Entropy Changes Accompanying Specific Processes

Entropy, a measure of disorder in a system, changes during phase transitions like freezing or boiling. At the transition temperature T_trs, where two phases are in equilibrium, the phase transition is a reversible process. The entropy change can be calculated from a substance's enthalpy of transition using the equation ΔS_trs = Δ_trsH /T_trs.

When a perfect gas expands isothermally from one volume to another, entropy increases logarithmically with volume. Conversely, isothermal compression results in a decrease in entropy. Moreover, heating a gas at constant pressure or volume also increases entropy, which can be calculated using the substance's heat capacity.

For situations where an ideal gas undergoes changes in more than one parameter, such as both volume and temperature, the entropy change can still be accurately determined. This is done by considering any reversible path between the initial and final states, dividing the process into two steps, and then summing their individual contributions to calculate the total entropy change.

When two different gases mix, the entropy increases because each gas expands from its initial volume to the total volume. These individual entropy changes are invariably positive, rendering the mixing of gases a spontaneous process in an isolated system. This process is driven by an increase in entropy rather than an energy change. Additionally, the volumes of gas samples having the same pressure and temperature are directly proportional to the number of moles of gas present. It follows that the overall entropy of a gas mixture can be related to the mole fractions of its constituents.