Fourier's law cannot be used to predict heat transfer phenomena associated with individual molecules. Similarly, Fick's law describes the aggregate behavior of a large number of molecules, and cannot be used to predict the behavior of a small number of molecules.

The human nose can be sensitive to only a few molecules of an aromatic substance. In a classroom demonstration of volumetric heating, your professor microwaves a bag of popcorn and measures its change in temperature. One second after opening the hot bag to insert a thermocouple, students sitting in the last row of the classroom, located \(30 \mathrm{~m}\) from the professor, smell the hot popcorn. Is it plausible that the popcorn aroma reached the students by advection? Using Fick's law, estimate the time needed for the students to be exposed to a trace amount of the aromatic, \(C / C_{s}=0.0001\), using the penetration depth concept of Section 5.7 and typical values of the binary diffusion coefficient for gases in air. The concentration \(C_{s}\) corresponds to the maximum aromatic concentration located at the opening of the bag. Can Fick's law be used to explain the speed at which the aromatic substance moved from the front to the back of the classroom?