Controlling the Size of Popcorn

We present a thermo-statistical model of popcorn production and propose a way to control the final size of the popcorn by monitoring only the chamber pressure. P.A.C.S: 05.20-y, 01.55.+b, 01.90+g, 05.70-2. How can one control the size of popcorn? The food industry may have ample reason to seek for ways to double or triple the size of popcorn, because large popcorn may be pleasing to the eyes, possibly save energy through mass production, and thus render profits not only to the companies but also to consumers as well. The purpose of this note is to examine the physics of popcorn production based on a few thermodynamic principles and recommend ways to control the size of the final product. Before going into detail, let us first examine the underlying physics of popcorn production. First, there is moisture inside the corn, which, upon being heated in a chamber (e.g. a microwave oven), is subject to expansion. When the temperature of the chamber exceeds the boiling temperature, the moisture turns into a gas with a sudden expansion in its volume. But because of the hard shell that surrounds the corn, the moisture is trapped inside and its pressure rises. When the gas pressure reaches the yield point of the shell, the shell is broken and the trapped gas undergoes a rapid adiabatic expansion, because the process is so fast that the gas does not have enough time to exchange heat and equilibrate itself with the environment. This adiabatic expansion stops when the gas pressure P reaches that of the chamber, Po, which is, under normal circumstances, the atmospheric pressure. Since our primary interest here is to control the final size of the popcorn, and we do know when the expansion stops, all we need is to write down the governing equations of the interface right after the rupture of the shell. Hence, this problem is reduced