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Kinetic theory of gases. Boltzmanns Law and Maxwell distribution

Problem 2.68

A gas consisting of \(N\) -atomic molecules has the temperature \(T\) at which all degrees of freedom (translational, rotational, and vibrational) are excited. Find the mean energy of molecules in such a gas. What fraction of this energy corresponds to that of translational motion?

Reveal Answer
 2.68. (ε⟩={(3N−3)kT for volume molecules. (3N−5/2)kT for linear molecules. 1/2(N−1) and 1/(2N−5/3) respectively \begin{aligned} &\text { 2.68. }(\varepsilon\rangle=\left\{\begin{array}{l} (3 N-3) k T \text { for volume molecules. } \\ (3 N-5 / 2) k T \text { for linear molecules. } \end{array}\right.\\ &1 / 2(N-1) \text { and } 1 /(2 N-5 / 3) \text { respectively } \end{aligned}
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