kinetic energy 問題

rms speed is not the same as average speed. The rms speed is related to the kinetic energy of gas molecules, but average speed is not.

The pressure of a gas, in microscopic point of view, is the force exerted onto a surface (container walls) when the gas molecules perform elastic impact with the surface. It can be shown from kinetic theory that, the force F (or pressure, which is the force per unit area) is proportional to the square of the rms speed..

When a gas expands so that its volume is doubled, because the pressure remains constant, the gas temperature will be doubled.
[PV = nRT, P is kept constant, n and R are constants, V is thus proportional to T]But molecular kinetic energy is proportional to temperature, doubling the temperature implies doubling the molecular kinetic energy. The mean-square-speed (i.e. square of the rms speed) is also doubled. The rms speed is thus not doubled (it is only square-root [2] of the original rms speed).

SInce average speed increases with rms speed, the rms speed is not doubled indicates that the average speed is also not doubled.