- Why is the entropy change 2nR ln 2 and not zero? Doesn't the pressure equalize, so nothing really changes?
- The entropy increase is due to the increased spatial disorder of the molecules, not a pressure change. Initially, each gas molecule is confined to half the container. After mixing, every molecule can be anywhere in the full volume, vastly increasing the number of possible microscopic arrangements (microstates). Even though the final pressure is uniform, the irreversible expansion of each gas into a larger volume generates entropy. A zero entropy change would only occur if the gases were identical, a subtlety known as Gibbs' Paradox.
- Is this mixing process reversible? Can we separate the gases without doing work?
- No, the mixing depicted is thermodynamically irreversible. To fully separate the mixed gases back into their original pure states, you must perform work (e.g., using a semi-permeable membrane or a diffusion apparatus) and expel heat to the surroundings. This required work is a direct consequence of the entropy increase; reversing the process would require reducing the entropy of the system, which cannot happen spontaneously.
- Does the temperature change during mixing in this simulator?
- In this specific model, the temperature is assumed constant (isothermal). This is a simplification that isolates the entropy change due purely to the increase in available volume. In a real, adiabatic container with different gas species, there can be a small temperature change upon mixing (the Joule-Thomson effect for non-ideal gases), but for ideal gases with no intermolecular forces, the internal energy and temperature remain constant during free expansion into a vacuum.
- What is the real-world significance of entropy of mixing?
- The entropy of mixing is a crucial driver in many chemical and physical processes. It explains why gases and liquids spontaneously diffuse, why salts dissolve in water, and is a key factor in determining the equilibrium state of chemical reactions and phase separations. In industrial applications, understanding this entropy is essential for designing separation processes like distillation or gas purification, which must overcome the natural tendency to mix.