Kinetic Theory of Gases--State Equations and Specific Heats
The ideal gas equation of state can be derived from the kinetic theory of gases.
• According to kinetic theory, the pressure exerted by an ideal gas on the walls of a container results from the action of a great number of molecules striking and rebounding.
• Let’s first look at one molecule in a box, with mass m and velocity components Vx, Vy, and Vz.
• Consider a molecule striking the wall at x=L. When it rebounds, there is no change in Vy and Vz, but Vx changes to –Vx.
• The corresponding x-component of momentum changes from mVx to –mVx. Thus, the =magnitude of momentum change is 2mVx.
• Also, the molecule travels the distance L in time L/Vx. Thus it could cross the chamber and return in time Δt=2L/Vx. The number of collisions per unit time (collision frequency) is
• Now, the change in x-momentum per unit time is the product of the change per collision and the frequency of collision,
• Thus, the force on the wall is
• The force of all molecules is
or, since m and L are constant,
• Define the average V2 of n molecules as
then • The pressure is thus
• If it is assumed that the pressure is the same in all directions, and that all directions of velocity are equally probable,