A layer of silicone oil is heated uniformly from below
PHYSICS · Multi-part · Fermi University Physics · Fluids & Continuum Physics · Thermal, Statistical & Complex Systems · Convection, rotation and geophysical flows
Many Parts, One Behaviour, Ch Emergence and self-organisation: collective order from local rules
Problem
A layer of silicone oil is heated uniformly from below. Below a critical temperature difference the layer is featureless; above it, an array of convection rolls appears, each roll a width close to the layer depth, and the rolls persist for as long as the heating is maintained.Someone argues: "The still fluid has molecules moving in every direction with no preferred pattern: high entropy. Once the rolls appear, every parcel of fluid moves in a fixed, repeating pattern: low entropy. A spontaneous drop in entropy is forbidden by the second law of thermodynamics, so either the rolls cannot really be spontaneous, or something else, not heat flow, must be organising them."
((a)) Identify the flaw in this reasoning.
((b)) State the single experiment on this apparatus that would show whether the rolls are equilibrium self-assembly or self-organisation sustained by a flux of energy, and state what result each of the two possibilities predicts.