1. The problem statement, all variables and given/known data When deriving the Ideal Gas Formula from the Kinetic Theory of Gases, we assumed that the gas molecules made perfectly elastic collisions with the walls of the container. This assumption is not necessary as long as the walls are at the same temperature as the gas. Why? 3. The attempt at a solution My reasoning didn't lead me to the book's conclusion, so I will post my thought process and hope someone takes the time to read it and correct my thinking. Since we are talking about the temperature of the wall, I presume we must describe the wall on a microscopic scale. So gas molecules are now colliding with "wall molecules." In a perfectly elastic collision between two molecules, kinetic energy is conserved. So if both particles are moving with the same speed and collide, they will both rebound with the same speed they had originally. If they are moving at different speeds, one molecule will impart some energy to the other, and lose speed in that process. But the total kinetic energy of the two molecules will be the same before and after the collision. Which leads me to believe that if the wall and gas were at the same temperature, elastic collisions with the wall would not, on average, reduce the speed of the gas molecules. However, if the wall were cooler than the gas, the gas molecules would tend to transfer energy to the wall, losing kinetic energy in the process. Energy would still be conserved, since the wall molecules would gain kinetic energy. But the derivation of the ideal gas law would only work for elastic collisions if the wall and gas were the same temperature. In an INELASTIC collision, some kinetic energy will always be lost, even if both molecules have the same speed initially. So even if the wall and gas were at the same temperature, the gas molecule would not rebound with its full initial speed, and the ideal gas law does not follow. So that's my reasoning, but it did NOT lead me to the conclusion the book asked for. So where am I going wrong?