Thermal conductivity does not directly affect the mobility of a material. Mobility refers to the ability of charge carriers (such as electrons or holes) to move through a material in response to an electric field.
However, there is a relationship between thermal conductivity and electrical conductivity in some materials, known as the Wiedemann-Franz law. According to this law, the ratio of thermal conductivity (κ) to electrical conductivity (σ) is proportional to the temperature (T) of the material:
κ/σ = L * T,
where L is the Lorenz number, a constant.
In materials that obey the Wiedemann-Franz law, an increase in thermal conductivity generally corresponds to an increase in electrical conductivity. This means that a material with high thermal conductivity will tend to have high electrical conductivity as well. Consequently, in conductive materials like metals, higher electrical conductivity generally leads to higher charge carrier mobility.
However, it's important to note that this relationship is not universally applicable to all materials. In non-metallic materials or materials that deviate from the Wiedemann-Franz law, the relationship between thermal conductivity and electrical conductivity can be more complex, and the mobility of charge carriers may be influenced by other factors specific to the material's structure and properties.