Consider a system of fixed volume I thermal contact with a reservoir. Show that the mean square
Question:
Consider a system of fixed volume I thermal contact with a reservoir. Show that the mean square fluctuation in the energy of the system is
<(ε – < ε >)2> = τ2(∂U/∂τ)V (89)
Here U is the conventional symbol for <ε>.
not fluctuate in value when the system is in thermal contact with a reservoir Any oilier attitude would be Lncon5itent with our definition of the temperature of a system. The energy or such a System may fluctuate, but the temperature does not. Seine workers do not adhere to a rigorous definition of temperature. Thus Landau and Lifshitz give the result
<(Δr)2> = τ2/Cv
but this should be viewed as just another form of (89) with Δτ set equal to ΔU/Cv. We know that W ΔU = CvΔτ, whence (90) becomes <(ΔU)2) = τ2Cv which is our result (89).
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