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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_{B}T)^{3/2} v^{2} exp(−mv^{2}/2k_{B}T) .
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 (<v^{2}>^{1/2 }= [ ∫v^{2}n(v)dv ]^{1/2}).
Find an expression for each (in terms of m and k_{B}T). Identify which peak is which characteristic speed.