Particle speed distribution in a gas (1)

In this post, all I have done is to annotate and expand on the excellent notes of Prof W Salzman. He gives by far the clearest explanation of what was to me a mystery: the fact that, in a gas at equilibrium (ie uniform temperature), there are few low-speed particles, very few high-speed particles but huge numbers of particles with intermediate speeds. I hope the notes I’ve made here are useful to you. This is the first of 2 posts on this specific topic.