Classical Gas Laws

 Before going into the depth of Gas breakdown of gases, it is important to describe various gas laws. In the absence of electric or magnetic fields charged particles in weakly ionized gases participate in molecular collisions. Their motions follow closely the classical kinetic gas theory .The universal gas equation is; Pv=nRT; Equation then describes the state of an ideal gas, since it is assumed that R is a constant independent of the nature of the gas

uWe start with a container of volume V

u Inside is a gas consisting of N molecules

uEach molecule has mass m and is moving with Velocity “v”

uWhen molecule collides with Area “A” it will be moving with Velocity Vx

uIts momentum will be mVx

uAfter collision it will have momentum –mVx

u Change in momentum is (Final momentum-initial momentum)= Δ(mV) = -mVx-mVx= -2mVx

  The magnitude (absolute value) of the change in direction is then simply 2mvx. Over time interval, Dt, a certain number of molecules will hit Area A. We need to determine how many molecules that is in order to find the total change in momentum over that period. That number is determined by how close the molecules are to Area A when we start the time interval. Since they are moving with velocity vx, they must be within a distance x, or they will not arrive on time. Distance x is given by: vx(Dt)  as shown in the diagram

uIn addition, we must multiply this by ½ to account for the fact that, on average, half of the molecules will be moving to the left and half will be moving to the right Mathematically:

        Now the total change in momentum, Δmv, is the # of molecules times the change in momentum per molecule (which we found before, 2mvx):