ABSTRACT
If N is the total number of atoms in the box, then they all strike the wall in the time ∆t so the total force, F, is just N∆F and the pressure, P, is given by P = F/L2, so
P F L
N F L
Nmv L
Nmv V
2∆ (5.3)
where V = L3 = volume of the box. Rearranging this, for an ideal gas
PV Nmv nRT N N
RT Nk Tx A
B= = = = 2 (5.4)
and therefore mv k Tx B2 = where NA is the Avogadro’s number and kB is the Boltzmann’s constant. The kinetic energy in the x-direction, KEx, for the atom is defined by
KE mv k Tx x B= = 1 2
1 2
2 . (5.5)
The velocity vector has three-components, one in each of the x, y, and z directions as shown in Figure 5.2. Therefore,
v v v vx y z 2 2 2 2= + +
and the total kinetic energy, KE, is given by the sum of the kinetic energies in each direction
KE mv mv mv mv
KE k T k T k T k T
= + + =
= + + =
1 2
1 2
1 2
1 2
1 2
1 2
1 2
3 2
.
