Conductivity Ratio: Understanding Temperature Dependence

The ratio of thermal conductivity ($k$) to electrical conductivity ($\sigma$) is related to the physical properties of a material. This ratio, when multiplied by temperature ($T$), forms the Lorenz number ($L$):

$ L = \frac{k}{\sigma T} $

The Wiedemann-Franz law states that for metals, the Lorenz number ($L$) is approximately constant at high temperatures. However, a more detailed analysis shows that $L$ is fundamentally dependent on temperature ($T$), especially at lower temperatures.

Key Dependency Analysis

• Temperature: The ratio of thermal and electrical conductivities (Lorenz number) is primarily considered a function of temperature. This dependency is predicted by theoretical models and observed experimentally.
• Mean Free Path: While the mean free path influences both thermal and electrical conductivities individually, it is not the sole factor determining their ratio. Its temperature dependence contributes to the overall temperature dependence of the ratio.
• Density: Material density does not directly determine the ratio of thermal to electrical conductivities.
• Fermi Energy: Fermi energy is crucial for understanding electrical and thermal properties in metals, but the ratio itself is more directly linked to temperature variations.

Therefore, the ratio is fundamentally dependent on temperature.