Question
Prove that for an ideal gas, $\langle v\rangle=\int_{0}^{\infty} v p(v) d v=$ $\sqrt{8 k T /(\pi m)}$, where $p(v)$ is the Maxwell speed distribution given by $(15.32)$.
Step 1
Step 1: First, we start with the Maxwell speed distribution, which is given by the equation: \[p(v) = \sqrt{\frac{2}{\pi}} \left(\frac{m}{kT}\right)^{3/2} v^2 e^{-mv^2/2kT}\] Show more…
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