What property must parts of a single substance have for conduction to occur?

For conduction to occur, parts of a single substance must have different temperatures. This temperature difference is crucial because conduction is the transfer of thermal energy through a material without the material itself moving. When one part of a substance is at a higher temperature, its particles have more kinetic energy and are vibrating more vigorously. As these faster-moving particles collide with neighboring, slower-moving particles, they transfer some of their energy, causing the slower particles to speed up. This process continues, allowing heat to flow from the hotter region to the cooler region until thermal equilibrium is reached.

The other properties listed, such as texture, particle size, or color, do not directly influence the conduction process. Texture may affect the surface area or airflow, particle size may influence the material's overall behavior under certain conditions, and color is related to absorption and emission of radiation, but none of these properties are necessary for the conduction of heat between different parts of the same substance. Thus, the requirement of different temperatures is fundamental for effective conduction to take place.