How does the chemical potential vary with temperature for a pure substance?

The chemical potential of a pure substance is a measure of the chemical potential energy per unit amount of the substance, often influenced by factors such as temperature and pressure. For a pure substance, the chemical potential generally increases with temperature due to the increased kinetic energy of the molecules, which leads to greater disorder or entropy in the system.

As temperature rises, the molecules of the substance move more vigorously, enhancing their tendency to escape from the liquid or solid phase into the vapor phase. This is especially evident in phase transitions where the chemical potential plays a critical role. The relationship between temperature and chemical potential can be quantitatively described using thermodynamic relationships, particularly those derived from the Gibbs free energy.

Therefore, the chemical potential is directly proportional to temperature for a pure substance, indicating that as temperature goes up, the chemical potential also increases. This direct relationship is essential in understanding the behavior of substances under varying thermal conditions and is a key concept in thermochemistry.