Entropy of Mixing

Two initially separated ideal gases share a common initial temperature and pressure. Their initial volumes are therefore proportional to their mole counts. For physically different species, removing the partition lets each gas occupy the full volume and increases entropy. For the same physical species, labels on the initial portions do not create distinguishable components, and there is no entropy of mixing.

Native experiment

Use the Entropy of Mixing module with these exact controls. Each valid edit updates the two contributions and total changes; the figure compares before and after configurations without simulating time.

1. Choose Species relation = Different gases, set Moles nA = 1, Moles nB = 1 and Common temperature T = 300. Check fractions 0.5 each, entropy about 11.5262926433 J/K, Gibbs change −3457.88779299 J and enthalpy change 0.
2. Set Moles nB = 3. Fractions are 0.25 and 0.75; entropy is R(4 ln4 − 3 ln3), about 18.7020581552 J/K, and Gibbs change about −5610.61744657 J.
3. Set Moles nA = 2 and Moles nB = 2. Entropy is 4R ln2, about 23.0525852866 J/K: twice the one-plus-one result. Gibbs change is about −6915.77558597 J.
4. Set Moles nA = 0 and Moles nB = 2. Fractions are 0 and 1, each contribution and every total change is 0; no log(0) is evaluated.
5. Set Moles nB = 0 too. The status is No gas, both fractions are unavailable and all changes are 0 by the declared empty-process convention. This is distinct from an invalid raw input.
6. Restore Moles nA = 1 and Moles nB = 1, choose Species relation = Identical gas, and keep T = 300. Both entropy contributions and all mixing changes are 0. The initial labels identify portions of the same species.
7. Return to Different gases and set Common temperature T = 500. Entropy stays unchanged while Gibbs change scales with T. Set both mole amounts to 5: entropy is about 57.6314632164 J/K and Gibbs change about −28815.7316082 J.
8. Clear Moles nA and observe the accessible error and removed calculations. Restore 1, set Moles nB = 5 and Moles nA = 0.00000001. Tiny positive entropy contributions are retained in scientific notation rather than rounded to zero. Pan and choose Reset view; inputs stay unchanged.