Consider a solid of N atoms in the temperature region in which the Debye T3 law is valid. The solid is in thermal contact with a heat reservoir. Use the results on energy fluctuations from Chapter 3 to show that the root mean square fraction energy fluctuation is given by

Suppose that T = 10^-2 K; θ = 200 K; and N ≈ 10¹⁵ for a particle 0.01 cm on a side; the n P ≈ 0.02. At 10^-5 K the fractional fluctuation in energy is of the order of unity for a dielectric particle of volume 1 cm³.

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