What is entropy? In general, how does the entropy of a system change with time?

The Second Law of Thermodynamics is a fundamental principle that governs the behavior of energy in our universe. It states that, in an isolated system, the total entropy can never decrease over time. This law effectively predicts the direction of thermal processes and sets the ultimate fate of energy usage. It indicates that energy systems naturally progress towards equilibrium, a state where energy is dispersed or spread out evenly.

The concept of entropy increase underlies various phenomena such as the melting of ice, the cooling of a hot cup of coffee, and the mixing of two or more substances. Each of these processes shares a common trait—the spontaneous movement towards a state of higher disorder and lower energy potential.

In thermodynamics, properties are attributes that help define the state of a system. Thermodynamic properties are macroscopic characteristics observable or measurable in a thermodynamic system such as temperature, pressure, volume, and entropy. Unlike other properties, entropy is unique in that it is a measure of the disorder or randomness within a system and can be considered a property that quantitates the irreversibility of a process.

This interconnectedness of properties lets us understand and predict the behavior of systems under various conditions. For instance, knowing the pressure and volume of steam in a boiler allows engineers to calculate its temperature and energy content, essential for the safe and efficient operation of power plants.

A microstate is a specific microscopic configuration of a system, which corresponds to a particular arrangement of particles. The concept of microstates is crucial in understanding entropy, which can be thought of as a measure of how many microstates are associated with a macrostate of a system. A macrostate is defined by macroscopic properties like temperature, pressure, and volume.

Imagine a game of dice; rolling a seven has more microstates (different combinations of numbers on the two dice) than rolling a two or twelve. In terms of entropy, a seven is analogous to a higher entropy state because it's more disordered as it can arise from more combinations. Similarly, in a thermodynamic system, the greater the number of microstates, the higher the entropy, meaning there are more ways the particles can be arranged without changing the overall conditions or energy of the system.

Diffusion is the process by which particles spread from an area of high concentration to an area of low concentration until they are evenly distributed. It's a spontaneous process that increases entropy, exemplifying the Second Law of Thermodynamics. It can involve solids, liquids, or gases and is driven by thermal motion.

Consider perfume sprayed in one corner of a room; over time, the scent spreads, filling the room uniformly. This process happens without any work being done; it increases the entropy of the perfume molecules as their positions become more randomized. In biology, diffusion enables essential functions, such as the distribution of nutrients and the exchange of gases in lungs.