What is the relationship between temperature and entropy?

The relationship between temperature and entropy is fundamentally rooted in the second law of thermodynamics, which states that the total entropy of an isolated system can never decrease over time. When the temperature of a system increases, the kinetic energy of its particles also increases, leading to greater molecular motion. This increase in motion allows the system to explore a wider array of microstates, or configurations.

As the number of accessible microstates increases, the entropy, which is a measure of disorder or randomness in a system, also increases. Therefore, higher temperatures typically correspond to higher entropy because the particles have more energy and can occupy more states.

This established relationship also implies that at lower temperatures, the movement of particles is restricted, resulting in lower entropy. Thus, as temperature rises, so does entropy, supporting the choice that states when temperature increases, entropy likewise increases.