Entropy and the Second Law of Thermodynamics

Entropy quantifies the disorder of a system by measuring the number of possible molecular arrangements. A larger volume allows gas molecules more possible positions and velocities, creating more microstates and greater disorder. As molecules transition from ordered states, like ice, to disordered states, like liquid water, entropy increases. This molecular randomization directly reflects the system's entropy value.

The second law states that the universe's total entropy never decreases during any thermodynamic process. In irreversible processes like free expansion, the universe becomes more disordered as entropy increases. Even when a heat reservoir loses entropy during phase changes, the entropy gain of the melting substance exceeds this loss, ensuring net universal entropy increase.

Adiabatic free expansion is irreversible because the gas expands into a vacuum without exchanging heat with the environment, and the process cannot spontaneously reverse. The gas molecules spread into a larger volume, increasing disorder and entropy. Since entropy is a state function, its change can be calculated by comparing reversible processes with identical initial and final states.

For reversible processes, entropy change is given by the formula ΔS = Q/T, where Q is heat transferred and T is absolute temperature. This relationship quantifies how heat distribution at different temperatures affects system disorder. The formula applies when processes occur quasi-statically, allowing the system to remain in thermal equilibrium throughout the transformation.

A microstate describes the complete condition of each gas molecule, including its position and velocity. More available microstates correspond to greater disorder and higher entropy. When gas expands into a larger volume, the number of possible molecular coordinate combinations increases dramatically, resulting in more microstates and increased entropy of the system.

The heat reservoir contains vastly more molecules than the melting ice, so its average kinetic energy change is negligible when heat is transferred. Although the reservoir loses entropy, its enormous molecular population means the entropy decrease is minimal compared to the ice's significant entropy increase from molecular disorder. The universe's total entropy therefore increases.

The third law states that absolute zero temperature cannot be reached through any finite number of cooling steps. As temperature approaches zero kelvin, entropy approaches a minimum value. The proof of this law requires quantum mechanics and represents a fundamental limit on how cold a system can become.