Two gases, and a wall that is freed or removed
30 October 2026
Statement Two compartments of 10 L and 15 L are separated by a fixed, adiabatic and impermeable wall. In the first we put O₂ at 288 K and 2 atm; in the second N₂ at 300 K and 1 atm. Both are taken as diatomic ideal gases (c_v = 5R/2).
Original (Basque) 10 eta 15 l-ko gordailuak finkoa, adiabatikoa eta iragaztezina den hormak banandu ditu. Lehenengo gunean O_{2} gasa sartu dugu: 288 K-ean eta 2 atm-n. Bigarrenean, N_{2} gasa; kasu honetan, 300 K-ean eta 1 atm-n. Biak gas ideal diatomikotzat hartuko ditugu (c_{v} = 5R/2).
What to watch Both processes end at T_\mathrm{f} = 293.0\ \mathrm{K} and p_\mathrm{f} = 1.40\ \mathrm{atm}; what differs is where each gas ends up. Freed, the wall overshoots, swings and is damped by the gas, then drifts for a few seconds while heat flows from the nitrogen to the oxygen; each gas’s lumped state moves in the p–V plane and settles at 14.53\ \mathrm{L} and 10.47\ \mathrm{L}, and the entropy chart ends at 0.81\ \mathrm{J\,K^{-1}}. Removed, the wall leaves a millisecond rush that equalises the pressures (the oxygen cools to 263 K, the nitrogen warms to 335 K) and then hours of interdiffusion, shown in time-lapse with the temperature along the vessel on a strip; the entropy ends at 9.04\ \mathrm{J\,K^{-1}}, of which 8.23\ \mathrm{J\,K^{-1}} is the entropy of mixing. A switch puts the same gas on both sides: then removing the wall from the equalised state changes nothing, which is part 3. The entropy is computed at every instant from the model’s states and never decreases.
The vessel is drawn 0.5 m long with a section of 0.05 m². Freed, the wall (40 kg) slides without friction; each gas is lumped at one pressure and one temperature; the gas drags the wall with 500 N s/m and that drag’s heat returns to the gases, half each; heat crosses the wall at 12 W/K. Energy is conserved exactly by construction. Removed, the wall leaves a rush modelled as an interface of the gases’ own mass with a drag of 90 N s/m, and then interdiffusion in 100 cells with D = 1.5\times10^{-5}\ \mathrm{m^2\,s^{-1}} for the species and the same for heat. Because the end state is uniform, the entropy ends at the thermodynamic value whatever the parameters: only the time changes.