Entropy and the Second Law of Thermodynamics

Entropy, denoted by 'S,' is a physical quantity that measures the degree of disorder or randomness in a system. When a hot object transfers energy to a cold one, the constituents of the cold substance become more disordered as they absorb heat. This increased disorder is quantified as entropy, which increases as molecular randomness grows at higher temperatures.

For an isothermal reversible process where temperature remains constant, entropy change equals the heat exchanged divided by the absolute temperature. Mathematically, the infinitesimal change in entropy (dS) equals the infinitesimal energy input (dq) divided by the temperature at that moment. This provides a straightforward method to determine entropy changes under constant-temperature conditions.

Reversible paths provide a well-defined mathematical method to find entropy changes because they follow a predictable trajectory between states. Although reversible processes are theoretical and do not occur in reality, they allow precise calculation of entropy as a state function. Real irreversible processes follow the same entropy change between initial and final states as the corresponding reversible path.

The Second Law states that the total entropy of an isolated system always increases for any real irreversible process, while remaining constant for reversible processes. This means all natural and spontaneous processes tend to maximize overall entropy. Heat spontaneously transfers from hot objects to cold ones, never vice versa, reflecting the universe's tendency toward greater disorder.

When a system undergoes a reversible process from state A to B at varying temperatures, entropy change is found by integrating the incremental heat supplied at each stage over the corresponding temperature. This integration accounts for temperature variations throughout the process, providing the total entropy change. The entropy change depends only on initial and final states, not the path taken.

The First Law articulates conservation of energy among processes, ensuring energy is neither created nor destroyed. The Second Law governs the direction of spontaneous processes, which proceed toward states of higher total entropy. Together, they establish that while energy is conserved, the universe naturally evolves toward greater disorder and entropy.

Real processes are irreversible and generate disorder, causing total entropy to increase. Reversible processes are theoretical ideals where the system remains in equilibrium, so entropy stays constant. Since reversible processes do not exist in reality, the total entropy of any system plus its surroundings always increases during actual chemical reactions and physical processes.