p,v,t的物理問題

It can be shown, by the kinetic theory of gases, that the pressure p of a gas is given by,

p = Nmv^2/3V
where N is the number of molecules in a volume V, m is the mass of a molecule and v is the rms speed of molecules.

Doubling the volume implies decreasing the pressure. The reason is apparent. Molecules now have to travel double the distance between successive collisions with the container walls. Because pressure (or impart force with the container wall) is proportional to the frequency of molecular bombardment onto the wall in a unit time. A longer distance of travel indicates that the bombardment frequency is reduced, thus leading to a lower pressure.

Increasing the temperature increases the rms speed of molecules. The molecules are now moving faster than before. As such, the time between successive collisions with the container walls is shortened. That means, the frequency of bombardment is increased, as molecules are now able to make more collisions in a unit time. The pressure is thus increased.