TL;DR: In a recent camping trip we noticed just how cold our propane tank was getting after cooking for a while - we started out pretty chilly anyway (about 50 F). The physics of this is cool and I wanted to play with modeling it.
I have one of these little two burner propane stoves that we use when camping, it looks something like this:
While we were cooking breakfast and boiling water for coffee, we noticed that the propane tank was getting super cold - there was not only a thick layer of frost forming on the outside, but a small chunk of solid ice on the bottom of the tank where it met the picnic table…
Newton’s method is a root-finding algorithm that can be used to find the roots of differentiable functions. It is a very simple algorithm to implement, and it converges quickly in most cases, of course depending on the function. It is often used to find the roots of polynomials. For instance, in Chemical Engineering properties calculations, often cubic equations of state are used to model the behavior of fluids. These equations of state are cubic polynomials and most solved for their roots in most cases in order to compute fluid properties and phase equilibria.