Final answer:
The energy of the particles in iron will be higher at 500K compared to 250K, due to the increased average kinetic energy at the higher temperature.
Step-by-step explanation:
The key difference in the energy of the particles in iron at 250K and 500K will be their average kinetic energy. As temperature increases, so does the kinetic energy of the particles. According to the kinetic molecular theory, at 500K the particles will have higher average kinetic energy compared to at 250K. This is represented graphically through energy distribution curves, where a higher temperature results in a flatter distribution curve, indicating a wider range of kinetic energies but also an increased average kinetic energy. Therefore, at 500K, the energy of the particles in iron will be higher.
It's essential to understand that temperature and kinetic energy are directly related. At a lower temperature (250K), the particles will have less kinetic energy than at a higher temperature (500K). This principle is a fundamental aspect of thermodynamics, which also impacts other physical properties such as the rate of chemical reactions, as reactions typically occur more rapidly at higher temperatures due to the increased energy allowing particles to overcome the activation energy barrier more readily.