4. Heat transfer

One of the conditions for the applicability of thermodynamics is that the number of atoms involved is "sufficiently large". What is "sufficiently large"? Let's consider a cube of side L with N atoms per unit volume. The relative temperature fluctuation is δT/T ≈ (NL ³ ) ^–1/2 , or L ≈ (δT/T ) ^–2/3 N ^–1/3 . In solids and liquids, N ≈ 10 ²³ cm ^–3 and L ≈ 20 nm. So for condensed systems with a size of less than 10 nm, the use of the heat diffusion equation becomes inappropriate. Nevertheless, there are examples for which the temperature gradients are very large, yet the heat diffusion equation works well. For example, under...