What is the relationship between energy and temperature based on Kinetic Theory of Heat?

In the context of the Kinetic Theory of Heat, the relationship between energy and temperature is fundamentally tied to the microscopic behavior of particles in a substance. The Kinetic Theory posits that temperature is a measure of the average kinetic energy of the particles in a system. As the energy of the particles increases, their motion becomes more vigorous, resulting in an increase in temperature.

Therefore, when energy is added to a system—such as through heating—the average kinetic energy of the particles increases, which corresponds to a rise in temperature. This is a central concept in thermodynamics, showing that temperature serves as an indicator of the thermal energy within a substance.

This relationship can also be quantitatively expressed in ideal gases through equations such as the equipartition theorem, which relates the average kinetic energy per degree of freedom to temperature, affirming that an increase in thermal energy directly translates into a higher temperature. Thus, with an increase in energy, temperature also increases, supporting the choice that temperature increases with energy increases.