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An ideal gas is enclosed in a thermally insulated sealed container. During an adiabatic expansion, the mean interval between successive molecular collisions varies with the volume V as V^q. What is the value of q in terms of γ = Cp/Cv?

1. (γ + 1)/2
2. (γ − 1)/2
3. (3γ + 5)/6
4. (3γ − 5)/6

Correct answer: (γ + 1)/2

Solution

Mean free path lambda ~ V. Adiabatic: T ~ V^(1-gamma), so v ~ sqrt(T) ~ V^((1-gamma)/2). Collision interval ~ lambda/v ~ V^(1-(1-gamma)/2) = V^((gamma+1)/2), so q = (gamma+1)/2.

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