity of a metal. It states that the ratio of the thermal conductivity (K) to the electrical conductivity (\(\sigma\)) is directly proportional to the absolute temperature (T) of the material.
Mathematically, the Wiedemann-Franz law can be expressed as:
\( \frac{K}{\sigma} \propto T \)
This proportionality can also be written with a constant of proportionality, often denoted as L, which is known as the Lorentz number:
\( \frac{K}{\sigma T} = L \)
Here:
- K is the thermal conductivity of the solid.
- \(\sigma\) is the electrical conductivity of the solid.
- T is the absolute temperature of the solid (in Kelvin).
- L is the Lorentz number, which is approximately constant for many metals, especially at high temperatures. The theoretical value of the Lorentz number, based on the free electron model, is given by \( L = \frac{\pi^2 k_B^2}{3e^2} \), where \( k_B \) is the Boltzmann constant and \( e \) is the elementary charge.
The Wiedemann-Franz law highlights that materials which are good conductors of electricity are also generally good conductors of heat, and vice versa. This is because both thermal and electrical transport in metals are primarily due to the movement of free electrons.
Analyzing the Options Based on Wiedemann-Franz Law
We need to find the option that correctly represents the Wiedemann-Franz law \( \frac{K}{\sigma T} = \text{constant} \).
- Option 1: \( \frac{{KT}}{\sigma } = {\rm{constant}} \) - This implies \( \frac{K}{\sigma} \propto \frac{1}{T} \), which is not the Wiedemann-Franz law.
- Option 2: \( \frac{{K\sigma}}{T } = {\rm{constant}} \) - This implies \( K\sigma \propto T \), which is not the Wiedemann-Franz law.
- Option 3: \( \frac{{\sigma}}{KT } = {\rm{constant}} \) - This implies \( \frac{KT}{\sigma} = \text{constant'} \), which is the reciprocal of Option 1 and thus not the Wiedemann-Franz law.
- Option 4: \( \frac{{K}}{\sigma T } = {\rm{constant}} \) - This directly matches the mathematical expression for the Wiedemann-Franz law.
Therefore, the relationship \( \frac{{K}}{\sigma T } = {\rm{constant}} \) accurately describes the Wiedemann-Franz law.
Important Questions from Fourier Law and Thermal Conductivity
Unit of thermal conductivity is:
Which of the following correctly represents the SI unit of thermal conductivity?
Which of the following substances has the minimum value of thermal conductivity ?
- When an analogy is drawn between heat flow and electricity flow in circuits, the heat flow of thermal circuits is equated in the electrical circuit against
- The rate of flow of heat through a simple homogeneous solid is directly proportional to the area of the section at right angles to the direction of heat flow, and _______.
