How is the Maxwell-Boltzmann distribution consistant with the velocity distribution? How can there be a high probability of having a near zero velocity (vector), but a low probability of having a near zero speed (magnitude of the vector)?
Excellent question. One way to look at it: the distribution is a product of both the probability of a given velocity AND the number of states that can have that probability. So, even if a low velocity is high probability, there are very few (in fact just one!) state with zero velocity vector. Thus, it is very small.
How is the Maxwell-Boltzmann distribution consistant with the velocity distribution? How can there be a high probability of having a near zero velocity (vector), but a low probability of having a near zero speed (magnitude of the vector)?
Excellent question. One way to look at it: the distribution is a product of both the probability of a given velocity AND the number of states that can have that probability. So, even if a low velocity is high probability, there are very few (in fact just one!) state with zero velocity vector. Thus, it is very small.
thanks for the video! really cleared things up for me. do you have any good refrenceses if i wan't some more reading material?
Blundell's textbook..
WHY DOES THE AREA OF THE MAXWELL- BOLTZMANN VELOCITY DISTRIBUTION CURVE ALWAYS REMAIN EQUAL TO UNITY ?
Because the area corresponds to the total probability, which should be one