Please wait for the animation to completely load.

In this animation N = nR (i.e., k_B = 1). This, then, gives the ideal gas law as PV = NT. The average values shown, < >, are calculated over intervals of one time unit so that the average rate change in momentum is equal to the pressure times the area, A (where A = 1).  Restart.  This animation shows the distribution of speeds in an ideal gas based on the Maxwell-Boltzmann distribution as shown by the smooth black curve on the graph for a given temperature:

n(v) dv/N = (2/π)^1/2  (m/k_BT)^3/2 v² exp(−mv²/2k_BT) .

What happens to the distribution as you increase the energy (temperature)?  Since there is a speed distribution, when we talk about a characteristic speed of a gas particle at a particular temperature, we use one of three characteristic speeds:

• Average speed (<v> = ∫ vn(v)dv).
• Most probable speed (find maximum of n(v)).
• Root-mean-square (rms) speed (<v²>^1/2 = [ ∫v²n(v)dv ]^1/2).

Find an expression for each (in terms of m and k_BT).  Identify which peak is which characteristic speed.