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Kinetic theory of gases. Boltzmanns Law and Maxwell distribution

Problem 2.69

Suppose a gas is heated up to a temperature at which all degrees of freedom (translational, rotational, and vibrational) of its molecules are excited. Find the molar heat capacity of such a gas in the isochoric process, as well as the adiabatic exponent \(\gamma,\) if the gas consists of (a) diatomic; (b) linear \(N\) -atomic; (c) network \(N\) -atomic molecules.

Reveal Answer
 2.69. (a) CV=7/2R,γ=9/7; (b) CV=(3N−5/2)R,γ==(6N−3)/(6N−5); (c) CV=3(N−1)R,γ==(N−2/3)/(N−1).\begin{aligned} & \text { 2.69. (a) } C_{V}=7 / 2 R, \quad \gamma=9 / 7 ; \text { (b) } C_{V}=(3 N-5 / 2) R, \gamma=\\ =&(6 N-3) /(6 N-5) ; \quad \text { (c) } C_{V}=3(N-1) R, \quad \gamma=\\ =&(N-2 / 3) /(N-1) . \end{aligned}
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