Temperature and Average Kinetic Energy
We will now study what the velocity of the gas molecules is as a
function of the temperature. First we introduce the average squared
velocity, 2>. This is
obtained by taking the square of the velocities of each molecule in
the gas and averaging (indicated by the angular brackets). One can
show that in this case
2> =
2.
The relationship between pressure, volume, and average velocity
square is:
pV = 1/3 $\cdot$ N m 2
Here N is the number of molecules in the volume V, and m is the
mass of one of them. Combining this result with the ideal gas law
gives:
(3/2) kT = (1/2) m 2
In the simulation, a hot gas (represented by red balls) is mixed
with a cold gas (represented by the blue balls). As time passes, the
gases interact with each other and reach equilibrium.