So we learn in basic thermo that for any system, the derivative of entropy with respect to volume is pressure over temperature: ∂S/∂V＝P/T. Suppose we have a box with two partitions, and a moveable wall in between the partitions. The box and wall are both insulated to prevent heat transfer. The wall will slide until the entropy of the entire system is maximized. This occurs when the change in entropy with volume is equal for the two sides: (∂S/∂V)1＝(∂S/∂V)2. (P/T)1＝(P/T)2. When both sides are at the same temperature, this result is obvious. The wall simply stops sliding when the pressure is the same on both sides. However, what happens when the temperatures are very different? If you fill one side of the box with a gas at 100K and 1atm, and the other side with a gas at 200K and 2atm, will the wall really not slide, despite there being a pressure difference of 1atm between the two sides?